Treatise on Mine-surveying

Bennett Hooper Brough · 1906 · Historical

Treatise on Mine-surveying by Bennett Hooper Brough (1906). Full text and reference in the Mountain Man Mining Library.

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A Treatise

oit

Mine-Surveying.

A Treatise

oit

Mine-Surveying.

N

MIHE-tURVEVIttO. Br riKMNETT H. Gboudh, ASIOC.R.S.M., F.a.S., lonnerlr InatnicUn' in Uiiie .Hiirvfylng. Rofnl .School of MlDe, TWKLFTH EtilTIOR, BTtd. 7i. fill.

ORE AND BTOME MmiNO, liy Sir C. Lk KKva Foster, D.Sc., F.R.S., ud Bukmitt H. HKiiiiiii, A.K.S.M., F.O.a. SiXTn SiiiTioH, Thorcmghly ReTted Mi,

BOHL HINIHO. Fnr the IT- gt Colliery .MHiiiigen uid othera. li; H. W. Huaun, V.Q.S. Illiistriitiil. Fifth Ebction, KeYlud und Eolirged. Ma. uet.

PRAOTieAL OOAL MINIHO. For thote employed in and about CulUsiiM. It} O. L. KlRR,

XMiijt.M.B. VerjrmiljfllluiMmted. Fopatn F.dition, EeyJaed nd KnUrufd. l2i.M.

BIASTIMQ. A HuDilttook for the Uu ol Engineers nod others ens nged in lliiilug, Tun- nelling, Qimrrrltl. AO- BjOSOa OUTTILUIH, AMM.U.l!Ul.ClK lOl. Bd.

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ELEOTRIOAL PRACTICE IM COlLIERIEt. Ky V. BDRHS, l(.Ilui.H.E. SSMITt) BDITION,

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By EuwiK R i'lELLi, M.IiiBl. M.M Piwket iiii, Lextliar. Sa. ed.

MINIHO LAW OF THE BBIT1BH EMPIRt. B; CiiAKiJU J. JilMtH, F.O.S., U.Init,M.M.

Cloai. W. (H. net. pnoSPEOTIHO FOR MIHEtALS. A FnctlciJ Handbook. By H. HnraUT CoX, Auoc R,.S,M.,M.!iist.M.M.,F.0.9. Withllliislrationi. Third En iTiOH.RevlMd. CloUi. ta.

IHTRBDUBTIOH TO THE STUDY OF METALLURQT. B7 .Sir W. itOBEHTB-AcanH, K.C.B., U.C.L.. F.R.S. LanciiSvo. Cloth. IlliiJlrEtfd. Fin-H XidTioN. 1S.

THE METALmnCY OF BOLD. H) 1'. KiRKK RusG. D.Sc, Clienilit and Aaufer, ILojtl

SliEjt. Fit'] ii Ei'TTii'N. Ri>\i0t.'<'J fioid Enlarged. FuHy Illustrated. SIL

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THE METALLURQV OF IRON. By TUONAfi Tubnek. M.So., A>h.&.S.M., F.LC. Witb uniniTOii- 111 list ratiriTH 3*00(11) Eumos. Large 8to. ISi.

THE METALLURQT OF STECU By F. W. Harbohu, Aauic B,3.M,, F.I.C. With Section i.u .Mill Pmitice liy /. W. Hall, A.H,Jnit.C.£. Boob Einiiotr, Rerlied and

ELEMENTS OF METALLUROY. By J. AntHUK Phillips, I'.R.s,, M.Inat.C.B., and B.

liAtEKMAN, K.ti.a. THini} BipITIOK. Hiilarged and Keirlied. Sfla. OETTINO OOLD. A Praotlii1 Treatiie (nr PraspecCotm, lllnen, and Btadenta. By J. 0.

F. JijHNSOs, F.G,S., A.I,M.B. Third Edition. Sa M. THE BY AH IDE PSOOESS OF BOLO tXTR ACTION. By JAUBS PAJtK, P.O. 8., U.Hut.&LM.

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M.M. niiiLratw1.

OTANIDINQ DOLO AHB SILVER ORES A Frnctieal Treatlae on tbe Cjanlde FnneH. By U. FonuEHJoLiASiaud EiiOAKSUAKT. With FUtt.'i, Map*, and lUuitntlDni. 2!i. net,

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MlNKO>ritVKV(Nti IN TUB MinilLt A(iK.S.

{Facaimi/e o/a dtau-iiuj in AyriedfCs de rt Mttailka, 1556.)

A Tbeatise

On

Mine-Sueveying.

Bt

.t

Bennett H. Brough,

4S800IATS OF THE ROYAL MIHOOL OY HINKS ; HEMBER OF OODKOIL OF THB HimTUTIOIl OF MHIINa ESOINEESd ; FELLOW OF TUB OEOLOQIOAL SOOIITT AICD OF TBI IRBTITUTE OF CUKminRT ; FOKHERLT IBSIBUOrOR IS Kllta- ' SUBVITUCO AT TBI BOTAL SOHOOI. OF MIHIS.

Twelfth Edition, Revised.

TIQlttb flumerous Dtafltama.

London:

CHARLES GRIFFIN <fe COMPANY, LIMITED;

Exetkr Street, Strand.

/1906.

lAU KlghU Reserved.] ''..'.

Hp '2.

DUPLl'-ATB

No fonfer tliB DrOBtrtv Of

Columbia Unlvertlty

DatAr.-i is 1918

Note To The Twelfth Edition.

This Edition has been thoroughly revised. Deacriptions of sppliaaces invented since the publication of the Eleventh Edition and references to some important papers lately published have beet) inserted. Among the additions will be found notices of Mr. MtirriottB results in surveying bore-holea in the Transvaal, of the Meyer-Wiesmann tacheoineter used at the Siraploa tunnel, of the Uaiiiiuer Fennel tocheometer, of Mr. Burr's method of surveying with stretched strings, of tlie resulta obtained in setting-out the Simplou tunnel, and of the maguetio obaervationN made in the very dee]i shaft of the Tamarack mine. £ecent examination papers havt" also been added.

May, 1906,

Note To The Eleventh Edition.

r The Eleventh Edition has been carefully revised. References ' to some papers published during the year, and recent values of the magnetic elements have been inserted. The chief additions consist of noticea of Mr. Ferguson's cyclograph for exploratory Borveya, of Mr. Pollitzer'a methods of ahaft-aurveying, of Mr, Justice's experience in survey iag bore-holea ia Weat Africa, and of the Thorn so n-Thalen iastrument for magnetic-aurveya of iron ore deposits.

OetoUr, I'JOi-

Preface.

No apology U required for any well-conaidered attempt to pro- Tide a manual of Mine-Surveying for the use of Engliab readers. The absence of any general work on the subject baa long been a source of praotical JDOonveoienoe alike to teachers and students. The text-books recommended to candidates for the examinatioa in Mine-Surveying held by the City and Guilds of London Institute, namely, Budge's Praetieed MirwrB Qtiide, published in 1826, and Hoakold's Practi&d Treatise on Mining, Land, and Saitioai/ Surveyinff, pabliabed in 1863, are too limited in their

pe, the former dealing only with the mineB of Oomwall, the tter only with those of the Forest of Dean ; besides which both works are out of print, and increasingly difficult to procure.

The present work is intended priraarity for students, and embodies the substance of the course of instruction in Mine- Surveying given at the Boyal Sofaool of Mines. At the same time, it will also, it is hoped, be found useful as a companion to the standard works of reference on Land-Surveyiag.

Id the plan of the book, the surveying of collieries and that of metalliferous mines do not receive separate treatment. The two have much in common, and the one may often advan- tageously borrow a method from the other. Few mine-surveyors

Great Britain appear to be acquainted with the methods

d instniment.<i tvsed abroad. This is the more to be regretted, as no mine-surveya made in this country approach in accuracy those ol the collieries of Pennsylvania, or tliose of the metal- liferouB mines of the Harz. Attention therefore has been directed to the reoent improvements in foreign practice. With the exoeption of a few diagratus borrowed from Professor

Till

Preface.

N

Kankine's Manttal of Civil Engineering, the figures elucidating the text h&re been BpeoiftUj draws for tbiB book.

The Appendix of examioation-queations and exercises for plotting has been culled from recent papers set at the examine- tiouB of the Science and Art Department, of the Oity and Guilds of London Institute, of the local boards under the Home Office for granting certificates of competency to Colliery Managers, and of rarious Mining Schools. These will, it is trusted, be found of use to such atudeuta as have not the advantage of regular instruction in the subject. It must, however, be borne in mind that th mere reading of a text-book will never make a mine- surveyor. The most that a book can do is to help the student to obtain B knowledge of the theory of the subject. The mechanical manipulation of the instruments can only be learnt under the personal supervision of a teacher, whijat the technical skill re<)uiaite for carrying out subterranean surveys must be obtained in the mine itself.

I have taken for granted on the part of my readei's an elementary knowledge of mathematics, such, for example, as would enable them to pass the second stage of the Science and Art Department's examination in that subject.

In the preparation of the work, I have received valuable help &om numerous friends at home and abroad. In particular, I indebted to Mr. H. W. Hughes, Assoc R.S.M., F.Q.8., for 1 several important additions to the text, and to Mr. A, Pringle, M.A., B.Sc, who ably assisted me while the volume was passing through the proaa

Bennett H. Brough.

Tb Rotai, School or Minks, LOMDON, FtbnMry, tSSS.

Contents.

Chapter L

OiNERAI. EXPLjUIATI01(&

ftMt

Snrrejlng, . , , , , ,

HiBborical sketch,

Importance of mise-ntrre/iiig, . .- .

HiBenl depoaita,

Uming tenna, ,,.

Angul&r meuurea,

Trigooomatric&t fonaula

OHAFTBS n.

Tkb MsjUimuiKNT or Dutasou,

etbods of nieimtariiig, (a.) The ctiain,

Chaming on dope*, .

OffMte,

ObstactM to mcsrorement,

Surveying witb the chitin only,

Chikin uMd in trigonometriiul anrrey*, C6.) Rod*. . (c) Steel bandi, . {d. ) Meunring whael, Pacing, Locnrscy of linear metuurementa,

a n

Is Is

le

£3 M

CHAPTER in.

Tbi Mihsb's Dial,

irective notion of the earth's magnetiam, orical aketch,

2S

CONTBtm,

J

H

tJMt

2M

(a.) The mognetio-inHKlle, ,

(6.) Spirit- levels, ..,,,,

(c.) The tripod,

(1.) Taking underground obearratiaoe with the dial,

Taking vertical angtea,

Keeping l!ie dialling-book,

(2.) Surfaoe-Burvejs with thu miuer'n dial, .

(3.) ColUeiy-turveya with the miner'i dial, . ,

3S

Chapter Iv.

Tks Variation ot tbi Maonctio-Nikdlb

Definitiotii, . .

(a.) Selar varintiotu,

{b.) Dinranl variation,

Iiregular variation b,

1. Method of ahadowB,

% Method of oorreapondijig altitudea, .

S. DetenninatioD of the meridian by meanB of the Pole

Btar, . 48

Setting ont the meridian line.

4d

Kecent magnetic obspryationn ,

Chapter V.

StrnvsTiNO WITH THB Maonetio-Nkedle im thx Presi

KOI or Iroh.

Influence of iron rMa, ...

fi4

Local attraction in the mine,

es

Surveying with the dial in the presenoe of iron.

Dialling-book,

M

Error! in compau Burveya,

Action of ttUotrio ourreati on mtne-anrveying instrumenta.

Go

M

80&VKrUt9 WITH TOE FtlTtTI NCKDUE.

Vernier,

Ml

J

OONTBNn.

rAM

Various forma of dial, Gl

(a.) Lean's miner'a dial, .

(6.) The Henderson dial, .

(e.) Davis's miner's dial, .

Dial-joint,

id.) Whitelaw's dial,

(e.) Thornton's dial.

Tnveraing underground,

Surveying in inclined shafts, .

The vernier oompass, .

The sight for miners' dials, .

CHAPTER Vir.

The Oibman Diau

InventiOD of the German dial, 81

Measoring station -lines,

The clinometer,

Use of the clinometer, .

The hanging-oompass, .

Surveying with the German dial,

Plotting the survey, .

Surveying with the hanging-compass in the presence of iron

Use of the German dial, .

CHAPTER Vm. Ths Thkodoiits.

Historical sketoh,

Description of the theodolite,

The telescope,

Various forms.— (a.) Hoskold's transit-theodolite.

(ft.) The Everest theodolite,

(c) The Hoffman tripod head, .

{d.) American theodolites,

9S

{e.) Traveller's transit-theodolite.

Adjustments of the theodolite, . .

Measuring horixontal angles,

Repetition,

Measurement of vertical angles,

The solar attachment, . . . .

Th

ooinKHTa.

Chapter Ix.

TfULTKBSIHa UlTDEROROinm

Ue of the ttieodotite in the mine, . , .

Comparison of the theodolite uid compiua, .

lit lU

Chapteb X.

SuRFACX-SoRVgyS WITH THS TaKmOLITB.

TriiiQgiil&tioD, Ckimputiiig the sides of the triangles. Interior detail of the triangalation, , Aineric&n mining olaims, . .

Surveying in Sooth AfricB, . .

1'23 12y

m

CHAPTER XL Puynuia thx Su&vxt.

Soalea,

1. Simply divided Bcalet,

2. Diagonal ecalea, .

3. Vernier sea leg, . , Plotting scales, . Plotting with protractor, , Plotting by meann of chordu, . Plotting by rectangular oo-ordinatM, . CBdcolating scaloa. Traverse tables, Combined Eurreyfaig and plotting inairument, Plotting colliery aurveys in Scotland, CalcuUtiog the M-ordinateii of a triAngulation,

Ul U-2

ua

lfi7

I Measnret of area, . H Methods of calculating areas, , 1. Method of triasglcs, .

2. Method of ordinatcB, .

CHAPTER Xn.

Cal0Eii.Atioh Op Arkas.

J

A

Prodaoe of ooal seuiu, . J6(S H

Tha cklcnlbtion of ore-reaervM, . . , , iff; 1

CHAPTER lOTT

F LivtixiitB.

Definitiona utd pHociplra, ... , . . 170

The maBOD's level emd boning itaTei, , ,

The iplrit-leTel,

. . 171 1

(a.) Tlie dumpy tevl,

, 171

(b.\ TbeY-ievel

1 (e.) The Tmnghton level,

The KdJiutroeDta of the level, .

Ciubing'a reversible level, , ,

The levelling-,

Mine levelliDg-atnvei, , , ,

Pnctioe of levelling, . . i ,

SectioD levelliDg,

ISl

Bench marki,

ie&

(e.) The refleotiiig lervel, , , , ,

Iso

Sources of error in ipirit-levelling, .

Plotting aectionB,

(/ ) The water-level,

lei

TrigoDOmetrioal levelling, . , , ,

The clinometer, ... ,

. Iw 1

Physical levelling, . , . . .

Contour lines,

Applicatioos of levelling, , . , ,

aot J

OoMNcono!* ov THi Umdibokoukd- aho Scrtaok- 8 (.

Methods employed. ... . , . .SOS

1. By meui* of ti adit level, , ,

3. By meuu of two sbafte, .

3. By means of one shaft, .

4. By means of a transit inatrnment.

81S 1

4a. The Severn tonnel method, .

6. By means of a tiDsit- theodolite, . .

6. By means of the magnetic -needle, . 1

Siv

Oonterts,

Chapter Xv,

Tlieory of telescopio meoauromeiat,

m

Caloulutious,

23S

The pmtrivotor, ...

The tachen meter,

Theatnvos, ...

The ti old -work, . ...

The topographical stiidia,

23S

The theodolite and stadia,

S3S

Tfleseopio meaeurementa in mine-aiirveyi,

33a

'Vhe grndientteleineter mining dial,

m

The DunUui-St'itt mine tAcheomoter, . . ,

m

Sis

Chapter Xvl

-out.

Ranging Rtraigbt' lines, 3M

Plotting the undergrouod trsTerM itn the turbo*,

Setting'Out railways to mini.

U6

Eangiiig curves,

Driving lerela uaderfronnd, ,

Curves for engine planes, . . ,

Settmg-out tuimeln, . .

ast

Chapter Xvil

Uinb-Sdrtjetikq Psosussis,

Ueterminatioa of the directioD tuid iooliiiatiou of a miiiorl deposit Detarmioation of ft point at the anrfaoe direoUy above one under-

ground,

Haling from one excavation to another,

Sinkiag shafts from several levels,

The cnbioal content of a mine-reservoir,

Detcrmiuation of the strike and dip of the tine of intereection of two

veins, ,,

aci J

'm

C0Ktbht8.

It

earcb for dislocated bodiaii 'J'S

Okregntaxitiea of gcuuna and beds, 27g

DobaideDM KuA draw caused bf working coal 980

tlSke volume exc&rftted in open workmgf, 84

CHAPTKR XVin,

MrNx Puuia.

PUn and section, , , 2BS

(u. J Met&UiferouB mioes, .

28S

(6,) Colliery plwia, ,

Surface plans, .

(e.) Ainericati colliery plans,

IiDportoiice oi correct sections,

S91

Uniformity of scale and ooDventicin&l signs.

Pweraticm of plans,

2D3

Prwitictd lUDts for (xmstnictlng mine plans, ,

2m

Gopjing plans,

11.} Copying by tracing, .

Copying on tracing paper, .

(3.) Copying by transfer, .

(4.) Pricking through,

ats

(&) Copying by photography,

28

Reducing unfl enlarging plans,

Tsometric plana of mine*.

Rdief plAQs and mine modob.

Mine plana in the Upper Hare,

Colliery plans in Weatphalia, .

Sos

Mine plana in Sweden,

ArpuoATioNe or tbx MAotmio-Hittt>i.i m Mnrnro. 1

Exploring for iron ore, ... . . , , S07

(1.) Brooka' method,

' (2.) ThaMn's method.

ai2

(3, J Tiberg's method.

(4.) Combined Thalt'n and Tiberg method

821)

(S. I Thomson- Thai dn metliod, ,

Um of the magnetic-needle in surveying bore-holes,

Employment of a powerful maet in cases of nacerUkin boUn, . 'SrV '

.

XTl

oomiuin.

CHAPTER XX. Photoobaphio Svbvktino.

PhotogTsmmetry, . IcstrumenU naed, Applioatioii to miDing work, . Advantages of photogrammetry,

Appendix L

Bzamination qnntiona,

APPENDIX n.

Bibliography, . Imdkx.

aM

A Teeatise

Mine-Sueyeying.

CHAPTER I. Gknsral Explanations.

Sunrejiilg is the art of making such measnrenients as are aecessarj to determme the relative positions of miy poiuts oa the earth's surface. From such meastirements a map, or plan, of any portion of the surface may be drawn, and its area calculated. All surveya are cooducted upon nearly the some principles, the difference consisting in the style of instruments used in the work, uid the amount of attention bestowed on the various det-ails.

The branch of surveying specially applied to mining is known

05 Mine-Burveying or, locally, as " dialling " or " latching. " It consists in measuring, with a view to subsequent delineation on

6 plan and sections, first, the underground workings of a mine, nd, secondly, the mine-buildings at the surface and the mine- concession or royalty. Thirdly, it requires an accurate method of connecting the underground- and sar&ce-surveys. Trust- worthy plans and sections are of value for giving a condensed riew of &11 the facta connected with the works and explorations of a mine ; for affording data to assist in the farther prosecution of workings after temporary abandonment of the excavations ; and for the avoiding of destructive and lamentable effects — such, e.g. , as disastrous litigation respecting trespass on adjoining royalties, loss caused by driving in the wrong direction, or irrup- tions of water, quicksand, or firedamp, giving rise to loss of life and property— which have too often resulted firom incorrect or imperfect mine-plans.

Historical Sketch The origin of mine-enrveying must be

ought with that of mining in very esrly tiinea. The oldest mine-plan known is a papyrus, preserved in the museum at

k.

miE-StlRVBTlNa.

Turin, depictiBg the situfttioii of an Egyptian gold-mine. It was drawn in the reign of the king Mineptah, 1,400 years before the Christian era. Land-surveying weis first practised in Egypt, There the annual overtlows of the Nile, and the consequent deposit of mud, destroyed the land-marks of the different pro- prietors, Eo that it became necessary to determine them by measurement every year. The oldest evidence of the Eolution of mathematical problems is afforded by a papyrus in the British Museum, which is believed to have been copied, 1,700 years B.o., from a much older work It gives rules for the calcula- tion of areas of triangles, trapezoids, and circles.

That the important mines of the ancient Greeks necessitated the solution of mine-surveying problems is shown by the &ct that such problems are fully aUcussud by Hero of Alexandria (b.o. 286-223), several of whose works are extant. The greatest advance in survey practice mode by Hero was his invention of the diopter, a sighting instrument for surveying purposes. Th oldest Instrument for measuring angles, like the cross-head which is still in use, only permitted right angles to be set out. This primitive instrument consisted of two straight-edges fiutfned together at right angles, a pointed vertical staff being fixed to the point of intersection. The two straight-edges were pronded at each extremity with sight vanes, from which plumb-lines were suspended so as to enable the instrument to be levelled. With Hero's improved instrument, any angle could be measured. Indeed, it must be regarded as the origin of the highly perfect theodolite of the present day. It consisted essentially of a beam resting between two uprights on a pillar-like stand. The beam was movable in both directions by means of spiral screws acting on horizontal and vertical cog- wheels. It was hoUowed out, and contained a metal tube, at right angles to which were glass cylinders at each end of the beam. The cylinders had special covei made of metal plate, which could be raised or lowered by means of screws. They were furnished with vertical and horizontal slits for sighting. The instrument was thus a com- bined theodolite and level. Two staves with sliding circular yanes were used Ln conjunction with it

From the beginning of the Christian era until the Middle Ages, mining records are wanting. An ancient charter relative to the mines of the Mendip Hills is in existence. Of this Mr. Robert Hunt gives a fac-simile in his Britith Miniiig. It dates from the reign of Edward IV., about 1480, It is a rude attempt at plan-drawing, representing the " Myne deeps," as they were then called.

The first writer who treated mining systematically, Georgiua

fgiua I

Areola, in his work re MtaUiea, published in 1556, devotea

an entire section {Book V.) to mine-surveying. He atfttes, aa has been f'retuently repeated since, that the sncient mine- snrvejots strenuously endeavoured to keep their art a secret. Itt the Middle Ages they were in consequence superatitiously regarded as sorcerers. The divining-rod was closely associated with the practice of their profession, and in many cases that hasel-twig was trusted more implicitly than the most scientlfia surveying opi ration.

In 1686 apptared the first exhaustive treatise on mine- nurveying, the Gcometria Subt-erranea of Nioolaus Voigtei. This was followed by the treatises of J. F, Woidler, 1726 (in Latin) ; and of H. Beyer, 1749, and von Oppel, 17+9 (in German), These works, by advocating the plotting of mine-surveys by means of rectangular co-ordinates, lifted mine-surveying to a higher plane.

In Great firitain, Lnslraetions for making mine-surveys were publtahed by Thuraas Houghton in 1681 lor the Derbyshire miners, by WilHam Pryce in 1778 for the Oomish miners, and by Thomas Fenwick in 1304 for the Newcastle colliers.*

Importance of Miae-Sorveyittg. — When the enormous value of m.inoral resources is considered, the high importance, from a com mercial point of view, of the art of mining is apparent. In fcbe United Kingdom alone, the annual value of minerals raised has approached £136,000,000, the result of the labours of some 908,000 persons directly employed in their extraction. It thus becomes a matter of the utmost importance that the extent and charaoter of the mineral deposits should be made known. This can only be effected by careful and accurate surveys.

Mine-surveying, unfortunately, has not kept pace with the advances made in other branches of surveying; for it is to be regretted that, in many oases, mine-surveys are still made with instruments which have long been set aside as too inaccurate for Burveys aboveground, altliough the latter rarely present such serious difficulties as are encountered underground. This ia, in part, due to the conservatism of miners, a conservatism which has frequently led them to regard with contempt every kind of knowledge except that learned underground. It is a fact, as Mr. R. Hunt points out, that the untrained mind, as a rule, treasures every truth as a mystety to be carefully guarded for individual use only. Experience has often stored an individual mind with \'aluable facts, which are rarely recorded. The miner trusta to his memory, and, when he dies, the results of his experience die with him. The son has to begin where the father

The history of raine-snrvDying is fully dealt with by D. D. Soott, Iran*. InM. M.E., vol. xxiii,. 1902, p. 575 j vol. xxviii., 1905, ?. 624.

be-jan, and this is repeated from genenktion to geaer&tion, ao tbat there has been no advance. Tliese renmrks apply more parti- cularly to thp itiinera of the county of Cornwall, wher the mimng proverb, "Where it is, there it is," still holds its own.

Happily, a better system is beginning to prevail, Ooal-miaing ia now carried on with a high degree of skill. Colliery managers, who formerly were generally ignorant of the theoretical principlei upon which practice is bused, are now submitted to a seyere edttcational test before a certificate of competency is granted. It is, however, to be regretted that a similar examination has not been instituted for the agents of metalliferous mines. The mining schools which have been founded in various districts offer suitable opportunities for the necessary theoretical training, as also do the local classes held under the Board of Eklucation, and under the Oity and Guilds of London Technical Institution.

Another cause which ha.i retarded the progress of mine-sur- veying ia the uncertain and speculative nature of mining. Casual failures, caused by the want of easily accessible information, fre- quently lead to the abandonment of highly promising mines. Mining, though speculative, is not entirely the work of chance; and he who, avoiding vague and unsatisfactory speculations, con- stantly stores up facts, and can grasp the extent and object of mining works, is frequently enabled to avoid expensfs, in which those who are without Huch data would soon be involved.

In this connection. Sir Warington Smyth, in a lecture on raining, says: " At the present time, few large collieries &t metal- liferous mines are conducted without the aid of a satisfactory plan, but there are very numerous mines in which this depart- ment is much neglected. Moreover, there is generally a want of uniformity in system, an absence of details which should give all the information that can he laid down on paper, a deficiency of Burface-objecta by which the workings can at a future day be referred to their proper position, and (what may sometimes lead to the most fatal errors) a neglect of observation or notice of the variation of the magnotic-aeedle, according to which mining plana are almost invariably conatrueted. It is too often the case when mines are worked by companies, that the shareholders are so regardless of what does not as they conceive, lead to immediate gain, that they grudge the moderate sums needful for the employ- ment of properly qualified surveyors, and either wink at the total neglect of plans, or leave them to be carried out by men already sulicieatly tasked or incapable, although they may dial with accuracy, of repreaentiag on paper what they have measured."

Aa an example of an arror involving great loss, serious danger, and future grave embarrassmentB, it may be mentioned that.

OKNERAT, EXPLASATlOJfS.

ftcoording to Mr. P. \V. Stuart-Menteath, at an important tome in Spain an incorrect survoj caused an error ol'6 metres to be made in driving a main tunnol less than 200 loetrea in lengtli. In ooUieries, too, examples are not wanting. Thus, in 1875, at a small ooUier in Nottingham there was an accident owing to soma old -workings. Trusting the old plans, which showed a barrier 100 yards away, the men worked into the old headings with disastrous results. Another case is recorded by Mr. J. Dickinson in 1678, vben an inundation occurred by which two lives were lost, from a {bnoer working being cut into without any bore boles in advance. Ib this instance, there was a correct plan of the former work, bat by a mistake of the surveyor, a wrong direction was set out

Mineral BeposltS. — For practical purposes mineral deposits may be divided into tabular deposits, including mineral veins, beds, and seams, and irregitlar depeniu, including masses, stock- works, and pockets. Tabular deposits are those in which two dimensions predominate. The third smaller dimension, the per. pendicular distance between the two bounding planes, is termed the thickness. The adjacent rock on both sidea of these two planes is termed the country, the portion on which the deposit lies tii/ootwcdl, and that covering the deposit is the hanging-waU. With beds and seams, these are known as the floor and roof respectively. The strike or eourai of a deposit is the angle formed with the meridian by the direction of a horizontal line drawn in the middle plane. Its dip is the inclination downwards measured in degrees from the horizontal. As the dip of veins b usually great, it is sometimes measured from the vertical, and is then termed urtderlie or hade. The portion of a mineral deposit occur- riog at the eur£u:e is known as the outcrop, baaiH, or (U,S,) apex.

Mineral veins or lodes are defined by Sir 0, Le Neve Foster as tabnlnr depofits of mineral, which have been formed sub.sequently to the rocks by which they are surrounded. Usually, they occupy tissureB in the earth, frequently cutting across the planes of stnitiiicatton of the rocks. They may occur in eruptive or in sedimentary rocka Their contents v.ary, some parts containing worthless vein-matter or gangue, others being filled with ore. The productive portions are termed shoots or courses of ore, bunches, or ore-bodies, Oroas courses are veins coursing nearly at right angles to the chief lodes of any particular mining district.

The characteristic feature of beds and seams is, that they are members of a series of stratified rocks. They may be inter- stratified deposits, or superficial oues, such as ptat, bog iron ore, gold placers, and tin stream- works. In the former case, they are younger than the floor, and older than the root, ii& &\.TOS.\i. deposits, they were originally deposited ia o. more qi Votv.-

MlNB-BDRTEyme,

zontat form, and follow all the coatortioiia of their country rock. The iiiiiitrala occurring in bedded deposits are coal, anthracite, lignite, iron ore, cupriferous-shale, lead-bearing sandstone, gravels containing diamonds, or gold, or tin, 3ulplmr,3alt, olaya, limestone, gypaum, oil-shale, alum-shale, and slate. Miners often erroneously apeak of " veins " of coal or ironstone ; these, geologically, are true beds " or seams.

" Masses " are deposits of tnineral of irregular shape, which cannot be recognised as beds or as veins. Such, for instance, are the red hwrnatite do' posits of Ulverston, the brown haema- tite of the Foreat of Dean, the iron ore deposits of Missouri, the iron mountains of Gellivare and Taberg in Sweden, and the pipes of diamond-bearing rock in South Africa. They may be filled-in cavities or metaniorphic deposits, such as tbs zinc ore deposit of Altenberg, which is 2G0 yards long and 6.5 yards broad and deep. When the whole rock is permeBted with mineral matter, accumulated in minute veins, the deposit id termed a Btocktoork. Examples of such deposits occur at Oarclazo and other places in Oorawall, and at Altenberg in Saxony,

No classification of mineral deposits can be quite satisfactory in all (£e8. A bed, for instance, even of coal may be so folded and contorted as to lose its original tabular form, and to assume the shape of an irregular mass.

Mining Terms. — Many local as well as technical terms are used in mining. The following are definitions of some of the objects most frequently named on mine-plans ; — A is a pit sunk down from the surface. In the mining of stratified deposits, the shafts sunk are usually perpendicular. In vein-mining, they may be sunk perpendicularly to cut the vein, or they may foUow its underlie. Levels are horizontal excavations along the course of a vein, or horizontal passages, by which access is gained to the workings of the mine. A level driven from the surface, to draw off the water, is termed an adit level, or (U.S,) a funnel A drifl or gallery driven across the usual direction of the veins generally for the purpose of searching for a new vein, or of connecting two known veins, is termed a croga-out. The extreme end of any level or cross-cut is called the forebreast or end, A slope is the working from which the ore is extracted. Above a level, the working is an " overhand " or back stope ; an " underhand " atope is the working downwards from the floor of the level. A winze is a shaft which connects two or more levels, but does not come to the surface. A rise Is an upright winze commenced from a level ; a gunip is a winze worked downwards. Surface workings include open cuts, pits, and excavations of Umifced extent. A. of

6Ekbral Kxplanations.

hmd let for mining purposes is known as & ett, rtftill, eoncft- fiori, or claim.

In coal-mining, the p&lr of galleries driven from the shaft are vaiioaslj known aa dri/tSf headings, levels, way-gaies, gate-roach, and rolley-way. The winning of the coal is effected in different ways, following a variety of modifications between the two extremes, namely, the "post and ilali " syatem, otherwise known as the " bord and pillar," or in Scotland aa " stoup and room," and the " long-toall " system. In the former a given district is at first worked by narrow excavations, so that no considerable fall from above shaU take place ; in the latter, the whole of the available mineral is removed in smcceasive slices, and the roof Allowed to fall in.

MeaEores of Lengtb.The standard measure of length in the United Kingdom is the yard. In addition to the yard, the fol- lowing units of length are used for surveying purposes : —

The inch, one thirty-sixth part of the standard yard. The/oot, one- third part of the standard yard. The fathom of 6 feet or 2 yards. The chain of 66 feet or 22 yards ; divided into 4 poles of 5i yards, and 100 linkt of T'92 inches. The tfaltite mile of 1,765 yards or '>,280 feet or 80 chains, divided into B furlongs.

The standard yard is the distance between two fixed points on a certain metal rod at the temperature of 62° F., and under the mm atmospheric pressure. The British and United States standards are identical.

To obviate the inconveniences of the innumerable units of length used in diSerent countries, attempts were made towards the middle of the 17th century to introduce a natural unit, which could at any time be again determined if the standard should be lost Two proposals were considered ; one being based on the length of a pendulum vibrating seconds, the other on the magni tude of the circumference of the earth. The former suggestion was due to Huygens, who proposed to divide the length of a pen- dulum vibrating seconds into three parts, and to term each part a foot. Til is method was found impracticable, since the length of the seconds-pendulum varies with the latitude at different places ; thus, at London it is 39 '1393 inches, whilst at New York it is 39-1017 inches.

The second plan was therefore adopted — that is, a fraction of the earth's meridian was taken as the standard. For this pur- pose, at the time of the French Revolution, the distance from Dunkirk to Barcelona was determined. Both these places are in the same meridian as Paris. The measurement was subsequently extended to the Island of Forment<*ra, and, from the length determined, the distance of the pole from tYie wfaeAftt iR.-

UINK-SDBTEYIIta.

Uted to be 5T30740'74 French fethoBOB (toises). The tet millionth part of this length (0'613074 toise) was termed the ntetre, and was adopted as the French unit of length. Ln 1799, two airailar rods of platinum were constructed as standards, having that length &t 0° centigrade, The given length of the metre being thus determined, it ceased to be a natural measun. With the present improvements in measuring-instruments, it is poasible for us to determine the circumference of the earth with greater accuracy, whilst the length of the metre is fixed. Indeed, it ia now known that the metre was determined a not inoonaiderable fraction too smaJl.

The French measures of length are multiples and Bubmultiplei of the metre. The value of the latter in British measure is 3'2808693 feet, or 39-37043 inches. For mine-surveys the metre is the unit now almost exclusively used in continental European countries. It ia also employed on Government surveys in the United States.

Special units of length used for mining purposes in various countries are the following : —

Brlttali rttbom.

Fml

Fathom

I'Ooo

Metre,

os4e

Swedtih FBton, .

Russian Soahon,

riM

Au3triii Klafter,

Bavarian Laohter,

Wilrtteinberg Lacliter,

Hanoverim Luuliter,

iSaion Lachtar,

Fmuiau Lachter,

Spanish Vara, .

Frennh ToiM, .

l-0fl5

6 '394

Angnl&T MeaBurefl. — The circumference of a circle is divided into 360 parts ; eswh part being termed a " degree." The degree is divided into 60 minutes, and the minute into 60 seconds. This is known as the sexagesimal division.

The French centesimal division of the quadrant into 100 degrees, instead of 90 degrees, is rarely used except for surveys with the tacheometer. Each cBntesimal degree is divided into 100 minutes, each of 100 seconds.

OEMEBAt. RXPLANATI0K8.

Tngonometrical Formolffi. — The foMowing is a summary of the principal trigouometrica.1 formule used in surveying : —

The trigoaometrical functioas of a given angle may be defined AS the ratios to each other of the sides of a right-angled triangle possessing the giTen angta Assuming that A, B, represent the three angles of a right-angled triangle, being the right angle, and that et, b, e represent the sides respectively opposite to these angles, e being the hjpothenuse ; then the trigonometrical functions of the angle A are —

Bin A

a . e

; cosec A - e a

COB A - : sec

e'

A

b

a i b

tan A i- ; cotan A -

ffl

The following equations give the most important relations amongst the trigonometrical functions of the angle A : —

tan A —

cosec A

cotan A

cosec A

sec A

cotan A

sin A

cos A

tan A

VI -coflA

- sin* A

V8ecA - 1

/l

+ cotan* A

s/1

/cosec* A - 1

tan A sec A

cotan A cosec A

sin A cos A

sec A

tan A

cosec A cotan A

cos A sin A

The complement of an angle is that angle which must be added to it to make a right angle, and

sin (90* A) cos A ; cosec - A) sec A cos (90° - A) ein A ; sec (90* - A) cosec A ton (90* - cotan A ; cotan (90° - A) tan A

M1Nk-8Drteting.

The supplement of an angle is that angle which must be &dded to it to make two right angles. Oompared with the trigonometrical functions of the angle A, those of its supplement i

sin (180° - A) sin A ; cosec (180' - A) cosec A cos (180° - A) - cos A ; sec (10° - A) - see A tan (180* - A) - - tan A ; cotan (180' - A) - - cotan A

The formulae for the solution of plane triangles are deduced from the principles that the sum of the three angles of a plana triangle is equal to two right angles, and that the aides of th triangle are proportional to the ainea of the opposite angles. For right-angled triangles the most useful formulae are —

b — a sin B b c tan B b e cotan

— d COS B

e b tan

e b cotan B

For oljlique-angled-trlangles, the moat useful formula are

a sin B sin A

a sin sin A.

TRB HEASDEtEUKNT OB DtSTANORS.

OHAPTEE IL The MEAstTBUMEitT or Dibtanof.b.

Methods of Measoruig. — The straight lines whicli have to he measured by the miae-surveyor may be horizontal, vortio&l, or incliiipd. The measurement of horizontal lines is of the most frequent oocurrenca When a line inclined towards the hori/on has to bo measured, the operation is, as a rule, performed mth the object of determining the horizontal and vertical projcctiouB of the line. It is then necessary, in each case, to determine the angle of inclination formed by the measured line and the horizon.

Lines are usually measured with chains, tapes, or rods, divided into fathoms, yards, links, feet, or some other unit of measure- ment.

(a.) Chain. — The instrument most frequently used in sur- veying is the chain. In coal-mines and in field<eurveying, Gunter's chain is employed. It is 66 feet in length ; 80 chains being equal to 1 mile. This length was chosen by the inventor, Edmund Ounter, in 1620, with the object of facilitating the compulation of areas ; 10 square chains being equal to 1 acre. The chain is composed of 100 links of iron or steel wire, each bent at the end into a ring, and connected with the ring at the end of the next piece by means of three rings. The chain is thus prevented from becoming twisted or kinked. A couple of swivels are also inserted in the chain, so that it may turn round without twisting. Every tenth linl is marked by a piece of brass with one, two, three, or four points, corresponding to the number of tens that the brass represents, counting from the nearest end of the chain. The middle, or fiftieth, link is marked by a brass circle. A swivel-handle is provided at each end of the chain. The wire used in the construction of iron chains is usually Ko. 8 W.G.; that used for steel chains is No. 12, or No. 8 W.G.

The hundredth part of the chain is called a link, and is equal to 0-66 foot or 7 92 inches. All calculations with chains and links can thus be easily perlormed by means of decimals. The following table will be found useful for converting chains into feet and feet into links :—

Mine-Bdrteyihg.

Oatiiii IKTO Fsn.

Fun una ]Awt.

Cbilna.

Feet.

PsiL

OflS

3-m

5-2S

For collier; use, the chain ia sometimeB made with tea links in brass at eaAb end, in order to prevent the oompass-needle being attracted.

It must be remembered that an; error in the length of the cli&in will cause erroneous measurement throughout the entire survey. It should, therefore, be tested and adjusted before the commencement of every survey, or at any rate from time to time. This is beat done by having a standard marked on a level path- way or on the top of a wall, showing not only the accurate length of the chain, but also the length of every ten links. Standard C6-feot and 100-feet chains have been fixed by the Government in Trafalgar Square and Guildhall, for the use of surveyors in London.* If a line has been measured with an incorrect chain, the true length of the line may be found from the proportion : — As the length of the stjindard given by the incorrect chain is to the true length of the standard, so is the leugtfa of the line given by the measwrenient to its true length.

Accompanying tLe chain are ten arrows or iron pins, which are used in succession to mark the end of the chain in measuring a line. They are a foot long, and are made of stout iron wire ProfesBor H. Louif, Trans. Imt. M.E., vol. ixiii., 1902, p. 85, draws attention to the various precautions that should ba oljserved in Bcttiuct out Euoh a standard teogtli, and details tlioso he employed in laying down standards of 66 feet and 100 feet at the Durbam Co\\bjic dV Scvonce.

J

Tbe Ueaiuskment Of Distances.

ibarpened at one end and bent into a ring at the other. A pieoQ of red tape is usually attached to the rings to render the arrows visible from a distance. The chain ia folded by taking it by the 50-liuk mark, and folding the two ends simultaneously, taking care so to cross the links that the body of the chain when folded may be smaller in the middle than at the ends. The chain is opened by taking both handles in one hand, and throwing the chain oot with the other.

The chain is used by two persons, the leader and the follower. The former having been BUpplied with the ten arrows, stretches the chain in the required direction, while the follower holds one end of it at the starting-point. An arrow is then driven perpen- dicularly into the ground by the leader at the point where the chain ends. He then proceeds onward, drawing the chain after him, and repeats the same operation throughout the length of the line ; the arrow last put down serving as iha mark to which the follower has to bring his end of the chain. The arrows are taken np by the foUower as he advances, until he has them all, when they are returned to the leader to be used over again. The arrows are thus changed from one to the other at every 10 chains' length ; care being taken to note each change in the field-book. At the end of the line, the number of changes added to the number of arrows in the foUower's hand, and to the number of links extending from the last arrow to the end of the line, gives the total length of the line measured. If the ground is so hard that an arrow cannot be driven in, the leader marks the ground and lays the arrow down. Eleven arrows are usually pre- ferred. The eleventh is used to mark the end of the eleventh chain ; another being substituted for it before the leader goes on. During the operation, the follower has to see that the chain is tight, straight, and unentangled, and to direct the leader so as to enable him to place the arrow in the ground exactly in the alignment.

In measuring lines in a colliery, the arrows are usually dis- pensed with ; the end of each chain being marked with a piece of chalk.

The chain used in metalliferous mines is 10 fathoms or 60 feet in length, and is provided with brass marks at every fathom. Each link of the chain is 6 inches in length. The chain is soine- times made entirely of brass. No advantage ia gained by using Gnnter's chain in a metalliferous mine, since acreage baa never to be calculated, and measurements have to be made with such precision that the inch is to be preferred to the link as a unit.

Chtitting oa Slopes. — In chaining up or down a slope, the distance must be reduced on the plan to the proieotion of that

u

HINB-SUBVKTIira

distance on a horizontal piane. If the slope is gentle, the lover ead of the chain may be raised until the chain is level. To

QunUr't OlulD.

IChfltboiu ChklD.

loo- foot diiiii.

OorriKUnn In UbU.

Id FePt

CometlcM

1 in 19-08

1 in 14'30

0-at

1 in 11-43

0-3S

1 in O-SI

1 in 814

0*74

1 in 7*11

1 in ti-31

1 in 5-07

0'91

u

1 in d'14

liu 4'70

I in 4-33

4-01

Un 3-73

I Id 3-48

1 in 3-27

I iu 3 07

4-S9

le

lin 2-90

6 '44

i in 2-74

2S

1 in 214

lin 1-73

The rate of ilope (the mtio of the hy potbenuie to tho perpendicular) ia the cooeooDt of the angle of inclbatiatj. The rate of inchnation (the r&tio of the base to the perpendicalar) ia the cotangent of the angle of inoUnation,

Thb Mbabtfreubnt Op Distances.

ensure the raised end being exactly above the right spot, the chain may be raised along a vertical staff, or an arrow may be carefully dropped, or, better still, a plumb-line may be employed. The process is called stepping, and, on steep ground, roay ba carried on by half-chains, or even shorter distances. A more accurate method is to measure the angle of the declivity. The cosine of this angle, multiplied by the measured bypothenuse, gives the length of the horizontal distance.

The most convenient method is by means of a aorrection to be deduct*-d from each chain. This correction, being known, may he applied mechanically during the chaining by pulling the chain forward at each chain-length through a distance equal to tho required correction.

The preceding table gives the correction for each chain measured on the slope.

In order to save calculation, many mining dials and theodolites have the correction for declivity marked on the graduated arc on which angles are measured.

OffsetB are ordinate s or transverse distances measured &om known pointa on a station-line to objects the position of which is to be ascertained. Offsets, as a rale, are measured at right angles to the chain. The length of the offset having been deter- mined, the position of the object is fixed with reference to the main line.

Otfsets may he measured with an oJfMi rod, 10 links in length, painted black and white in alternate lengths, or, preferably, with a meagiring-(ape. This is divided on one side into links and on the other into feet and inches. It should be tested frequently, particularly after use in a wet mine. It is not advisable to use offsets more than a chain in length. When the offset does not exceed this length, with practice the eye may be relied upon to give a right angle with precision. The crotagtqf and optical square, recommended hy some surveyors for erecting perpendicular lines, are mrely necessary in mine-surveying practice.

The optical aquare consiats of two small mirrors placed in a brass box at an angle of 46°, thus reflecting an object through an angle of 90*. The unailvered half of one mirror gives a direct view of the object, whilst the reflected and true object can be exactly superimposed in the observer's field of view when they ure at right angles to each other. The oro-staff' haa two pairs of sights fiaed at right angles to each other on the upper end of a staff' having a spike at its lower end for fixing into the

In taking offsets, the surveyor reads the tape at the chain.

Hink-Bdrtbting.

The ring of the tape is held &t the point to which the oBmA required. The surveyor then turns the tape in s horizontal plane until he obtains the shortest measurement, and ascertains the link on the chain where the offset forma a right angle.

In cases where additional accuracy is required, ohlifue offtefs may be used. From two points in the chain, ofTeets are measured obliquely to the object, and the triangle thus formed, when plotted, shows the accurate distance of the object from the station-line. When tlie object is the corner of a building, such as D in Fig. 1, it is convenient to make each of the offsets, if possible, lie In a straight line with a face of the building. Obstacles to Measoiement. — Obstacles sotne- timea occur in a long station-line, rendering it impossible to chain along the line with accuracy. In some cases it may even be impracticable to range the liae directly across the obstacle. These difficulties may easily be obviated by the use of angular iastra- tnents. It is, however, possible to -use the chain alone.

When the impassable obstacle can be seen over, a ranging pole is planted in the station-line at the further side D (Fig. 2) of the obstacle. At two marks, A and D (the nearer and further tides of the obstacle respectively), two lines, A B and D 0, are ranged at right angles to the atation-line. These perpendiculara are made equal to each other, and the distance B is measured.

ng-i.

Pig. s.

Kg. 4.

This measured distance will then be equal to the required dis- tance, A D.

In order to erect a perpendicular to a line at a given point, Euclid's proposition (1., 47) may be applied in the following way : — Measure 40 links along the line, and let one end of the

d

TBK I9EAaCKEU£irr or DISTANCES.

ebain be htd at that point, and and let the SO-link mark be held at the given point where the perpendicular is to be erected. Then take the 5U-link mark, and tighten the chain, drawing equally on both portions of it The 50-tink mark will then give the perpendicular required. It is advisable to repeat the opera- tion on the other side of the line, so as to test the accuracy of the result.

When the obstacle can be seen over, the length of the gap in the station-line may be determined by setting out a triangle ABO (Fig. 3) enclosing the obstacle. The triangle may be of any form or size, provided that B and are in one straight line with D, and that the angles are not very obtuse nor very acute. The lengths A B, A 0, B D, and D are measured. Then the inaccessible distance will be found either by plotting Bthe triangle and the point D in its base, or from the formula : —

The figure of the obstacle may be surveyed by offsets from the ides of a triangle. Let 6 and c, in Fig. 4, be points in the station-line on opposite sides of the obstacle. From a convenient station A, chain the lines A £, A c, being two sides of the triangle Abe. Connect these lines by a line B to form the triangle ABO. Then the inaccessible distance is obtained from the following formula given by Rankine: —

This formula will apply if the points E and are taken in the

prolongations of A c and A S beyond the station-line, as at B'

and C, or in their prolongations beyond A, as at B' and 0". The

formula is greatly simplified if A B and A O are set off so as

to be respectively proportional to A 6 and Ac. Then the

triangles ABO and Abe arc similar, B is parallel to b c, and

A b the inaccessible distance 6 e is equal to B j.

When the obstacle can be chained round, but not chained across nor seen over, the inaccessible distance may be determined by means of parallel lines. Thus in Fig. 5, from A and B two points in the station- line on the nearer side of the obstacle, set off the equal perpendiculars A O, B D, of length sufficient to enable a straight line to be ranged parallel to the station-line,

I and to be chained past the obstacle. Oouimence the cba-imw,

J

INS-S0RTETtNa.

of this line at D, in continuation of that of the atation4iae &t B. As Boon as the obstacle is passed, set ofi' the perpendicular £ G equal to A aud to B D. Then G will be a point in the station-line beyond the obstacle, and the inaccessible distance B G will be equal to D E. By repeating the process, an addi- tional point H in the station-line may be found.

The problem may also be solved by means of similar triat>gle& At A (Fig. (3) two diverging lines A F and A E are ranged past the two sides of the obstacle. In these lines, measure the distances A D and A of two points X) and C, which lie in one straight line with B. Oontinue the chaining of A F and A £, and make those distances respectively proportional to A D and A 0. Measure D 0, noting the position of B, and measure E F, in which Hue take the point G, dividing E F in the ratio in which B divides D. Then G will be a point in the atatdon- llne beyond the obstacle. Other points may be found in a similar

manner. The inaccessible distance is equal to — r-pi —

When the obstacle can be seen over, but neither chained across, nor chained round, as in the case of a station-tine inte rupted by a river or ravine, a pole must be ranged and &sed at D (Fig. 7) in the station-line beyond the obstacle. BD being the inaccessible distance, at B set out B perpendicular to the station-line. At range A perpendicular to D, cutting the Btation-line at A, Measure AB, BO: then BB is equal to BC + AB.

BHg, &

Fig. 7.

Surveymg with the Chidii only In this method of surveying,

the aur&ce is to be divided into a series of imaginary triangles ;

THE MEASURtiMBKT OF DtSTAOES.

the triangle being the only plane tigure of which the form caiuiot be altered, if the sides remain constant. The triangles should be as large as thf nature of the ground will allow, ami as nearly equilateral as possible. The sides of these triangles are first measnred, and a straight line is measured from one of the angles to a point in the middle of the opposite side. This fourth line is called a tie-Hrie or proof-line, and is an ethcient means of detect- ing errors. Within the larger triangles, as many smaller triangles and tie-lines are measured as may be required for determining the position of all the objects included in the survey. The dtrections of the lines forming the sides of these secondary triangles are so placed that the offsets to be measured from them may he as short and as few in number as practicable. Pickets are placed in thu gronnd at each angle of the triangles, the general form and position of which are noted for reference in a hand-sketch, distinctive letters being written at each point of intersection. The points of intersection of all straight lines, as well as the angles of the triangles, are always points measured to or from. They are called stalions, and the lisca connecting them atationrlinet. Secondary stations are best marked by whitet, which are cleft sticks holding small pieces of white paper, on which a number may be pencilled.

In carrying out a survey with the chain only, it is necessary to attend to the following rules : — Walk two or three times over the ground in order to get a good idea of it, helping your memory with a rough sketch. The first line should be made as long as the place to be surveyed will allow, so that it may form a con- venient base with which the other lines may be connected. Select a suitable station on each side of the bast-liiie near the boundary of the work. To these stations, lines should be me&sured firom each end of the base-line, thus forming two large triangles, one on each side of the base-line, On the sides of these triangles, smaller triangles must be market! out, so as to cover all the ground to be surveyed.

The rough sketch is usually mode in the Jteld-book — a book in which every step of the operations gone through in the survey is to be carefully entered at tk tivte. The tield-hook is ruled with a column down the centre of the page. In this ai-e set down the distances on the station-line at which any offset is made, and on the right and left of the column are entered the olTseta and observations made on those sides respectively of the station-line. The middle column represents the chain. It is, therefore, advisable to begin the entries at the bottom of the page ; the chain and field-book being thus placed in the same position at the station-Vme with respect to t\ie sutvcjox, 'wVa

Mine'Scrybtino.

keeps his face directed towards the distant station. The croBsing of fences, roads, or streama is to be shown by joiaing lines in a way similar to the form which they present on the ground.

The following example shows the raanner in which the field- notes may be entered in the survey of a triangular piece of ground : —

From B From D

3G2

O

to D, tie-tins to A

From C

©

to D

From A

to C

to B, point fot tte-lioe

In booking, certain conventional signs are adopted for the remarks that occur frequently. The commencement of a station- line, for example, is represented by a small circle or a triangle, and its termination by a line drawn across the pago. A station left in a lino, to or from which another line is to be measured, is usually represented by its number enclosed in a circle. A turn to the right or left is indicated thus f i "I.

Proper attention in keeping the field-book saves much time in plotting, and guards against errors likely to arise &om reference to confused notes. In fact, notes ought to be kept so clearly that a draughtsman should be able to plot the survey without further instruction from the surveyor

In spite of its apparent want of accuracy, the method of surveying with the chain alone gives, in the hands of an accom- plished surveyor, very satisfactory results. At the same time, though sometimes used for the surface-surveys of small collieries, it is not considered sufficiently accurate for surveys of metal- liferous miuo royal 'iiis.

Chain aeed in Trigonometrical Surreys. — Before compensating bars were invented, steel chains wero employed for base- measurement in the Great Trigonometrical Survey of the

Tbb Ea8Crrubnt Op Distances. 31

Tnited Kingdom. In tisiag the steel chain, a drawing-post and & weight-post were used ; a 56-)b. weight being always applied to one end of the chain, whilst the other was fixed to the drawing-post. The chftin was made to rest in deal coffera supported by trestles, in order to obtain a perfectly level surface, and thermometers were placed at different distances in order to ascertain the temperature of the chain, so that the base might be reduced to its value at a given temperature. The chain was 100 feet long, and consisted of 40 links, each inch square.

(6.) Bods. — When very accurate measurements were required, deal rods were at one time largely used instead of the chain for measuring long lines. They were, however, soon discarded in exact operations, as experience showed that they were liable to sudden and irregular changes in length from dryness or humidity. Saturated with ooiled oil, and afterwards covered with a thick coat of vamish, veil-seasoned wooden rods will be found suffi- ciently exact for ordinary purposes. Buch rods are usually made of lauce wood, and are 5 feet in length. They must be placed in line very carefully end to end. They are rarely placed directly on the ground, which, as a rule, is too uneven. A horiKontal line my be constructed along the base to be

Tineas ured, by means of a stretched cord. On the Trigonometrical Survey of the United Kingdom, glass rods were substituted for wood in the measurement of the Hounslow base in 1784. Their ends were protected with metal caps. The results obtained were perfectly satisfactory, measure- ments with the glass rods and a check measurement with a steel chiiin of perfect workmanship, giving results that diifered by little more than hall" an inch in the Ijase-lLne of 27,404 feet Steel rods also have been found useful. A nickel sttel alloy, known as " Invar," with 64 per cent, of steel and 36 per cent, of nickel, and with exjiansions of one to three-twentieths of an inch for each degree Centigrade, gives the best results.

For the measurement of the Loch Foyle base, an apparatus was devised by Colonel Colby. In this he obtained an unalter- able linear measure by using compensating expansions. Two bars, one of iron, the other of brass, 10 feet long, were placed parallel to each other, and rivetted at the centre, it having been found by numerous experiments tliat they expanded or con- tracted in the proportion of 3 to 5. The brass bar was coated with some non-conducting substance, in order to equalise the susceptibility of the two metals to change of temperature. Across each end of these combined bars was fixed a tongue of iron, with a minute dot of platinum so situated on this tongue that, with every change of contraction or expSiiiwoTL, &ct\& each end aJways remained at the constant diataute feaV

Uine-Surtevino,

On the Continent, rods 3 to 4 jrards in length are employed, terminated Ly two points, and provided in the middle with a builder's level iind a. liaiidle. This apparatus is known af the Id-compaSBes, and is often used for filling in details.

(c.) Steel Bands, — The most suitable iiistrumeut for measuring lengths in miiie-aurveya is the steel band. It is more convenient and less liable to inaccuracy than the chain. It is usually 100 feet, or 100 links, in length, with feet etohed on one side and links on the other. It is provided with a handle at eiich end, and ia wound on a steel or wooden cross. It is employed in precisely the same way as the chain. Like that instrument, it presents the advantage of rapidity ; but it has the additional advantage of representing a length of which the variations are dependent only on the temperature, since it does not kink, stretch, nor wear ao as to change its length.

In surveying the anthracite mines of Pennsylvania, Mr. E. B, Ooxe uses a measuring-tape made of a ribbon of tempered steel, 0'08 inch hroad and 0'015 inch thick. It is 500 feet long, and weighs 2 lbs. oz. At each tenth foot a small piece of brass wire ia soldered across the tape, the white solder extending about an inch on each side of the wire. In the latter is filed a small notch which marks the exact spot where the tenth foot ends. The distances from the zero point of the tape are marked upon the solder by counter-sunk figures. The white soldier enablea the 10-feet notches to be found very esksily, and the countersunk figures, being filled with dirt, stand out upon the white ground of aolder. The tape is wound upon a simple wooden reel, 10 inches in diameter, which can be held in one hand and turned hy the other. Two handles, which can be detached, accompany the tape, and are carried upon the reel.

The advantagea of the tape are— (1) the greater facility in measuring up and down slopea, or along the face of the coal j (2) f;reater accuracy in measuring from one station to another, as the tape forms a straight line from one station to the other, and there is no error from the use of arrows ; (3) the tape does not stretch appreciably. Its disadvantages are — (1) it ia liable to break, unless carefully handled ; it is necessary to roll it up and unroll it again when the distances vary very much. The tape, however, can be easily mended when it breaks. For this purpose, a small sleeve of brass is made tinned inside, in which the broken ends of the tape are slipped and then Boldered by beating the sleeve with a red-hot poker.

Thfsre are three sources of error in the use of the steel tape.

Trn*. Amtr. InuL M.E., vol. ii., 187+, p. 219.

THB UEASDBeMKNT OF DIBTAN0E8

(1) tlie extension of the tape by stretch int ; (2) the shortening of the tape in conaequence of its tissttming the form of the catenarj curve ; and (3) the contrnction or expansion due to change of temperature. The tape does not stretch to ftoy appreciable extent, and any error thus caused is oompenaated hj the shortening due to the formation of the catenary curTO by the tape. The true distance indicated by a 500-foot ateel tape, when subjected to the usual tension of 40 lbs., is calculated to be 4909185 feet. With regard to the expansion caused by change of temperature, a tape measuring 500 feet in length at 33" F. becomes o00'6 feet in length at 212°, so that a variation of 60* causes a variation of only 0-'2 foot ia a 500-lbot tape.

A steel band, 300 to 700 feet long, is to be recommended for all important work in mine- surveying, whilst the chain should be nsed for filling in details, and where extreme accuracy is unnecessary,

(d.) MeasuriBg-Wheel. — The viameter, or measuring- wheel, is sometimea used for measuring station-lines. The wheel is rolled over the ground to be measured, and its motion is oommunicaited to a series of toothed wheels bo proportioned that the index-wheel registers their revolutions, and recoi'ds tho whole distance passed over. On very even ground the results are fairly satisfactory.

(e.) Pacing. — A line may be measured by pacing, with tolerable accuracy. This method consequently is frequently employed on explorations, preliminary surveys, and in levelling with the aneroid barometer. Tn order to obtain accurate results, the nrveyor must accustom himself to an accurate pace. This may be done by pacing a distance of 200 to 300 yards repeatedly, until the same number of paces is always obtained. An instru- ment, called a poMometer, made in the form of a watch may be conveniently used for registering the number of paces, thus preclading the absorbing attention required for accurately ooonting a considerable number of paces. The distance may be registered direct by a similar instrument, the pf.lcMne(er, which can be adjusted with facility to long or short steps.

The usual step is the military pace of 30 inches, 108 of these paces per minute representing a velocity of 3'07 miles an hour. If no unfavourable conditions come into play, for example, slope of the station-line or fatigue, a distance may be determined by pacing accurately to within 2 per cent. The pace of the surveyor should be re-measured from time to time, since after the age of 25 to 30 years, the length of the pace diminishes considerably with increasing age.

On slopes, the pace is always shorter than on level ground,

rofessor W. Jordan gives the following averes : —

u

UIKK-BtlRVETIirO.

[Uh.

Fdl

Pkc

r

IncllttL

iDchn.

5'

27 '0

10"

Iff"

Is-

15'

20'

20*

2fi*

25°

30"

30°

The relation between the height of the indiiridual and the length of hia pace, may be seen from the following averages ; —

HdftiL

Fus*.

Viet.

o

Fml Inehei. S 8

InrtiM.

S 10

S

S2-6

Accuracy of Linear MeaBorements.— Professor F. Lorber, of tha Leoben School of Mines, has made a careful study of the accuracy of linear uveasurementB. From 6,000 measurements, he deduces the fol lowing; table showing the mean error of each method employed. The error is proportional to the square root of the length, according to the theory of probabilities. The mean error m in measuring a line L by five different methodi is aa follows : —

lure root of L

multiplied bjr

Two rods along a itretohed cord,

, m O-0OO536

Two rods, without cord, .

, m 000327

Chain

. wt 003000

Steel band, . . . . .

. m 00021B0

Field ' com [insasi, . , . ,

. frt 0(J02120

Measuring- wheel, . , . .

. m 0O3tiOO

The Mkasurf.Mf.Nt Of Distancks.

Thp moan error is thus approximately —

1:2:6:4:4:7,

according to the method employed. Thug, a measurement with rods along a stretched cord is six times as exact as a measurement of the same line with the chain. From the results given above, it is evident that measurements with rods along a stretched cord are the most exact, whilst, with the exception of the measuring- wheel, the chain gives tiie most untrustworthy results. The steel band, too, gives results one and a half times more accurate than those given by the chain.*

Normal errors, such as those due to defects in the instrument, and errors in allignment, increase in proportion to the length. For the various instruments, with the exception of the rods along a stretched cord, where the normal error r is reduced to a minimum, these errors are as follows : —

Two rods, without cord, . . . r s - 0-00008 L

Chain + 0*00046 L

Steel hud. r - - 0-00032 L

Field-oompwMS, r - 0-00079 L

In the case of the chain only is the error positive ; that is to say, the length measured is longer than the true length.

The rapidity of measuring is shown by the following averages : —

Inniiinn

imaitm.

MiAii 8n ns Hiran.

AbMlntb

Per Auieteot.

Rods,

Cauun, Steel band.

Feet.

Feet.

Improved methods of ehaining are deeoribed by W. M. Thompson, Min. Proe. /tut. OB., vol. xcii., 1S88, p. 26. When excessive aconracv is required. M. Pnyborski, M(L, voL cxliv.. 1001, p. S56. recommends hooking a spring-baumoe to the steel band to maintain a constant tension. The buance is a brass tube, 4 ins. long, containing a spring and a pirton with an indicator working in a side groove. A small stop prevents over* Ktretching.

Mink-Sdktetino.

Chapter 111.

The Miner's Dial.

DIrectiTe Action of the Earth's Magnetism. — In determining

the linear direction of mineral deposits, and in acquiring in- formation to aid in laying down on paper the position and extent of mine- workings, the magnetic-needle has long len employed.

The action of the earth on a magnetic-needle is directive, is, it determines the position of the needle vith relation to the cardinal points of the horizon, hut causes no strain on the point on which the needle is balanced. Thus, if a magnetic-needle is supported at its centre of gravity, it assutnes a certain direction ; one pole pointing towards the north and the other towards the south. The pole of the needle directed towards the north ii called the north pole or, more correctly, the north-seeking pole, and that directed towards the south is called the south p<ke or south-seeking pole. The magnetic force acts through rooks, glass, and liquids as instantaneously and with as great intensity as through the air.

Eistoncal Sketch. — Although the use of the magnetic- needle by mariners ia described in a French poem of the year 1130, to Flavio Gioja (1302-1320) is usually assigned the credit of having first enclosed a magnetic-needle in a box. The use of the magnetic-needle for surveying mines is described by Gteorgins Agricola in the fifth book of his re Metailicd, published in 1556. The compass there described is of a very primitive character. It consist-s of a series of seven concentric circles filled with wax of different colours; in the middle is a depressed receptacle to contain the magnetic-needle. An old compass of this type is preserved in the collection of the School of Mines of Olausthal in the Hara. It bean the date 1541, and consists of a wooden plate, j inch thick and inches in diameter, in the middle of which is a small brass compass-box, 2 inches in diameter. The whole is placed in a circular receptacle in a wooden box, which may be closed by a lid, and which is provided with a hole in its base, probably to enable it to be placed on a stand. The compass has only a north and south line marked, and round its raised edge a double ruler revolves. The wooden plate has several cotlcitAxvc cvcaviVM

]

The Miners Dial.

'essioDS, filled witli wax of diilerent colours. When in use, inatrumeut was so placed tliat the needle pointed to tlie north, and the ruler revolved until it pointed in tlje direction, the Vieimng of which was required. A scratch was then made mi oiif of the wax circles to indicate this direction. The laying down of the results was effected hy repeating the survey at the Burfftce, commencing at the mouth of the shaft The object of ucfa surveys was merely to determine how near the under- ground workings wcro to the boundary of the concession.

In thf! 17th century, mines were surveyed in this country in somewhat similar manner. Tbomsa Houghton, writing in fihl, describes the method of surveying adopted in the Derby- shire mines, as follows ; — " Having provided yourself of a J}ial in Bijuaro Box, or a lone square Box, which is better ; and also of A Two Foot Rule, and a Btring or Cord with a Plummet at tliB End : first plum tho Shaft; Now suppose you couie to take L<n;,!th forwards into the Drift at the Shaft Foot, having first Mle A Mark there where the Plum fell, let a Boy hold one End

the String therein, and bid another Man take the Plummet, and go as far Lack into the Drift, as he can, till the Plum he hath in his Hand touches the Sidi-; and stretching the String streiglit that it touches no where betwixt that End he holds in Bo Mark, and the Plummet the other Man hath in his Hand, Bf it touchi*s the Bide bid him come nearer) then apply the Dial the Bide of the String, and when the String and Dial lie Bactly streight together, take the Point the Needle stands on, which suppose here to be 44 ; set down the Point, bid him make a mark at the Plunimet; then pull back the String and measure it, which 8u|.ipo8<' here to be 12 rules and 14 inches : Then go to Bke Mark iie hath , hold one End of the String in it, bid Kim go into the Drift with the Plummet as far as he can, ill tbn middle of the String begins to touch the Side; then the String 'ight, observe that it tout lies no where III .i<-m that hold it, apply the Bial to the Side of it, ani} Bk<- ill*- Point the needle Mtands on."

W firoei'ss was th<'U repeated until the end of the level was The lengthn and bearings thus obtained were pegged

pi <turfaoe, and thus a mark was obtained aliovM ground

laucily above that left at the end of the level undergrnund. pVoii itiiist observe," nays Houghton, "that your Rule and t' parallel with the Edge of your Dial, that is, wjually

mi ;nlB ; or rise you will miss in taking the true PoinL

Urouod the Dial is guided by the String; hut above Hround Uir String is guided by the Dial."

Evon in the middle of thn ISth century, dlalUu' iHkA

28 HIKE-aUBYETIIlQ.

nn with appliances of a very primitive character. " The iBstra- tnents used," writes Dr. W. Pryce in 1778, "are, a compau without a gnomon or style, but a, center pin projecting from the middle of the compass to loop a line to, or stick a candle upon, fixed in a box exactly true and level with its surGace, about 6, 8, or 9 inches square, nicely glazed with strong white glass, and a cover suitable to it hung square and level with the upper part of the instrument ; a twenty-four inch gauge or two-foot rule, and a string or small cord with a plummet at the end of it : a little stool, to place the dial horizontally : and pegs and pins of wood, a piece of chalk, and pen, ink, and paper."

The author warns " those who take no account of the points or angles of the compa.s3,|but in lieu thereof, chalk the bearing of the line they measure with, on the board the compass lies in ; for if they are not exceedingly careful and precise in their operations, they may commit almost unpardonable and irretrievable blunders: yet formerly, before penmanship and figures were so generally understood and practised among the common Tinners, as they are at present, moat of our Mines and Adits were dialled for in this manner."

Towards the end of the last century, the dial was fitted with sights, by means of which tha direction of the station-line could be taken with precision.

Description of the Miner's DiaL — In its simplest form, the miner's dial consists of a box of brass or wood, on the base of which is fixed a brass ring divided into 360°. The base of the box within this ring is also graduated, but each division contains 10°, and the numbers proceed from the north and south points to 90° on each side, thus dividing the inner circle into four quadrants of 90* each. On a finely pointed pin 6xed in the centre of the circle, a magnetic-needle is freely suspended, so that when the dial is placed in a horizontal position and the needle unchecked, one end points towards the north. This north-seeking end is distinguished by some mark. The instrument is supplied with a glass cover, and also with a brass lid to protect it when not in use. Perpendicular to the horizontal plane of the instru- ment, are two brass plates, called sights, one at the north, and the other at the south point. These sight vanes are divided into two parts, the upper one on one side having a fine slit cut throughout. The corresponding division of the opposite sight carries a plain wire. In the lower divisions, the relative positions of the slit and wire are changed. The compass-box is attached to a tripod- stand by a socket fitting on to a corresponding plug ; an inter- mediate ball and socket joint furnishing the means of levelling the instrument.

Fig. 9.

Fif 10.

(o.) The Mnetic- Needle. — In ahape, the laagnetic-needle is osnally rhombic (Pig. 8) or rectangular {Fig. 9), or its height may be ereater than its breadth, in which case the edgea are bevelled (Fig. 10). Magnetic-needles of the rhombic form have the advantage of lightness. It ia, however, not advisable to make the „

needle pointed, as it retains its mag- , g. i netism longer when the ends are square. In the form shown in Fig. 9, the points are replaced by a fine etched line, ropreseoting the mag- netic axis.

The needle is drilled through in the centre, and carries above the aperture a hollow brass cap, lined with soma hard stone conically hollowed out. Agate or cameliao is usually employed for the purpose ; but ruby is beat. The cap must be as light as possible, and it must be 6rmly fixed to the needle in such a way that its axis forms a right angle with the axis of the needle. The interior of the cap must be accurately conical. Oaps made of brass, silver, or steel should be avoided, as they cannot be poliished so well as those of agate, and they are very soon bored through by the centre pin. This pin is made of ood steel with a hard, smooth, round point, the angle of which is not too great. The more pointcci the pin and the more obtusely conical the interior of the cap, the less is the friction of the needle on its pivot.

The needle must be made of very hard steel, and bo con- structed that its geometrical centre line passes exactly through the centre of tho cap. It must be sufficiently magnetised, and, when placed on its pivot, must assume a horizontal position. A needle which is horizontal before being magnetised, will dip after having been subjected to that treatment, It is, therefore, necessary to make one end of the needle heavier than the other.

In order to preserve the pin from unnecessary wear, and from being broken off when the instrument is carried, a contrivance is employed for fixing the needle. This consists of a slide, pressed from outside, which raises the needle and presses it against the glass Ud of the dial. When required to be used, the needle should be lowered carefully, go that it gently rests and does not &II upon the centre pin.

Much depends upon the sensitiveness of the needle. A sluggish needle is utterly useless, Tho needle may be tested by bringing a piece of iron near it when at rest, observing whether it returns axactiy to tfs former positiou after lew tjRsJMaiaiwsi'

MtKB-SOHTETIHa.

The test sliould his made at several points round the dial Tho needle should not move when the dial is gently revolved.

All pavts of the dial, with the exception of the magnetic-needle and the centre pin, must be made of metal free from iron or nickel. They may be tested by bringing them near a sensitive magnetic-needle balanced on a centre pin fixed in a piece of wood, and noting whether the needle moves, as each separate portion of the dial is brought near it.

In making a survey with the dial, care must be taken that nothing capable of attracting the needle is carried about the person, such as penknives, keys, steel watch-chains, spectacles, nickel-plated studs, or iron rivets in the magnifier used to read the giuduations. Watches in which the movements are made of nickel, attract the needle almost as much aa when the movements are made of iron. The brims of felt hats are sometimes stiffened by inserting an iron wire round the edge. The surveyor should therefore examine both his watch and his hat before commencing a survey. Sometimes the needle persistently sticks to the under side of the glass. This is caused by the glass becoming electrified from rubbing against the clothes, or from being cleaned with a sLtk handkerclnef. The electricity may be at once removed by touching the glass with the moistened finger or by breathing on the gloss. An unsuspected source of error in roagnetio-needle readings bas recently been discovered to arise from the magni- fying glass used for reading the graduations becoming electrified. The magnifier generally used for that purpose has a hard, highly-polished, black frame, which is peculiarly liaijle to become electrified, even by the mere can-ying in the pocket, so that, when brought near the magnetic-needle, it draws it sometimes as much as half a degree from its true resting place.

In a good dial the centre pin of the needle should be exactly in the centre of the graduated circle, and the needle should be straight. If this is not the case, there will be an error of eccen- tricity in every observation. The conslant eccentricity, when the centre pin and the ends of the needle are not in one vertical plane, and the variable eccentricity, when the centre pin is eccen- tric to the graduated circle, may be detected by the i-eadings at the two ends of the needle not agreeing. In both cAses the error may be corrected by reading both ends of the needle, and by taking the mean of the two results. Oases of irregtdar eccen- tricity are sometimes met with — that is, when the point of suspension of the needle in the cap is variable. Needles pre- senting this error are useless.

(i.) Spirit- LevelB.— On the dial-plate are two small spirit- levels, consisting of glass tubes slightly curved and nearly

levels.

TBB MtKESS DIAL,

filled with Boa\o. limped liquid, & bubble of air being lefb. One

the sinrit-Jevels is parallel to the direction of the sights,

rhilst the other is at right angles to it. They are so aiJjusted

tJint whf n the hobbles are in the centres of the tuboa, the dial

is level.

Spirit-levels are usually filled with alcohol or ether. The bubble, being apecificully lighter than the liquid, always assumes tha hij|;hf>8t possible position ; and if the tube has beeu ground to a perfectly circular longitudinal seotion, the tangent to its ioner surface at th(< centre of the air bubble ia a horizontal line.

(e.) The Tripod. — The dial is usunUy supported on three legs, hod with iron, and conneotd at the top io such a way that they

Fis. lOo.

Fig. 106.

ie in any direction, lightness and rigidity being the leRiriid. Usually the legs are made with a 8rew-joint

33 HtNK-SCKTSTIHa.

in the middle, and a set of extra points ia provided to screw on, when the workings are low. The dial is connected with tte tripod by nieauB of a ball and tocktt joint, which consists of a ball at the end of a covered spindle fitting into a corresponding cavity under the dial-plate. The ball turns in a socket, and can be loosened or tightened at wilL It thus admits of motion in any direction.

In order to ensure accuracy, it is advisable in underground surveys to use three tripods, one for the inatrumeut and the others for the lamp or candle. The latter is fitted in a special holder {Fig. 10a) provided with two spirit-levt-ls, and capable of being levelled by a ball and socket joint and If veiling screwa One of the best forms of tripod is that made by Messrs. K T. Newton (t Son, of Camborne, who employ slotted legs with thumb-screws for tigiitoning them whett any wear takes placa owing to the shriakage of the wood under climatic influences, For surveying over very irregular ground, these tripods (Fig. 106) are provided with sliding adjustable slotted oak legs, a device that greatly economises time in levelling the iost- ment,

(I.) TaJdng TJndergronnd ObservatiouB with the DlaL—Tbu bmring of a line is the angle which it forma with the direction of the magnetic-needle. To take the bearing of any line, set the compass exactly over any point in the line by means of a plumb- line suspended from beneath the centre of the dial ; level the instrument, and direct the sights to an object at the other end of the line. Then measure the line, and note the distance measured in the dialling-book. The needle will thus have been allowed sufficient time to come to rest A second look along the line may now be taken in order to teat the accuracy of tlie observa- tion, the eye being applied to the south sight. The number of degrees to which the north-seeking end of the needle points is then carefully noted. This method of taking an observation with the north sight in advance is that generally employed. The results are called /ore-observations. Sometimes, however, it is desirable to place the eye at the north sight, and look back in a direction contrary to the order of the survey. Observations taken in this way are called baeh-obgenationt. The angle ia read from the north-seeking end of the needle, and eiitcred in the dialling-book as if it had been a fore-observation. This method is employed in dialling a line from the centre of a shaft, where the instrument cannot conveniently be set up. By using the back-observation throughout a survey, taking back-observations and fore-obfifrvations alternately, the instrument is moved only half the number of times it would otherwise be.

THE HIHEb'b dial.

The lettering of the miner's dial did'ere in an import&ut pa,r ticular from that of the mariner's compass or pocket geological compass. When we face the north, the eaat point is on our right hand, and the west on our left, and the graduated card of the mariner's compass is marked accordingly. In the miner's dial, however, the letters representing east and west are transposed. The reason of this will be seen from Fig. 11. Here the dial is represented with the east and west points 'm. their true position. The line of sight in which the observation is taken lies over the north and south line marked N S. This is to be placed in any required direction, and being fixed, the magnetic-needle is found to rest, we will suppose, in the position indi- cated bj the dotted liae A B, the north- seeking end of the needle coming to rest at 24* distant the north and south line. Th reading of this is not N. 24* W,, as might at be supposed, but K. 24° E, The reason is appareat on considering that the needle is the only representative of the magnetic hear- [ing If then a corresponding line D is drawn upon paper, the I end will represent the magnetic north. The line N S coincides with a line in the direction of the roatl to he surveyed, which on the plan will be represented by a line EF paraltel to N S, and this line of direction is clearly seen to be on the east side of tha magnetic meridian, forming with it an angle of 24°

In order to prevent confusion, miner's dials are, as a rule, graduated firom right to left, the east and west points being trans- posed. An illnstiation of the necessity of this change may be afforded by imagining a watch in which the dial-plate moves from left to right, whilst the hand remains immovable. It is evident that the hours must count from right to left for the watch to indicate the right time. Similarly, in the case of the miner's dial, the magnetic-needle always points to the north, and may consequently be compared with the fixed hand of the supposed ii'atch.

In some of the older patterns of miner's dial the tetters are not transposed, the east being on the right and the west on the left. In using a dial of this kind, the letters must be mentally reversed before tha bearing is noted. The best method to adopt for entirely avoiding all confusion is to disregard the lettering of the dial, and read the azimuth or meridian angle, remembering that 90" represents the east, 270" west, and 180° south.

Taking Vertical Angles. — In the old type of Tnm&t'k

UmE-SCBVEYlNO.

brass coyer protecting the glaoa fitted on in one position only. The edge was graduated to 45° on each aide of a zero-point, pin being fixed on tha edge directly opposite that point. The line joining the pin and the zero-point was at right angles to the line of sight. Yertical angles were measured by turning the instrument, by meaos of its ball and socket joint, until it was in a plane at right angles to its proper position for taking horizon- tal angles, the graduation of the cover being at its lower edge, A plumb-line was then suspended from the pin in the upper edge of the cover. This line coincided with the zero of the graduation when the sights were horizontal. On turning them upwards or downwards from that position, the number of degrees indicated by the plumb-line was found to represent the angle of elevation or depression.

Miner's dials are now made with a semicircular vertical arc which may be tixed at pleasure across the central line of the compass. It is provided with a movable Umb carrying a hori- zontal bar with a pair of sights. The semioircle is, as a rule, divided into single degrees, marked from 0° in the centre to 90 on the horizontal line on each side. Frequently a long spirit- level is fastened to the bar of which the sights are part. The sights are directed to the object, of which the bearing is required, and inclined the requisite amount. The horizontal and vertical angles can then be read.

This vertical arc is in general use in metalliferous mines. In collieries where the vertical angles required to be measured are never excessive, a tide arc is usually employed. This hits the advantage of leaving the &ce of the dial quite free. Fig. 12 illus- trates the best form of side arc In the dial here shown the sights are carried by an outer ring concentric with the dial. This arc was invented in 1S50 by John Hedley, H,M. Inspector of Mines.

The side arc with sights attached to it should be avoided. If the sights are directed to the forward or back object when taking a vertical angle, the bearing will be incorrect, as the deviation from the true line on looking through the side-sights amounts to half the diameter of the dial — that is, the distance from the centre of the dial to the line of sight

Eeephig the Dialling-Book - The survey is noted in the follo' ing manner : —

Fig, 12.

low

M

Work And Rest Mime.— Adit Level.

Wtam peruendicnlar line in engine abaft 3/- W, and 2 N, of centre, Shaft (90°) 14 by 7.

Kn.

BxASiyo.

DiSTAVCK.

Oftaiffe.

Bnjsii.

A

359' 46

fnu. n. iBi.

B. 2/-

3/-

B

3*6' 00

3/6

2/8

332" 21

2/-

3/-

N. 2/8 s. a/-

D

275° 03

4/-

6/-

E

254* oe

3 6

6/6

8/-

r

£92° 15

4/2

e/-

1S4*00

3/.

3/-

G

272' 00

3/9

3/9

H

264' 06

2/6

2/-

K

232° 00 232*00

3 6 S

2/. 2/6

2/6

2/a

Pe and nail, K. wall,

2/- N. of J,

Bnd.

The above are the notes of the aarvey of the adit level of a mpposed metalliferous miae the name of which was suggested by Mr. J. Henderaon, M.InstO.E., as showing the intermittent nature of many metalliferous mines, which are so frequently abandoned when the metal falls in price, and re-opened in better times.

The survey is made in the adit level, and starts from a per- pendicular line in the vertical engine shaft, which is rectangular io section, 14 feet long by 7 feet wide. The dial is set up at A, and a back-observation is taken to the perpendicular line, the observer looking through the north sight of the Lnstrumcnt, The bearing indicated by the northseeking end of the needle ia read and entered aa the first bearing. It will be found advisable to write the degrees and minutes as if the latter were decimals ; in this way any confusion between such numbers as 30' and 3' ia avoided. The length of the atation-line is measured, and the result, 12 fathoms 2 feet 6 inches, entered in the distance column. The best form of book to use is an ordinary account-book, tha £, 8., and d. coJiimna servings for fathoms, teet, and mcVftft.

MIKK-BDRVBTlKa.

la plans of metallileroua mines, it ia highly desirable to repr ent the variable width of the level after the ore has been extracted, ao as to clearly indicate the poBition of the various courses! of ore. Offsets should therefore be taken at the end of each atation-liiie at right angles to it. They are measured in feet and inches, and, in order to necessitate as little writing as possible — an important matter in a wet mine — may be written In a way similar to the abbreviated mode of writing shillings and pence.

At the survey line leaves the croaa-out driven from the shaft to the lode, and continues on the lode. As there is a sharp turn at thi.s point, oll'seta are oieasured to the north and south, as well as to the right and left. At F a cross-cut driven south of the lode. The dial being set up at F, aa observation is taken to a candle at the end of the oroas-cnt. The bearing is then read, and the distance, 1 2 fathoms, measured. This line is a branch from the main survey line, and is dis- tinguished by a small figure 2 attached to the letter that would have been assigned to the station had it belonged to the main line. With the dial stUl at F, an observation is next taken to G, and the survey continued as before. At K, the end, or/or*- breast, is reached, and a permanent mark has to be left, from which tho survey may be continued at a future date. The mark should not be placed at the end, where it is liable to be shattered in the next blasting operation. The usual practice is to measure a fathom liack along the line of sight, and to insert a peg and nail in the wall of the level, carefully noting its position for future reference.

The offsets to the walls of the level are sometimes omitted, the level being shown in the plan as a double coloured line. In this case, care must bo taken to keep the line of sight exactly in the middle of the level ; otherwise an incorrect representation of the workings will result

(2.) Snrface-Sunreya with the Miner's Dial.— For making the Burfaoe-aurvey of a miue-royalty, the dial may be used in the game manner as it is underground. There is, however, tho advantage that opportunities frequently occur of checking the work during its progress by means of tie-lines.

The manner in which the results should be entered in the field-book may be seen from the accompanying record of a survey of a four-sided field connected with the shaft of a mine.

The measurements in this survey are made in links. The dial was placed at A, and, when the instrument had been carefully levelled, the sights were turned in thf direction of the shaft. An assistant having by this time placed a staff at the

Tee Miners Dial.

Field Record Of Survey.

A

S12

fiT

lio

V_L

10

s

lie* 00-

©

12

11 )

17 /

220° 00"

©

M

17

23 /

asfi" 18'

©

2,

B

35

27 /

30° 00"

aao

©A

1,

Shaft to A

O

ir as-

centre of the shaft, the sights were turned until the vertical hair of the back-sight exactly cut the staff. This being a - observation, the observer looked through the sight at the north end of the dial. When the needle bad settled, the bearing indicated by its north-aeeking end was rad, and entered as 13* 33' in the field-book. The distance &om the shaft to A, 630 links, was then measured, and noted. The sights were then directed to a statf held at B. This was a fore-observation, and therefore the observer looked through the sight at the south side of the dial, turning the instrument until the vertical hair of the fore-sight exactly cut the staff. The needle was thou read, and the be-aring, 30' 00', entered in the field-book. The distance from A to B, 496 links, was measured, and offsets taken at the bends in the hedge along that line. The instru- ment was then removed to 0, and o back-observation taken to the staff still standing at B. This gave the bearing of Une No. 3, 285° 1 8'. Line No. 4 weis a fore-observation from to D. In order to obtain the bearing of line No. 5, the instrument was centred over the point at D, where the staff stood, and a fore-observation taken to a staff held at the original station A. In this way, by going round the boundaries, the outline of the field is obtained. In extensive surveys, this would not be suffi- cient ; a number of tie-lines would have to be measured in order to check the survey during its progress.

In the field-book, the date of the survey should be inserted, all the atation-lines should be numbered, and the bookiag should begin at the last line of the page, and be written upwards. In this way, the notes follow the direction of the survey and offsets to the right or left are noted on the corresponding side of the page. All objects, whether hedges, houses, or ponds, or what- ever offsets have been taken to, may thus be sketched in with facility. The notes should be kept so clearly and accurately that if necessary the survey may be plotted after the lapse of years, without trusting to the surveyor's memory for its details.

{3.) Colliery Sorreys with the Miner's Dial. — In surveying a colliery where safety-lamps are used, the surveyor must provide himself with a safety-lamp made of copper or brass, entirely free from iron, for reading the magnetic-needle. The method of con- ducting the survey is essentially the same as that adopted at the surface. Instead of the staves used in the surface-survey, lights must of course be used as signals.

The usual method of surveying a colliery is to start from the centre of the shaft and continue along one of the levels to the face, thence through the workings to the other face, and finally back tfi the starting point at the centre of the shaft. For all

A

THE miner's dial.

other ro&da that require to be surveyed, marks are left to retnm to. Id this way tie- lines are obtained, which are of great value in checking the accuracy of the survey. The size and direction of til faults must be carefully noted in the aurvey-book.

A GolUery survey, when no offsets are taken, may be booked in the way shown in the following example : —

gUtiao-LUw.

IHrtinu.

ClUlDi.

MtTDcUc anr\i)t.

Inellnitlon, DnMsadlng.

Shaft to A

4-5S

98° 25'

0°00'

Ab

S65

176° 00'

Bc

178° 13'

ir 15'

Cd

7 '58

2S6°67'

©"Oo'

De

88*

27r53'

o-w

Ef

B°08'

7*15'

Fg

14'4fi

r08'

6° 45'

Oh

78° 43'

O°0O'

When offsets are taken, it is best to l>egin booking at the bottom of the page and write upwards as in the example of a surface-survey. Except against ribs and in main gateroads, off- sets are seldom taken in a coal-mine, since the position of the face has probably changed before the surveyor reaches the anr- face. In the method of booking generally adopted, both bearings and distances are entered in the ruled column, and the line drawn across the page at the end of each draft, as shown in the preceding field-record, is always omitlod.

The accuracy of a closed survey made with the magnetic needle may be tested by reducing the observed bearings to included angles. To do this, from the fore-bearing, increased by 180', the back-beai-ing is subtracted, the difference being the included angle between the two lines. The sum of the included angles should, with four right angles, be equal to twice as many ight angles as the polygon has sides.

4l>

HtNB-BURTEYlKO

OHAPTEE IT. The Vabiatioh of tbb Magnetto-.

DeflnitioEB. — A magnetic- needle when suspended hnda its posi- tion of rest in a line joining two fixed points on the horizon. At certain places on the earth's surface, these points correspond with the north and south points of the horizon ; but, as a rule, though near, they do not coincide with these. A vertical plane passing through the points on the horizon indicated by the needle, is called the magTielic meridian, in the game way as a similar plana possiug through the north and south poles is known as the trui wteridicm of the place. The angle formed by the magnetic and true meridians is termed the deelination or variation of the needle.

A knowledge of the declination is of the utmost importance in preparing mine plans, as this does not remain constant in the same place, but is subject to continual, though slight, variations. These variations are either regular or irregular. Under regular varia- tions are included necular and diunial variations.

(a.) Secular Variations. — Obsprvations of the amount and direction of those variations have been made in all parts of the world. The first observation appears to have been made in Paris in the year 1541. The declination of the needle was at that date easterly, and amounted to 7°. In 1550 it was 8°, wkUst in 1580 it amounted to 11° 30'. Thus, between the years 1641 and 1580 the magnetic meridian veered 4° 30' further towards the east. From 1580 the declination decreased, the magnetic meridian moving towards the west, until in lOGG there was no variation; the n)ajj;netic and true meridians coinciding. Ever since that date, the variation has been westerly, attaining its maximum of 22' in 1 820, and then gradually decreasing, so that the magnetic meri- dian is now gradually approaching the true meridian.

The magnetic history of Paris does not apply to London ; every place, as far as has been ascertained, has a magnetic history of its own. The following table shows the change in the position of the magnetic-needle near London from the earUest observations up to the present time : —

TBE VARIATION OF THX MAONETtC-ltBEOLE

Tm*.

DMlinttion Wta.

Dmte.

DsoIImUud Wot.

iri5' E

24° 36'

20° 10

6" 00' E

24° 38'

20° 00'

4'06'E

24° 36'

19° 58

O'Cio'

ir52'

]"2i'Vf

1S5S

21° 54'

19* 41'

2*30' W

21° 47'

ir 32'

itisra

00' w

21° 40'

19° 22'

14* ir w

21° 32'

19" U'

17' 40' W

21*23'

19°06'

31* Off W

21* 13'

18* 57'

17S7

23* 19' W

21° 03

18" 50'

23" 57' W

20° 59'

18° 45'

1S02

24* 06' W

20° 51'

Is" 40'

20° 40'

18*33'

24* 15' W

20' 33'

18° 25'

24* 22' W

20° 26'

16° 52'

24° 28' W

20° 19'

16' 37'

From this table it appears that the magnetio-needle has required 300 years (1S8O-1880) to move an arc of 11° 15' + 24° 3S' + (24* 38' - 18* 68') 41° 33'. The average annual movmeiiL waa consequently From 1881 to 1900 the avtrage annual move- ment was lesB than 6'. The figures given in the table from 1858 are the mean values of the magnetic declination as determined at

At Newcastle and Swansea the declination is about 1° 45' greater than at London ; ut Liverpool 2°, at EJinbuigii 3', and at Glasgow and Dublin about 3° 50' greater. At Yarmouth and Dover the declination is about 40' less tliau at London.

The mean value of the magnetic declination for any particular place in Great Britain, at which no magnetic oljsecvationa are made, can generally only be inferred from iVie ma.' ewtfti. va.

k.

1872 by Sir F. J. Evaiia. This is given in the PhilotojJtieal 7'rangaetions, 1872, vol. 162. Allowance initst be made for the change which has since occurred. A similar map of Blngland and Walea is published every year by tLe Colliery Guardian.

lu certain parts of the earth, the magnetic and true meridians coincide. The irregularly curved imaginary line joining the points where there is no declination is called the agonie Une. Such a line cuts the east of South America and, passing easi of the West Indies, crosses the XTaited States, passing just exist of Charleston, South Oaroiina, and just west of Detroit, Michigan. It then passes through the North Pole, crosses Laplaud to tbe Caspian, cuts the east of Arabia, and passes through Western Australia to the South Pole.

Itogonic lines are imaginary lines joining the places on the earth's surface wboae declinations are equal at any given timei Maps on which such isogouic lines are shown are called dtdina- tion maps, and a comparison of these in various years shows the variation to which the declination is subject.

The great variation in the declination shows the necessity of recording the date and declination of the needle on all mine- plans, with a note stating whether the bearings given were magnetic bearings, or were reduced to the angleB, which the Unei would form with the true meridian.

The antiquity of the workings on an old undated plan may be approximately ascertained from the meridian line shown on it. Thus, if a plan is found to be constructed to a meridian with a declination of 24* 0' west, it is reasonable to suppose that it was drawn about the year 1800, for, according to the table, the declination in 1802 was 24° 6' west

(b). Diurnal VariatioiL — On observing a magnetic-needle throughout an entire day, it will be found that the variation does not remain constant, but changes more, and in a different way, than is demanded by the secular change. Observations at London show that at about 8 a.m. the needle reaches its furthest point east, and that at 1 p.m. it shows the greatest westerly dexriation from the mean magnetic meridian. The declination then decreases until 10 p.m., when it remains stationary until 4 a.m. It then decreases again until 8 a.m., by which time it has again reached its furthest point east. The needle stands at its mean position a little after 10 a. m., and a little before 7 p.m. The diurnal changes are much the same over the whole of the northern hemispbere, though the amount differs.

The following table shows the diurnal variation for London (Kew), Trevandrum, in Madras, and Hobart Town, in Tasmania Of these places, the first is a station in middle latitude (northern

r '

Diurkal Tartation.

it

Boin.

Itasonii.

TuTiiiDXIia.

HauiT Towi.

Hlmtla.

Hlnnte:.

UlUtltH.

+ 1-35

1 p.m.

-6'19

-0'45

+ 350

2 p. m.

+ 4-66

3 p.m.

-4-2S

+ 013

+ 4-40

4 f.m.

+ 0-28

+ 3-35

6 p.m.

+ 24

+ 2-00

6p.li].

+ 0-13

+ 1-15

7p.m

+ 22

+ 0-04

+ 0-50

8 p.m.

+ 0-6S

+O0O

9 p.m.

+ 0-99

10 p.m.

+ 1*24

-O'OtS

11 p. m.

+ 137

+ 0-01

12p.ro.

+ 1-43

+ U-09

+ 1-29

+ 013

2 a.m.

+ 1'39

+0'15

3 A.m.

+ r51

+ 0-09

4 a,m.

+ 1-88

+ 0'02

5 a.m.

+ 2-51

S&.tri,

+ 3-07

+ 018

7 a.m.

+ 3-58

+ 0-32

8 a.m.

+ 3-80

+ 0-24

9s.m.

+ 2 '95

+o-m

10 a. m.

+ 0'4(i

-0'22

-O'M

-I'lS

,

i tliln table defleotioDa towards the mairtietio are cticnu towmrdt tnagnetio wett negative.

reckoned pcuitiva,

44 UINE-SURTETnte.

hemisphere), the second is an equatorial station, and the third n itauon in middle latitude (southern hemiBpliere).

The diurnal variations are found to vary with the seasoaj of the year. They are much greater in summer than in winter. The cause of the variations is frequently ascribed to the influence of sunlight. Other influences appear to he at work, aa is abown by the fact that the variations of the declination of a magnetic- needle at a place on the earth's surface coincide with the varia- tions observed aimultaneoualy underground. This was found to be the Ciisie at a magnetic observatory established, at a depth of 3,280 feet below the aurfiice, at Przibram in Bohemia. Similar results were obtained in 1905 at the Tamarack copper mine, Lake Superior, the deepest mine in the world, at a point 4,760 feet bi'Iow the surface. The slightest movements of the magnetic-needle observed at the earth's surface occur at tie same time and to the same extent even at the greatest depths to which roiuiny i.s ahle to [lenetrate.

Irregular VariationB. — The magnetic-needle is subject to violent and irregular disturbances, which are sometimes considerable, amounting in extreme coses to 1 or 2 degrees. These irregular disturbances or inagnetie ttormi appear to be coincident with the appearance of the aurora borealis, earthquakes, and volcanic eruptions. The cause of these storms haa not yet been deter- mined. Sabine, liowever, found that they are most frequent every eleven years when the spots on the sun are moat numerous. Experience shows that places of the same longitude have similar disturbances at the same time, that those on opposite sides of the globe diflering by 180° of longitude, have disturbances equal in amount but opposite in direction, and that places situated 90* west or east of the disturbed regions have practically no dis- turbance. Atmospheric storma have no effect on the needle.

Notices of the occurrence of magnetic storms are pubEshed by the Superintendent of the Magnetic Department at Greenwich in the mining journals, and deserve the careful attention of mine- surveyors.

Determiitatioii of the True Meridian— In order to find out the extent of the declination of a magnetic-needle, it is necessary to determine the true meridian. For this purpose various methodi are employed.

1, Method of Shadows.— This method is based on the &ct that, at equal distances of its passage across the meridian, the sun is at pijual altitudes above the horizon. Consequently at these times it gives shadows of equal lengths.

A staflfis planted vertically in the ground, and the ends of its ahadowB are joined when they are of equal length. On joining

THE VABtATION OF THE KAGSBTIO-NEEDLK.

4fi

these points to the projection of the axis of the stalf, an auglo ii obtained, the bisectrix of which is the true meridian. The obser- J vation may be made nion? accurately by deaoribing a number of ' conoeutrio circles (Fig. 13) with the foot of the staff as centre,

Rg. 13.

uid marking the points, o, 6, c, d, d', J', where each of them is touched by the shadow. Tha arcs thus obtainett are bisected, and the points of bisection are joined to the centre of the circle. The line ni m thus obtained is the mtridiaa. This method, though a fair approximation, is absolutely correct only at the time of the solstices (June 21, December 22). It is tlie oldest method known ; it was used by the early Ohriitians for determining the east for their churches.

The method is considirably improved by placing a thin metal plate provided with a small aperture, at the top of the staff. The

I latter is inclined so that the aperture is

--v perpendicularly above the centre of the

Nj\. concentric circle* In the shadow of the

metal plate, a bright spot appears, the

I centre of which can be found with coii-

I siderable accuracy. This method has been

I used on a large scale by placing perforated

— t- metal plates in the roofs of high buildings,

a notable example being in the dome of

Ppj-_ 14 The shadow method may be applied on

a small scale by employing a vertical pin >]aced in the centre of a number of concentric circles on a drawing- >oa7d. A mole convenient apparatus may be made of a brass rod about 7 inches in length, provided at its lower end with a screw and at the top with a very ihiu plate of brass about 2 inches

4S

MtNK-SUBVKTlNO.

Irng and H inch broad, so arranged that it forms with the pin ao angle of about 120°. In the middle of the plate b, fine hole ii drilled. The pin being screwed into a board, half an inch square, near the edge, a portable inatrument. Fig, 14, termed a , is formed. This can be placed on a table or drawing-board in the open air, and used in the manner described,

2. Method of Correspoading Altitudes.— If a good theodolite (see Chapter VIII.) is available, the meridian of a place may be determined in the following manner : — The theodolite, after careful adjustment, is Eet up at the point, the meridian of which is to be determined, a station commanding a free view being selected. Vernier I, of the thecwiolite is then brought to zero, and the position of vernier II. observed. The limb is then turned borizontallj, and the telescope moved vertically until it is brought to ber upon a fixed Etar of the first or second magnitude several hours before its culmination. As soon as the star passes the cross-wires of the telescope, the latter is clamped, and both the horizontal and vertical circles of the instrument are read. The telescope Is then allowed to remain with its inclination unchanged, and after a time the star will not be visible through it. After its culmination, the star will, in the course of time, have the same altitude that it had at the first reading. The star is followed with the telescope, and at the instant it crosses the wires of the latter, the horizontal circle is read a second time.

Assuming that at the second reading the telescope had the same inclination that it had during the first reading, the direc- tion of the meridian will be represented by half the sum of the two readings on the horizontal circle. The limb being turned horizontally until vernier I. gives the calculated angle, the axis of the telescope will give the direction of the meridian. The method is baaed upon the fact that a star at equal altitudes above the horizon of a place is equally distant from the plane of its meridian.

It is evident that the accuracy of the result depends upon the perfection of the instrument employed. The best results are always obtained by observing the star at various altitudes before and after its culmination, and by reading the horizontal circle each time with the telescope clamped at the corresponding altitude. Both verniers should always be read, and the arith- metical mean of the readings taken If they arc not identical. The direction of the meridian is thus obtained repeatedly, and if there Is no error, the result will be the same with each inclina- tion of the telescope. If the results differ slightly from one nnother, the mean must be taken ; with larger differences, the oY" '---ns must be reoeated. As a check, the observations

THE TARIATIOK or THE HAaNXTIC-KEEDLB.

should repc:\ted on the following night with the telescope inverted. The result should not differ from that obtained on the previous night. If there is a alight difi'erence, the mean of the reanlt of the obsrvation8 on the two nights will give the direc- tion of the meridian.

As an example of tbia method of dcterminlag the meridian, Boue of the observations may be given which were made for fixing the meridian for the magnetic observatory belonging to the OUustiial mines. The determination was eDectcd with an 8'inoh thoodolite. The instrument was set up on a atone foun- dation, and accurately levelled. The vernier I. was brought to zero, and the position of vernier II. noted. With the upper plate clamped in this way, the telescope was brought to bear on A signal on the top of the tower of Olausthal Church. The following observations were then made with the stars S and y Virginis : —

KUfilJTOi 0:r TBI llDKIIOSTlL ClftCUL

AwwiS OP TBft BT4.

or TBI Tw

VlLKtUA.

AHaLl 70UIRII KT TBI DtlAITTmjr or

Alter the OoJiulnAUoD'

VirgiaU)

18* W

66* 16' 37'

196*22 W

IZe* 18' 61'

ir*)'

W 15' 12*

Ih' 22' 43-

12e° 18' 68'

sroo-

00* 18' 62*

182° Is' 30'

9V-i0f

81* 21' 42*

191* 16' 80'

ise'is-ar

22* ac

2' 2a 5-'

1&0*11'4S'

12C 18' 61'

J6*20'

6r40'32'

194* fir' 26'

126* 18' 68*

16" -to'

192' 67' 55'

120* 18' 69'

jrao'

191* 66' 15'

126* 19' or

isew

81* 43' 57'

190" 53' 65'

126* 18' 56"

18-40'

mr 47' 07'

189* 50' 06'

126* Is' .16'

4S HINE-SURVETtN8,

The sero of the horizoatal oirole represented the direction ol

Olftnathal Church. The arithmetical mean of the results shows that the ineridiau formed an angle of 126° 18' 51" with the direction of Clausthal Church. Obserratioos made the next night gave exactly the same results. The same number of obser- vations were made on the two following nights with the telescope inverted. The mean of all the results obtained during the four nights gave 126° 18' 49". It must he noted that in these obser- vations the stars employed were not first sighted and the angle of altitude then read. The vertical circle was clamped at a given division, and the star then brought on to the vertical wire of the telescope, and followed by means of the tangent screw of the upper plate until it also paasod the horizontal wire.

If the theodolite is set up on a fixed point, and if the terres- I trial object, the azimuth of which is determined, is also a secure point, a further raarking-out of the meridian is not absolutely necessary. In the preceding case, however, it was thought advisable to mark out the meridian by means of a large square atone buried io the earth on a mountain in the vicinity. A hole drilled in this stone accurately in the meridian served for the reception of a figual Hta£P.

The meridian may be determined during the daytime bj sighting the upper edge of the sun before and after mid-day, a dark glass being placed before the objective of the telescope. A correction has, however, to be made on account of the obliquity of the ecliptic — a correction that is not taken into account in the shadow method. This method of determining the meridian is not to be recommended, as the astronomical almanacks required for making the correction are not always available. The croes- wires, too, may be directed to a star with far greater precision than to the sun.

3. Detennination of the Meridian by Means of the Fole-Star.—. Of the bright stars of the northern heavens, the nearest to the pole is the first star in the tail of the Little Bear, or the Pole- star (a Ursse Minoris). It is a star of the second magnitude, and may easily be found by imagining a straight line to be drawn through the stars $ and a of the Great Bear, and continued for about five times the distance from to counting from a. These two stars are known aa the pointers.

The meridian may be determined by observing the pole-star either when it is in the meridian, or when it is at its ex- treme elongation. The pole-star is not situated exactly al the north pole of the heavens, but is now about 1' 12' from it. Twice in each sidereal day (23 hours 56 minutes) it ia in th* meridian.

TBK TJIRtATIOir Or THE MAGKBTIC-NKEDLE

A very simple metliod of dutermmin the meridian of a plaoe onaists in sigfiting the pok'-star, marked A in Fig. lo, wbea it appears ia the same vertical line with the star AHoth in the Great Bear (i Ursje Majoris). This vamy be done bj watching for the moment, when a. suspended plumb-line will cover hotli atara. They will then be sjiproKimately in the ineritlian. The pole-star is exactly in the meridian about 29 minutes after it haa been in the same vertical plane hb Aliotb. lu tlie southern hemisphere a similar process may be applied to the stars a' Crucis and Hydri.

The meridian may also be determined by ob- erving the pole- at its extreme elongaiiou, tbat ia, when it is at its greatest apparent angular distance east or west of the pole. At this instant, the horizontal projection of ifae apparent movement of the star alters its direction, and the motion of the star appears to cease for a short time. The greatest and least horizontal angles made by the pole-star with any given line when the star ia at the greatest distances cast and west of the pole, are observed and the mean of the angles taken. This will be the angle made by the given line with the meridian. This method is rarely practicable with an ordinary theodolite, us one of the observations must generally be madt' bv dtiylight.

4. Determination of the Heridian oy means ot a Map For

an approximative determination of the meridian, a large-scale map may be employed. The direction of the meridian is hown by joining the degrees of longitude marked at thi top and bottom of the map. The angle formed by the meridian and some line easy to determine on the ground, is measured on the map. With the aid of this lino, the angle ia marked otf on the ground. The approximation thus obtained is at most 1 5 minutes.

Setting-out the Meridian Line. — In every mining district it is very desirable that aU difficulty in ascertaining the true meridian should be at once removed by the erection of two conspicuous objects placed exactly on a meridian line, to remain for per- manent reference. T. Sop with, writing in 1822, urged that it would be a work of enormous advantage to the prosperity of mining districts to have meridian lines carefuOy set-out at distances of 1 mile from each other, and tall posts placed on these meridian lines at every mile in length, the undulating sur- fe,ce of the country being truly reduced to a horizontal base,

A method of eoadnoting daylight obaervations U desQribe4\i-j ',Q, OwuM, /isr. and Miu. J., vol. Iixv., 1903, p. 84.

I Owrau

MINE-SUBVEYIKa

BO tliat these poets ov stations should indicate squares of exactly I sijuare mile.

The best method of itemianently marking out the tueridian is to iuBert, to a depth of 3 to 5 feut in ilie ground, a liitrd etone, 6 to 8 feet long and 2 feet square. The portion of the stone pro- jecting from the ground is faced, and the top plane is made at right anglei; to the axiK. To avoid as much as possible the action of frost, it is udviealile to give the stone a good foundation and to iix it in cement. On the top of the stone a brass plat, a foot square, is fastened, so that it is exactly horizontBl, and on this the dirt'ctioD of the meridian Htte is shown hy a fine line.

When the direction of the meridian is to be shown by two stones a distance apart, points must be marked on them exactly in the meridian. For this purpose, it is best to drill holes into which staves can be inserted

For practical purposes, a simple method of ascertaining the annual variation is to take the bearing of some remote permanent object, such as a church steeple, from a fixed point. The bearing of this so-called line of orientation is recorded iroro year to year, the difference in the readings giving the annual variation.

This line is also of great value if several dials are used in the same mine. In consequence of small errors in the construction of the instruments, the bearing of one and the same line is found to vary when determined with different dials. By observing the line of orientation, the error of each dial may he determined, and applied as a constant correction to all subsequent readings.

Inclination of we Magnetic-Needle. — If a magnetic-needle is free to move vertically, it does not, at most places on the eartli'a surface, rest in a horizontal position, but inclines more or less from it. llie angle between the needle and the horizontal line is called the dip or mc/inatvm of the needle, provided that the vertical plane in which the needle moves is the magnetic meri- dian of the place. Tlie dip varies at different places ; at the magnetic equator there is no dip, whilst at the magnetic poles the needle stands vertically.

The dip is not of great importance to mine-surveyors in Britain, as the needles of dials are carefully compensated when sold. Surveyors going abroad with an English dial should be provided with a Binkll sliding balance for the needle, which may be adjusted when necessary, should the dip prove troublesome.

Like the niagnetii.- declination, tbe dip is subject to secular variations. Tbe following are results of observations near London extending over a series of years : —

d

Tee Tabiatiqn Of The Uagnktic-Mkecle,

tuclliiitlun.

Ysar.

lucUiiatluu,

71" off

ar 35'

72" Off

e7'34'

74° 42*

18S2

67 34'

70° 35'

67' 31'

H9° 38'

67° 30'

68° 48'

67° 27'

es' W

i8se

67"' 27'

Secent Magnetic Observations. — The following are the valu(8 of tlie TOrtguetic elenienta observed at Greenwidi cluriDg receut

Ymt,

18Si 1S92 1Ss6 189§

UetB Decllnitian weit.

17' 34 y

17° 28 -6' 17° 23 4' 17° 17'4' 17" 11-4' 17* 4-6' 16' 57-0' 16° 520' 16* 39 fl' 16° 24,-'2' 16° 29-0' 16°26-0' 16" 22-8'

16* 19 r

16* 15ff

Mmo iDdloatloo.

67-24-9'

67° aay

6r2l-4' 67* 19 S' 67° 17-8' 87° 17 '3' 07° 14-7' 87° 16 -ff 67° I3ff 67° 12-ff 67° lO-S- 67' 8-6' 67" 8-1' 67* 3-4'

er 0-9'

86° 57 2'

W S3

m If K-SURV EYING.

Dr. C. Cree, Snperinteadent of the Kew Obsenratory, hu 1

published the following summary of recent values of declinA-

ion at the principal magnetic observatories of the world : —

Litituds.

LoDgtttide,

Pawlowsk, .

Br 41' N.

30° 29' E.

0*41'9'E.

Katheriiimliurg, .

56" 49* N.

60° 3S' E.

Jo' 8 6' E.

Copenhagen, .

65" 41' K.

12° 34' E,

10°12'2'W,

StonyhuraL, .

63" sr N.

2° 28' W.

18° 4-3'W.

53° 34' N.

nr 3'E.

11° 18 -6' W.

WilhelniplmveT],

53° 32' N,

8° 9'E.

12° 21 2' W.

Poiadam,

52° 23' N.

I.V 4'E.

9°56-3'W.

Irkutsk,

52° 16' N.

104' J6' E.

2" 0-8' E.

Utrecht,

52° 5' N.

5° 11' E.

13' 46-2' W.

Valencia (Irpland),

fll* 5fl' N.

10° 15' W.

21° 18-7' W.

Eew

sr 28' N.

0° 19' W.

I6°40-5'W.

Greenwich. .

51° 28' N.

0° 0'

16'22-8'W.

Bruasula,

54)° 4S' N.

4° 21' E.

14' 8-3' W.

Falmouth, .

50° 9' N.

6° 5'W.

18" 18-3' W.

Prague, . ,

14° 25' E.

8°67-6'W.

Jersey, . , , .

49° )i2' N.

2° 5'W.

16° 50-4' W.

Paris, . . , .

4S° 48' N.

2° 29' E.

14' 49-6' W.

Vienna, .

48= 15' N.

16° 21' E.

8°24 1'W.

Munich,

48° 9' N.

1 1" 37' E.

10° 27 -9' W.

Budapest,

iV 63' N.

18* 12* E.

ru'Cw.

Odessa,,

46* 26' N.

W 46' E.

4° 36-7' W.

PoU

44° 52' N.

15° 51' E.

9°15 1'\V,

Nice,

43° 43' N.

7° 16' E.

12° 40' W.

Toronto,

i.V 47' N.

79° 18'W.

5°2S'8'W.

Perpiunan, ,

4'2° 42' N.

2° 53' E.

13* 37-3' W.

Tiflis

41' 43' N.

44° 48' E.

2° 6-6' E.

HaplcB

40° 52" N,

14° 15' E,

5-7' W.

Madrid.

40" 25' N.

3° 40' W.

1S99

1B*48-4'W.

Ooimbra,

40° 12' N.

r 26' w.

17" 93' W.

Lisbon,. . ,

38° 43' N.

fl* B'W.

17' 18-0' W.

Tokio,

36° 41' N.

13S° 45' E.

4° 29-9' W.

Zi-ka-wei, .

31° 12' N.

121° 26' E,

2°247'W.

Havana, . ,

23° 8' N.

82* 2S' W.

r 7-4' E.

Hons Kong, . . Bombay,

22° 18' N.

114* 10" E.

Ciso'E.

18° 64' N.

72* 49' E.

ClOS'E.

Manila,

14' 35' N,

120° 69' E.

0°52-2'E.

Batavia, . .

6° 11' S,

lOe* 49' E.

r 14-9' E.

Mauritius, ,

20° 6' S.

67' 33' E.

Imo

9° 29-0' W.

Rio do JiiDBiro, .

22" 55' 8.

43° 11' W.

S'HirW.

UelbouiTie, .

37° 50' S.

144° 58' E.

8°ao-7'E.

In the years 1884

to 1888 I

)r. T. E. Thorpe and Sir A

W, Rilcker made mag

netic obaer

vations at 205 places in the

United Eingdoin. Tfa

e work was

subsequently extended, and

siaU Laboralt

try Seport 1904. p. 44.

the magnetic cotistftnta have now been determined at 862 places in Great Britaio and Ireland. The results have been published by Sir A, Eiicker,* who gives n map showing the true lines of ecual declinations for Januarj Ist, 1891. By means of the table of secular change it will be possible to determine the value of the decimation at any place in the United Kingdom for some y>'arB to come.

The neglect of the secular variation of the magnetic-need Is resulted in a sad catastrophe at Wheal Owles in Oornwall, where, on January 10th, 1893, an irruption of water from an abandoned portion of the workings led to the loss of twenty lives. According to Mr. J. HendBr5on,t this catSiStrophe was found on investigation to have been due to ignorance of the lecalar variation, as in the plan of the underground workings,

I periodically kept up to date with care, the same magnetic meridian was used for a period of forty years. Thus, the levels of some extensive old workings full of water were holed at a point where the plan showed a safe barrier of solid ground.

Considerable attention has been devoted on the Continent to the variation of the needle, and magnetic obaervatories have been erected in most of the mining districts At Beuthen, in Upper Silesia, for example, a photographic recording declino- Meter has been installed. The records are copied every five ™ days at the Breslau Mining Office, and issued to all the mine- surveyors of the district, A similar instrument has been in operation at Bochum, in Westphalia, since 1895, and Mr. Lenz lias published a record of the readings for every hour of the day and night during 1905. The maximum amplitude, or differfince between the highest and lowest readings, during the year was 43'1 uiinutes on November 12th, and the least amplitude was 3'5 minutes on December 16tb.

Mr. H. Qannettg has collected all the data available regarding magnetic declination in the United States, wiih a view to meet the needs oi those who have occasion to use the magnetic-needle in surveying, or have to deal with surveys that have been run with the needle in past times. The results are presented in the foini of tables, showing the approximate reduction to the year 1900, the declination being given in the tables by counties, cities, aud towns. Tables of magnetic declination in the United States for 19Ui have been drawn up for the Coast and Geodetio Burvey by Mr. L, A. Bauer.

Tram. Fed. Irut. J/.B., vol. ix., 1895, p, 417.

ilbid., vol. viii., IS95, p. 273.

tQiaehttij; vol. xlii,, 1906, p. 28*.

S UjiiUd atatta Geolo</kal Swity, Stciiiitinlh Aimval Btfiort, 1S9U, 201.

Chapter V.

SuBTBTrNO WITH THE MAaNBTIO-NKKDLB IN THK PREBBNOB OF IrON.

Influence of Iron RailB. — The method of Burrejiiig described in the preceding chapter cannot be used in mines where m;iietio substances deflect the needle. On account of the increasing usa of iron and steel in mines in the form of roils, props, &c., ths number of mines in which the magnetic-needle is not affected it extremely small.

Rails placed end to end on the ground become, in the course of time, permanently magnetised, and if a magnetic-needle is brought near the junction of two rails, it assumes a position parallel to the two rails. Some interesting experiments to determine the influence of iron raits on the magnetic-needle were made by Professor Oombes of the Paris School of Mines, He found that the nearer the direction of the rails approached that of the magnetic meridian the more highly polarised they became. The following deflections were observed when a miner's compass was brought near rails which were placed in the direction of the magnetic meridian :—

DiitooH ftom tbe tLtOi.

Ajlmatli Otmind.

19 ft, S in.4. on ooe tide, ,

InchM.

80* 00'

6 ft, 3 ius. OD one side,

83° W

Above the first rail, , ,

83* 15'

Between the two raila,

83-30'

Above the Recond rul,

83° 46'

6 It. 6 ius. on the other side,

83" 30

SUBVETIira WITH THE MACNETIC-HEEDLR. 5S

With the rails ptaoed at right angles to the magnetic meritUaix, the following angles were obtained i —

13 feet 1 inuh od one iride, 329*

Above the first rail, 328° 00'

Between the two roiU SW 00'

1 foot 10 inches on the other side, . 32S° 30'

When the comp&ss was only 15 inchea ahove the rails, deyia- tiona amounting to 7° 30' were observed.

Experiments made at Freiberg, in Saxony, hj Frofeasor Junga coo&rm these results, and permit the following conclusions to be drawn : —

1. Iron rails identical as regards weight and dimensions may- act dilfercntly on the compaes, the deriution caused by one being sometimes double that by another. The influence of two parallel rails on the magnetic-needle cannot he neutralised. It ia not Bulficient, as ao many miners imagine, to place the dial exactly midway between the two rails.

'2. The influence of the rails on the needle is increased by sharp blows. Four blows on a rail with a hammer was found to increase by 2° the deviation produced,

3. The iniluence of the rails is greatest when they form an angle of 45° 67° 30' with the meridian. The deviation then decreases until the rait is at right angles with the meridian, when the deviation is intermediate between the maximum and that observed when the rails make an angle of 22" 30' with tha meridian.

4. The influence is very considerable when the compass is as much as 47 inches above the rails. In such a case with rails at an angle of 45° with the meridian, deviations amounting to 3° 25' bare been observed.

No experiments appear to have been made with iron or steel sleepers. There can, however, be no doubt that their influence on the magnetic-needle is at least as considerable as that of iron rails.

The only practical conclusion that can be drawn from the results obtained by Professors Oombes and Junge, is that an accurate survey cannot bo made with the miner's dial in the manner described in the preceding chapter, unless the rails ara taken up.

Local Attraction in the Mine.— In many metalliferous mines, local attraction, due to the presence of magnetic iron ore in the lode, is very considerable. At Botollack mine, in Oornwall, for

Mine-Sukveviso.

example, the needle has been known to be deflected to the extent of 60" from its proper bearing. Experience shows thut cf>Ftain eruptive rocks, notable those of a dark colour with a baea of hornblende or augite, alfect the needle in the same way as magnetite or magnetic pyrites. In districts composed of magnetic rocks, the dial cannot be employed, as is shown by observations made at Ammeberg in Sweden, where at equidistant points aloag a straight line, the following bearings were obtained : — 3" 61', 3° 4', 3° 2J', 1', 2° 7f , and T 6'. To make a number of observations along a straight line is the best method of finding out if there is any local attraction affecting the needle. The influence of magnetic deposits on the compass has been utilised in Sweden and the United States in exploring for iron ore.

Snnreying with the Dial in the presence of IroiL— With the general employment of iron rails in mines, the question arises to what extent may surveys be made with the ordinary dial with* out fear of deflections of the needle giving rise to error ! As a matter of fact, the magnetic-needle may be used for the purpose oif obtaining the true bearings of the traverse lines in places where attraction exists, provided that the mode of procedure ij slightly modihed. The method is based upon the fact that the deviation of a magnetic-needle remains the same, if the relative positions of the dial and the attracting object remain unaltered. All that is necessary is to note the back- and fore-bearing at each station, however much the magnetic-needle may be deflected. Then, if the needle is attracted on looking to the back object, it is attracted to precisely the same extent on looking forward, so that the difference of bearing of the two lines is unaltered. Consequently, if a correct bearing of any one line of the traverse can be obtained, an accurate survey may be made,

DiaUing-Book. — The best form of dialHng-book to adopt is an ordinary account-book, the £, s., and d. columns serving for fathoms, feet, and inches. If the measurements are made in links, only one column is required. The date column of the account-book serves for the number of the draft. In the space Iwtween the date and money columns, two lines are ruled, giving three columns, which may be used for the back-bearing, the fore- bearing, and the calculated true bearing.

The method of booking a survey is shown by the following example of a closed traverse, surveyed in the presence of a very large amount of iron. The bearings and distances were as follows ; —

HtJBVETIHQ WITH TBS UAaNKTIC-NEBSLB,

Mo.

Bx-fc-Bnulai.

Ytn-tmHnf.

OocnetBaur

Ini. Fbu.

Is.

A

r 36'

3*36

B

y ae'

r36'

i°3e

6*27'

32r 44'

323*53

H

D

319° 15'

224' 53'

22y" 31

n

E

201' 57'

156° 41'

183' 18

u

F

167° 4S'

165' 03'

180° 33

G

166* 16'

79° 48*

94" 06

H

79° W

349° 04

The instrument was set up at 6, where there was no attraction, and a b&ck-bearing was taken. This was found to be 3° 36'. This bearing being correct, it was abo entered as a fonv-liearing at A. A fore-bearing was then taken at B ; this was found to be 36'. This also is correct, a.s there was no attraction when the back-bearirig was taken, and the dial was not moved to take fore-bearing. The instrument was then moved to 0, and a k-bearing to B taken. This should have read 36', the

rrect fore-bearing from B to 0. It was, however, found to be ' 27', showing that the needle was considerably deflected from its true position. Back, and fore-bearings were taken at each of the following stations, and in each case the needle was found to he seriously deflected. Consequently, hetbre the survey could be plotted, the correct bearings had to be calculated.

The bearings 3° 36' and 1° 36', being known to be correct, might be inserted in the correct- bearing column. The back- bluing at was found to be 5° 27' instead of 1° 36'. It was therefore 61' too great, and as the dial was not moved, the attraction remained the same, so that the fore-bearing at was also 3" 51' too large. The correct fore-bearing at 0, then, was 327' 44' - 3° 5r 323" 53'. The back-bearing at D, which should be the same as this, was found to be 319° 15', that is, 4° 38' too small. The fore-bearing taken at the same station under the influence of the same attraction must also have been 4° 38' too small, so that its correct value is 324' 53' + 4° 38' 229° 31'. The, back-bearing at E should be identical with this. It was, however, found to be 202° 57', that is, 26' 34' too small. The fore-bearing at the same station must also be 26° 34' too

J

U I K E-S U Byeting .

small. Its correct value, then, is 156° 44' + 26" 34' 183° 18'. This should be identical with the back-bearing at F, which was found t-o be 167* 48', or 15° 30' too Buiall. The fore-bearing at F ie also 15° S<y too small, and its correct value is 165° 03' + 15° 30' 180° 33'. This should be identical with the back- bearing at G, which was found to be 166° 15', or 14° 18' too small. The fore-bearing is also 14° 18' too small, and therefor© the correct bearing is 79° 48' + 14' 18' 94° 06'. This ehould be identical with the bearing at the last station, which was found to be 79° 34', or 14° 32' too small. The fore-bearing at the same station ia also 14* 32' to© small, and therefore its correct value ia 349* 04' + 14° 32' 363° 36', that is, 3° 36'. The last liae of this traverse is identical with the first, so that the first and last bearings should be identical. Thus, in a closed traverse the surveyor ia able to check the accuracy of his work.

The following page from the dialling-book at a metalliferous mine may be taken as an example for calculation : —

Ho.

Bwk-fiwniui

Fure-Beuliig.

True BviQF,

Fmi,

Ft.

lu.

A

.1,

245* 12'

245° 12'

B

245' 12'

254*30'

254-30'

i;

254° 30"

164° 46'

164° 45'

g

D

164° 06'

169"" 24'

170" 03'

E

178* 12'

161° 00'

152° 51'

F

167° 46'

174*0(1'

leroB'

G

171*27'

186*42'

184° 21'

e

n

183* 39'

178* 18'

179° 00'

J

177° 33'

222° 27'

E

221° 00'

79° 18'

80' 45'

S

80° 33'

80° (10'

71° 12'

M

71* 12'

82*48'

82° 48'

N

82° 48'

84° 24'

84° 24'

84*24'

90" 06'

90° 00'

P

90° 00'

91" 30'

91° 30'

SDRrEYINO WITH THE KAGNETIC-NEEDLE.

t9

If the first B.nd last bearings are not identical, and if the difference does not amount to more than a few minutes, the slight error, due possibly to the imperfections of the instrument employed, may be to a great extent eliminated by dividing the error by the number of station-linoa, and adding the result to, or subtracting it from, each bearing. Thus, in the example given, if the observed fore-bearing at H had been 349" 00' instead of 349° 04', the final error would have been 4'. It would be assumed that no error occurred in reading the first bearing. The error in each bearing would consequently be about and the calculated bearings could have been correctod for this error by adding V in each cose, that is to say, V to the calculated bearing of B, 1 to that of 0, 1|' to D, 2' to E, 2 J' to F, 3' to G, and 4' to H.

In applying this method to colliery and surface-surveys, it will bo found advisable to book upwards in the usual manner, noting the back-observation (B.O. ) at each station. A tabulated statement of the bearings may then be made, and the true bearings calculated.

Errors in Compass Surveys. — In all cases where the dial is used for surveying in the presence of iron, the greatest care must be taken in making the observations; otherwise very serious errors may arise, especially in long traverses. This may be illustrated by an example.

In making a survey in the ordinary way with the dial, any error in the readings will cause the next draft to have a false position when plotted. Assuming that a survey is made between the points A and E, Fig. 16, and that the bearings are read

direct from the dial without error, the plan of the traverse will be correct, as shown by the line A B D E in the figure'. If, on the other hand, a mistake is made during the progress of the — --.iu . survey, and the bv-aring, NAB, ' of the line A B incorrectly deter- mined to the extent of the angle pjg_ j6_ BAB' or a, then the following

drafts will have the same error. B' will be the end point of the first draft when plotted, giving a lateral error of B B'. The other bearings of the traverse being correctly determined, on plotting, the lines B' 0', C D', D' £' will be obtaiaed. These lines must be equal and parallel to the lines B 0. D, D E, and therefore B B' - C 0' D D' E E'. In other words, the lateral error B B' C6,\i?.ft4

k.

60 Uine-Bubvbyino.

incorrect detarmioRtioa of the beariag of the line A B is carried uniformly throughout the traverse, whatever its length may be. The magnitude of this error m found b; trigonometry to be

2 A 6 . sin

The magnitudo of the error is entirely different wheu the dial is uaed as an angle-meafurer in surveying over iron. Again, assuming that the bearing of the line A B has been iucorrectiy determined to the extent of the angle a, the angle NAB' having been read instead of the angle NAB, if now the dial is employed for measuring the angles, the bearing of the next line, B 0, is obtained by adding or subtracting the exterior angle at B, according as the line B is to the right or left of A B. The other bearings in the presence of iron may be assumed to liave been correctly taken. The bearing of the line A B incorrect, the bearing of the line B will also be incorrect to the extent of the angle Each of the following bearings will be incorrect to the extent of the same angle, so that on plotting the calculated bearings, tht line A B' 0" D" E" will be obtained. The error a thus affects the whole traverse from A to E, and increases in proportion to the distance apart of those points. The length from A to E being represented by L, the lateral

error, E E" is equal to 3 L aiu

It IB thus evident that a survey may be very inace urate, when the angles are not correctly measured. In applying the method of surveying with the needle over iron, the surveyor should not fail to make a check-survey, or reverse course of dialling, selecting fresh points for his stations. Not only in this method, but in all other surveying operations, it is highly desirable that the mine-surveyor should adopt the practice of always checking and verifying every part of his work.*

The Action of Electric Carrenta on Mine -Surveying Instm- mentB.— In view of the rapid increase in the number of electric trsmways in ihe Westphaiian coalfield and in the use of electric power underground, the question of the action of electric cttrrenta on iiiagtietic mme-aurveyiug instruments is of such great interest that Mr, W, Lenz has been induced to conduct a series of ex- periments. A point, undergrouud, was selected at a horizontal distance of some 100 yiirds from the rails of the Bochum-Herne electric tramway, and 1,420 feet below it. There, by means of a Fennel's magnetometer with quartz fibre suspension, a seriei of observations of variation was made based on a fixed line,

Tlie Iraustiiiesioii of errors in tranaversu surveying is uxhtmslively dealt with by G, K. Tliounwou, Tratui. Iital. iI.E., vol. xxi't., 1903, p. 75,

BURVBYING WITH THE MAGNKTIC-KEKDr.E,

Gl

w

The magnetometer was [irevioualy coraparetl for & long period with the apparatus in the Bochum Town Park, and the two instruments were found to coincide almost exactly. The first obserTatioD, in September, 1895, was uode by day, the second by night, when the line w&a free from current, and the last again by day. Whilst the curve of the day-resulta exhibited great irregularities, that of the night-resuUs was perfectly regular, and in accord with the magnetic records. The irregularitiea in quite small intervals of time amounted to 27 minutes to 5'4 minutes. As at first it was thuught that the deviations might be ascribed to the iron-free safety lamps employed, a third observation was made in the morning, the lighting being effected by a stearins candle. The results were exactly the same aa on the first day. As the ohservationa were made at a comparatively large distance om other workings, and as the shaft was 200 yards away, it is evident that magnetic observations can, under such conditions, be only satisfactorily conducted during the night in the absence of the electric current. Another source of error is the safety lamp. Composed of various metals, the lamp in a, hot condition sets up thermo-electric currents which act on the magnetic- needle. In order to obtain information on this point, the author placed six mine-surveyors' safety lamps free from iron, one at a lime, first in a cold condition, then heated, at the pole of a sensitive magnetometer. Of the six lamps examined, two, when cold, had no action on the needle, whilst all acted on it when hot. The deviations observed amounted to from 30 seconds to 160 seconds. A new benzene lamp, that had not previously been osed, caused a deviation of as much as 5 minutes. The deviation increased with the temperature of the lamp. A quite new aluminiam safety lanip caused the same deviation when cold as when hot. From these results, it follows that the mine- aarveyor, before making magnetic observations with delicate instruments, should carefully teat his lamp. The influence of alight magnetic properties may be lessened by holding the light in the prolongation of the magnetic axis. With side-lighting great care is necessary.

Chapteb Vl

warn thk Fixed Kxeslb.

r. — In the e d of Ae miner's dJAl, the com-

pi-1>n¥ is confrtwi vitk tkepkte Aat cBZiin it, ia a way

it caa RTotve oa tkk pbte. Motam is siTen to it hj

% ctreolv rack aad foStam wuil friMi bdov. Modified in thU

iraj, the in atiu a u rt is as tiie Mrcmyimtar, or raot-

dioZ. When tlie Tek-zev is tsmed, two msAs, msde opposite

to each other, one oa the piujectiag portion of the compass-box,

tad the other on the plate, will sepante. Their angular 'distance

apart is measured bj meaos of a vernier, which maj' be defined

as a contrivance for meaatttiiig analler portions of space than

those into which a tine is aetewj divided.

The principle of the Temier ia as follows: — If a line contaioiug

n units of measurement is divided into n equal puts, each part

will represent one unit ; and if a line contauning n — 1 of these

n - 1 units is divided into n parts, each part will be equal to

The difference between one division in the former case, and 1 — of the original unit,

nnits.

one in the latter wQl be

n n

Similarly, the difference between two divisions of the one, and

two divisions of the other, will be - of a unit ; between three of

the one, and three of the other, -, and so on. Hence, in order

n

to obtain a length of - of a unit, a division of one scale has to be

made to coincide with one on the other scale, and the space between the two corresponding arth divisions from the coinciding

divisions, on both scales will be the required length of of a

Ills Skins reasoning applies if divisions of the vernier are mads qual to n -)- 1 divisions of the limb. In this case, how

ow-

M

8Brtetixo With The Fixed Nkedle. 68

ever, the vernier must be read back w aids. There are thus two kinds of vernier, called direct or retrograde, according as they are read forwards or backwards from the zero points. Moat verniers in surveying instruments are of the direct type. In aU cases, the zero of the vernier scale marks the point on the limb, the reading of which is required.

The dilTereace between a limb division and a vernier division

is of the value of a limb division. This difference is known n

as the leagt reading of the vernier, and expresses the degree of

ntinuteness to which readings can be effected.

The circle divided to 30' is a common graduation for the

minfi's diaL If 30 divisions on the vernier are made equal to

29 on the circle, each division on the vernier wUl be equal to

— — 29', or 1' less than a division on the circle. The

vernier will therefore read to an accuracy of one minute.

As an example of more minute division, the sextant used in marine-surveying may be cited. The limb of this instrument is divided at every 10 minutes, and 59 of these parts are made equal to 60 divisions on the vernier. The least reading in this

The rule for reading an instrument provided with a vernier is as follows: — Bead the circle, in the direction of the graduation, up to the line preceding the zero of the vemier. This gives the nnmber of whole units of the circle. The line on the vernier coinciding with a line on the circle gives the number of fractional parts of one unit of the circle to be addf>d to the former reading.

RacMng. — Provided with a vernier, the compass may be used to measure angles in a horizontal plane, or assiTmiihs, without the aid of the magnetic-needle. ThJa method of surveying is known es/astneedU dialling or raclnng.

The word azitnutk used without qualiBcation, usually means the number of degrees, minutes, and seconds by which the direc- tion of a vertical plane passing through a station and a given object deviates to the right of a vertical plane passing through the station and the north pole. The r dative aziTnuth of any two objects may be measured at any given station ; that is to say, the angle by which a vertical plane passing through the station and one of the objects deviates to the right of a vertical plane passing through the station and the other object. An aumuth exceeding 180* denotes that the direction of the obje*t to vH. He

u

MINK-SDIIVETtlfa.

Fig. 17

measured lies to the left of the direction from which aziniu th are measured, bf an aagle equal to the difference between the azimuth and 360°.

The horizontal angle between any two directions is the

difference of their azimuths, if the difference is less thaa 180°. If it is greater than 180°, the angle between the directions is the ex- ceas of 360' above the differ ence of the azimuths, Thoa, in Fig, 17, the dial being set up at A, and A B having the azimuth of 0°, the azimuth of 0, an object to the right of A B, is equal to the angle B A 0. On the other hand, the azimuth of D, an object to the left of A B, is the angle subtended by the arc b' d, that is, the difference between the angle BAD and 360*. j

Vaiioas Forms of Dial : (a.) Lean's Miner's Dial.— There are a great number of di fferent types of mining circumferenters adapted for surveying without the use of the needle. They differ merely in details of structure ; the essential parts are the same in alL

Fig. 18 represents Lean's dial, as manufactured by Mr. W, F. Stanley of London. This form of dial is that most frequently used in metaUiferous mines. Like the ordi- nary miner's dial, it consists of a brass coni- pass-box attached to a tripod-stond by a socket fitting on to a corresponding plug. In addi- tion to the levels, sights, and niagnetioneedle of the ordinary dial, it has, above the main plate, a divided vernier piate by which hori- zontal angles may be measured indepenr dently of the needle. The same graduation thus serves for the vernier and for the needle. The movement of the circle is effected by a concealed rack and pinion, the head of which projects from the under side of the main compass-plate. The instrument is provided with a vertical arc for measuring vertical angles, and a telescope so that the instrument may be used as a theodolite for surface-surveys. The vertical arc and the telescope may be removed, and the sights used. The latter are made to fold down for convenience in packing. Under- neath oompasa-box is a pin to fasten tlit two plates together

Ftg. le.

d

BCRVBTIKfi WITH TBK FIXID KXEDLK.

at 360°, and a spring to throw the needle off its pivot ao aa to preserve it when not in use,

{b.) The Henderson Dial is an improved form of the Lean dial. It is 6 inches in diameter, well divided, and graduated to the left. This instrament is represented in Fig. 19.

In the coDStmction of the sights, the use of horse hiurs is avoided, as they are continually getting burnt by a flaring candle tmdezgronnd. Id place of the ordinary horse-hair sighU, the apUt' is adopted. There is a narrow slit in each sight, tiirtmgh which the object can be distinctly seen, and its bearing determined with precision. On the other band, if the vertical hair is used, it covers to a oertaia extent the object, which should be seen sharply defined.

Fig, 19. — HecdersoD Di&j.

The needle is mounted on a ruby instead of the ordinary Agate. Oare must, consequently, be taen to throw off the needle when not required, as Che shock, cauted \iy p\&C\tL% &% itrvA

(tfi

UtNIetTRVBTIirO.

auddealy on the ground, is apt to crack the ruby, 'which, though extremely hard, is brittle.

To the north-seeking end of the needle, an alunitrdam vernier IB fixed, the needle being counterbalanced at its other end. By the aid of this contrivance, a bearing can be read to thre© minutes, a degree of precision aufficient for general purposes.

The special featare of the dial is the attachment to the instru- ment of two seta of folding sights, one revolving within the other. The fixed sights are always in a line with the back object in fast-needle surveying; whilat the inner or revolving sights adjusted to the forward object give the angle of deviation from the origiiuJ direction. The sights are made to fold over so as to be out of the way, in case the new line should too closely approach the direction of the old one. From the joints of a dial working loose, an imperceptible movement will sometimes take place in the body of the instrument on turning it in a new direction. There results, of course, an error in the angle obtained when looking towards the forward object. In the Henderson dial, however, the back object can be again sighted through the fixed sights, and re-adjusted should any deviation be observed.

For taking vertical angles, a semicircular vertical arc is Gxed across the central line of the dial, when required. It is provided with a movable limb, to which a vernier is attached, as well as a horizontal bar carrying a pair of sights and a long spirit-level. A folding shutter is fitted to each sight, with the object of pre- cluding the possibility of the eye being directed to the wrong orifice. This dial was invented by Mr. J. Henderson, M.Inat.O.E.,* and is manufactured by Mr. Letcher, of Truro.

(c.) Davis's Miner'a Diftl. — This improved form of Hedley dial is the best instrument for ordinary colliery use. As represented in

Fig, 20, the dial combines all the latest improvements of the Hedley dial with the outside vernier of the theodolite.

It consistB of a compass-box S or 6 inches in diameter, divided into 360° on the com pass-ring, and into four times 90° on the plate, 0° being at the north and south points, and 90* at the east and west points. The needle ia mounted on an agate cap, and when not in use is thrown ofi" by There are two spirit-levels at right angles to eob Pnt, Min. Irut., Oomwaliy vol. i., 1883, o, 317.

Fig. 20l

a spring.

BCRTeVIKQ WITH THE TIXXD NEIDLI.

ether in the face of the instruraent, protected by the glass cover of the compass-box. The sights are the same as those of the older form of Hedley dial previously described.

Underneath the main-plate, there is a circle or limb divided into 360°, A vernier attached to the outside of the compass-box enables borisontal angles to be read with great precisioa. Being placed on the outside circumference of the dial, the vernier is more easily read thaa when placed inside the compass-box, and the necessity of raising the head above the dial-face is obviated. The upper and lower limbs of the instrument may be fixed together at 360', if required, by means of a pin under the body of the instrument. This dial, it will be seen, difi'ers from tho Lean and Henderson dials, in that the vernier is not movable, but remains rigid with the sights.

The Hedley form of side arc for taking vertical angles ii replaced by a fixed circular box inch in diameter, with a hand traversing a dial-plate divided into 90°. This new form of arc presents the advantages of always being in position, and of being so compact that it does not interfere with the manipulation of the screws under the body of the dial.

For surface-Burveys, a telescope may be substituted for the lights. The tripod on which the dial is supported is made of mahogany, with ft brass screw-joint at the centre of each leg. For very shallow seams, it is necessary to have an extra set of joints in the legs. All the joints in the legs are made inter- changeable, and great rigidity is obtained by increasing the diameter of the legs towards the centre.

The special feature of the Davis dial is the arrangement fay which bearings may be taken simultaneously with the magnetic-needle and wit the vernier, the latter automatically checking the former. Thus any error arising from incorrect reading or firom local attraction is at once detected. The graduationa of the vernier ring and of the needle ring are BO arranged that the readings correspond. This is efi'ected by numbering the dial from the north from left to right, and by numbering the vernier ring from the vernier also from left to right.

Dial- Joint,— The miner's dial is usually fitted to a slightly conical spindle, having on its lower end a ball, which is confined in a socket in such a way that it can be moved in any direction in the operation of levelling the instrument.

For facilitating the setting up of the instrument, an American invention, the Hot!inan joint,* has been adopted in conjunction

Tram. Amer. Jm(, Min. Efig,, vol, vii,, ij. 3U&.

MtSB-snRVBTiiro.

with the Davis dial. This tripod head combines the play of the ball and socket joint and the accuracy and rigidity of the theo- dolite parallel plates.

The ordinary form of tripod has the disadvantage that it is moat impoasiiile to level up a sensitive bubble, so that it will reuiain in the centre of its run long enough to take a satisfactory (right. On levelling the instrument and sighting, a second glancu at the bubble almost invariably showa that it has changed its position, and it ia necessary to level up again. This defect ia due to the fact that the levelling screws, when moved in or out to a considerable extent, do not stand perpendicular to the plate on which they rest, but on an inclined plane, so that, on turning them, their points have a tendency to slide down the plane. In this position, they spring, and turiting them is apt to bind or bend them.

Another imperfection in many tripod heads, is that tho plummet is attached to some point on the axis above or below the centre of the hall and socket. In either case, the plummet, after being set over a station, will, during the operation of levelling up, travel away from the point in a degree pro- portionate to the distance of the attachment of the plummet from the centre of the ball, and the deviation of the axis from the perpendicular at the time the instrument is placed over the ccntret

The Hoffman joint (Patent 1878, No. 2084) is free from these defects. Fig. 21 shows the form supplied with the Davis dial. It is claimed to possess the following adraa- tagea over the ball and socket joint: — 1. The pluiub-iine ia suspended from the actual centre of the dial. 2. The rubbing-sur&ee is some ten times greater, and consequently the joint is more rigid. 3. The joint ia manipulated with greater ease and rapidity, A slight turn of the milled flange from right

l/-— spheres. The dial is then levelled up, and

a slight turn of the flange from left to right secures the joinL 4. Only one hand is required to manipulate the joint. 5. The total height of the Hollrnan joint is 3 inches ; that of the ball and socket joint inches. The length of the centre is 21 inches, that of the ball and socket is barely inch. The Hofiman joint is not heavier than the ball and socket joint.

(d.) Wbitelaw'a Dial — In thia instrument (Patent 1878, No. 1592) the compass and lower limb are of ths same diameter

Kg. 21.

BURTEYING WITH THE PtXED NEEni-E.

(Fig. 22). The vernier is attached to the outside of the compass- box, &Qd is placed doM to the right of the line of Bight, so that 'adlnga caa be taken by the surveyor directly after sighting the object, without moving aside. The gradijated lower piato is covered by the compos&box ex- cept at the vernier. A circular spirit-level placed inside the com- pass-box serves for ap- proximately levelling the instrument before final adjustment with the long level suspended below the vertical arc.

The special feature of this dial is the manner in which the vertical arc is supported. I n order that the com- pass graduation shall not be obstructed, the standards are entirely dispensed with. In their place is a movable semi- circular arc carrying the

bar with the sights, or telescope if required. This are ia at right angles to the graduated vertical arc, and the axis, on which it turns, corresponds with the east and west points of the eonipass- box. Angles of elevation or depression up to 90° can be taken simultaneously with horizontal angles. The dial is thus well suited for surveying in metalliferous mines. It is manufactured by Mr. W. II. Harling, of London.

Thornton's Dial. — This dial is the patent of Messrs. A. 0.

omtou and Co., of Manchester, Its special feature is a

duated semicircular folding arc for taking vertical angles. This vertical limb ia. fixed by binge joints to the edge of the compass- box, and may be folded down out of the way of injury when the dial is being carried about in the mine. A groove is cut in the vertical limb, in which slides the bridge carrying the sights. The bridge may be fixed at any angle by a clamp- ing screw, and to it a vernier is attached for reading vertical angles. In order to ensure the rigidity of the hinged ver- tical limb, a pin is pro-vided to fix it securely, and when folded

Kbc

rniwrnmsKTETJicQ.

down it upoB k ledg, Biiid so relieves tlie hinged jomts of

Th compAsaUte is iacbea in dikmeter, and its edge is bereUed the divisions &re thus clear Ij seen, and readings can be ken ytrj readily. The dial is provided with a vernier within the oompBSB-boz, and with two spirit-levels let into the coiq- pM-face Kt right angles to one another. It is attached to the tripod in Uie osaal vay by a ball and socket joint with clamping screw.

TraTeraing Undegroond. — A traverse lb a series of consecutive courses, the lengths and aamuths of which have to be determined. With the vemieisiial or circamferenter, the mode of procedure is as follows : —

1. Three tripods should be provided, and two <ndles or lamps on stands fitting on the tripods of such a height that wheu the light is replaced bj the instrument, the axis of the telescope when horizontal shall be of the same height as the top of the wick. Having placed a tripod with a lp at station 1 (saj, the centre of the shaft) , set up the second tripod with the circuinferenter at the second station, and send on the third tripod mth the other lamp on it, as far forward as the light can be seen. With the pin of the circumferenter keeping tlie vernier at zero, take a back-observation to the lamp at station 1, Olamp the vertical axis of the instrument, carefully measure the distance from station 1 to station 2, and enter in tlie dialling-book the distance and the horizontal angle 0° 00'. Thea take out the pin, unclamp the vernier, and take a fore-observation to the lamp at station 3, moving the sights by means of the lack-work. Olamp the vernier, measure the distance from station 2 to station 3, and note the distance and the angle indicated by the vernier.

Then take up the first tripod, and send it forward, with th lamp on it, to a station beyond the third tripod, place the second lamp on the second tripod and the instrument on the third tripod, and observe the angle as before, by tirst bringing the vernier to zero by means of the pin. In this way any number of angles may be measured, a back-observation being in each cue first taken with the vernier clamped at zero. Thus, the last coarse is always taken as the base-line for the I'tllowing andle.

Thia method of surveying is illustrated by the accompanying notes of !► survey of a portion of a Durham colliery; —

BCBTETlNa WITH THK FIXED NEEDLE.

Tl

D

C— 181" 15'

M

Dipper W. 3 ft.

N. headway!, 20 jardi.

Utinaed 63 tialu to face

W. bord

W. bord

2,-343*45'

totN. i6'I5'W,)

©

of ridding,

Fermuieiit ranrk left in roof.

20 yda. E. bord and holed.

30 yds, E. bord and holed.

r

l._34ff' OO" (or N. 20- W.)

©

Porinwiant mark loft in roof and thill.

From winding shaft.

trey from winding shaft to north faes roMad wert and eaat face to ling shaft, main oo&l aeam.

19ISE-S0BTeYIKQ.

Bord coatmned SMt.

Ho. 9.-S' 00- 1

aoo

SO ydl. to rise tutcb.

Ho. 8.-256* Sy

Continued 3 yd*, to riwi liitoh.

No. T.-sr W

8S

20 yda. to UtoL

H& 6.~8Sr 07'

m

100 links to hitch, riss not proved.

41S

Continued IGO linki to rise hitch, not proved.

Ho. 6,-273' 21' 1

I2.-i3r 22*

Zd

11— 251' re-

O

Cod tinned 21) yda, to faoe. Peno&Dent murk left.

I crcusBei dip hitch of 2 ft, I iuB. going east.

H (nil ways coutinued 20 yd

to permanent mark left ome 20 years ago.

3,5 T/ila, to rise Mtoh,

30 V'in. to rUe hitoh.

r

wnHTFTINO.

End of

survey.

to oeatra of pumping tktSt.

22U

Water level, nunow pUog,

3*7

Ko.14.-95' 53-

r"

The local mining terms occurring in these survey notes have the following meanings : — A. bord is a passage driven across the grain of the coal. A headtoay is a passage driven in the direc- tion of the grain of the ooal. A sUrUon is a passage between two winning headways. The iU is the Qoor of the mine. A hiicA is a slight dislocation of the strata, which does not exceed the height of the seam. Ridding is clearing away a fiJl of rnbbish. The /ace is the extremity of the workings.

The distances are measured in links, and, in order to avoid

confusion, the total distance is given in each draft. Ths

first two angles were taken from the magnetic meridian. The

figures j— denote that liae No. 3 is from the distance 305, that

is, the end of line No. 1.

The angles taken with the oircumferenter are reduced to angles from one meridian by applying the following rule : — To the first meridian angle, add the next observed horizontal angle. If the suin exceeds 180*, deduct that amount from it. If the sum is less than 180°, add that amount to it The result will be the second meridian angle. Thus, the angles taken in the survey given will be reduced to angles from one meridian in the following manner : —

Meridian, . , 00' -t- 1 at angle 340' 00' Mf (KK=No.tmer. uigle. r 00' + and migle 343" 45' 343° 45' No. 2 mer. angle. No. I ner. angle, 340* OO" + 3rd angle 13S° 20' 478° 20*

478* 20' - ISO- 298- 20' No. 3 mer. Migl& No. 3 mer. ouigle, 298" 20' + 4tb ngk \SV 15'=429'' 35'

ig- 36' - 180' 00' 249° 35' No. 4 mer. angle.

Suhvkyimo With Thk Fixed Keedle.

No-4mer.i]gIe, 29'35'+5tb DglB273'21' 522°56'

822" se' - ISO" OC 342* 56' No. 6 raer. uml*. 342*56'+ 89° 07' 432" 03'; 432" M' - 1 80° 00' 252° 03' No. 8. 252*03'+ 87* 20' 336' 23' i 339*23'- 180* 00'=:169°23' No, 7. 159 23" + 255' 32" 414° 5r>' ; 41 65' -180" 00* 234* 55= No. 8. 234* 65'+ 93* 00' 327" 55'; 327° 55' - ISO" OC H7' 55' N o. a 147*55'+ 94'lfl'=:24ir lO'i 842* 10'- 18000'= 62* 10' No, la 62° 10' + 251* 16' 313° 26'; 313*26'- J80" 00'= 133° 2a' No, II. 133' 26' + 131° 22' 264* 48' ; 264' 48'- 180 a4*48' No. 12. 84* 4S' + 273° 20' 358° 08' ; 858* 08' - 180* 00'= 178° 08' No. 13. 178*08'+ 96° 53' 274' 01'; 274*01'- 180*00'= 94° 01' No. 14.

2k There is a second method of traversing with the fagt-needle, which the work ia continued from the original tiase-line by first taking for each line a. back-observation with the vernier at the angle last read. With the circumferenter at station 2, and lamp tripods at stations 1 and 3, take a back-observation to the lamp at station 1, the pin keeping the vernier at zero, as described in the first method of trsveraing. Olanip the vertical axis, take out the pin, and take a fore-observation to the lamp at station 3. Clamp the vernier, and instead of now moving it back to rero, let it remain in the position in which it was clamped, and set up the ciicnmferenter at station 3. Take a back-observation to station 2 by unclamping the vertical axis, leaving the vernier clamped. In this way any number of angles may be measured, the survey being always continued from the same meridian. This method, however, is not to be recommended, as any error made in one observation is carried on throughout the survey.

The observed angles may be reduced to meridian angles by adding the meridian angle of the first Hne in each case. The observed angle and the meridisn angle of any atatioii-linn

p

UlNE-SUKTEYIirO.

known, subtract the former trom. the latter, the difference is the meridian angle of the first stations-line. If the vernier angle exceeds the meridian angle, add 360° to the latter in order to enable the subtraction to be effected. The meridian angle of the first atation-line thus obtained is added to each subsequent v-ernier angle, the sum in each case being the meridi&n augls of the Une in question.

For example, the following angles were taken with the rack dial, the needle being thrown off except where correct bearing were taken at £, looking back to and forward to F ; —

Ko.

Aoflu.

Btsiiifi.

Dmuh.

Itawrta.

A

ccw

Fmt. n. In

/ From 2 ft W. centre shaft.

of

B

2-5* 06'

D

278* 51'

E

ass-otf

277* oy

¥

WTOff

2S3°Kf

G

290' 00"

Eko,

At station £ the angle and bearing are known. Oonseqttently, to obtain the bearing of line A the angle 286° 00' must be sub- tracted from the bearing 277° 09'. The latter being smaller than the former, 360* must be added, giving 360° + 277" 09' 637*09'. This result less 286* 00' is equal to SSI" 09', the bearing of Une A. The same result is obtained with line F. Thus;, (283° 09' + 360°) - 292' 351* 09'. The bearings of the other station-lines may be easQy found by adding 351* 09' to tha observed angle in each case.

The work may be plotted, without any preliminary calcula- tion, with the protractor and scale as if the survey had been mads with the magnetic-needle. The protractor must, however, be graduated in the contrary direction to that required for a neodls survey, if the dial is a left-handed one.

3. When the dial la numbered from the north from left to right, all calculation can be dispensed with ; the angles being

BtlAVETINa WITH THE FIXBD NEEDUa

Tead direct from the magnetic meridian. The Davis dial is graduated in this way. The horizonto! circle of that instrument being also graduated fi-om left to right, the hearings can be taken simultaneously with the looae needle and with the vernier, the latter acting as an automatic check on the former.

In making a survey in this way, select some disused road, where there is no iron present, and take its magnetic bearing from stations at the beginning and end. If there is no attrac- tion, the two results will be identical. Then with the dial set np at the end station, clamp the vertical axis by tightening the collar attached to the ball and socket, unclarap the vernier-plate by Blackening the clamping screw, and turn the sights by means of the rack and pinion screw, until the vernier reads exa,ctly the same angle as the mngnetic bearing just taken. This bearing ia used as the basis of the subsequent determinations of the angles of the traverse. Clamp the vernier-plate, unclamp the vertical axis, and by means of the loose collar direct the sights to the lamp at the first station. If the readings obtained with the needle and the vernier are identical, the dial ia in adjustment, and the whole of the underground workings may be surveyed firom this base-line. In taking a fore-observation, the surveyor must turn the south side of the compass fai.e towards himself, whilst in taking a back-observation, his eye must be at the north sight. L The following is an example of a survey made by this system: —

No.

Vernier AxK

Hirldiui Aiifli,

DtaEAnn

lUmu'lu.

A

30" 05'

30' 05'

Linlll.

From and of diauwd road.

B'

315* 58'

7Ta

f

61' 01'

D"

274° 68'

B

115* 12'

From A agiin.

10*33'

D

301* 18'

301* 10'

The lurvey was commenced in a disused road, the bearing of was found to be 30° 05'. The vernier reading was made to rrespond with that anle. Then with the mstrauiftTti wit

Hine-Survbyino.

N

A, a liack-observation was taken to tho lamp at the end of the dit- used road, the vernier remaining clamped at 3U° 05'. The vertical axis of the dial was then clamped, the vernier-plate tmcUmped, and a forward-observation taken to B*, The vernier was found to read 315" 58'. 01am ped at this angle, the dial was moved to B*, and the survey continued as before. The survey can be checked at any point by liberating the needle. If the vernier and needle readings differ, the amount of magnetic attraction ig the difference between the two readings.

The dial being graduated from left to right, 90° indicatei West, and 270° East, In plotting the survey a protractor graduated from right to left must consequently be used.

Sanreymg in Inclined Shafts.— The vemier-dial is of great value for surveying In inclined shafts containing iron pumps. The survey should be commenced in a level free from magnetic attraction. On the basis of the bearing thus determined, the survey is continued to the shaft.

Should the surveyor be called upon to determine the bearing of an inclined shaft, containing iron pumps, with a miner's did unprovided with a vernier, he may perform the operation with a croES-etaff, either a well-made brass instrument or an improvised one made by drawing two lines at right angles on a boaid, about 6 inches square and 1 inch thick. The lines must be cut half an inch deep with a fine saw. The instrument thus made is fixed on a three-foot stand.

The cross-staff is set up in such a position that a candle in the shaft can be seen through one pair of sights. In the line of sight of the other pair, the dial is sot up in the level out of the way of magnetic attraction. In this way, the candle in the shaft and the dial in the level form a right angle with the cross-staff. An assistant must now look through the sights of the dial to a candle held immediately above the crosastaff, and read the bearing indicated by the needle. Being exactly at right angles to thia line, the bearing of thf shaft may be at once determined. Thus, assuming that the needle reads 382°, if the underlie is northerly, the hearing of the shaft will be 12°; if southerly, 192°,

The Vernier Compass.— The vernier of the circumferenter may be used for reading the magnetic bearing. In this method of surveying, the compass-box is clamped with the needle lying upon tlie zero or north and south line marked on the dial. The sights being then directed to the object, the bearing is read direct from the vernier to 3 minutes, or by estimation upon a superior instrument to 1 minute. This method is very expedi- tious, and givea most accurate results. At any point in the traverse, a fast-needle observation may be made without difficulty.

aUETETINO WITH THE FIXED NEEDLE,

In working with the lost needle, it is advisable to invariably tart with a louse magnetic bearing, and, it' practicable, to cloas with one. Intermediate checks by the same means are desirable, bnt not essential. In this way, the needle lies upon the zero line at every set, except where local attraction prevails, of which the amonnt and direction are shown by the needle's deviation from that line. The result is that the traverse angles booked are also magnetic bearings.

In order to show grounds for confidence in this method, the details of an actual survey, made by Mr. W. F. Howard,* may be quoted. The survey was made between the Speedwell and

VcTDler Bftuinf

SlaUDU.

Baiuu-ki.

N. 34' 24' W.

Llolu.

f From Speedwell north qr down- cut sbaf t

N. 58° 35' E.

N. 45' 41' E.

p

t 4

N. 37* 29' E.

S

N, SMcyw.

S

N. IS' 02' a

N. 17° 57' E.

N. 11" 35' E.

M

N. 35" 37' W.

N. 18* 20' E.

p

K. 18° 14' E,

u

N, 69* 42' E.

3S4

8. 27*4S'E,

S3

N. 69* 32* E.

N. 71* 57' E.

To face of muD veiitUatiiig drift intended to hole into Nether-

Trafu. Jf. SagL Itut, M.M., voL xx., 18fI0, t- SV.

Bo

MIITE'SBK'rKTtNO.

Ketherthorpe shafts at Staveley, witli the intentioii of effecting k boliog into the latter. The straight distance between the measoied direct on the surface, was 3 M 3 chains, and the distanoa between t!b shafts bj the undergroand roads was 35*43 cbaina, making the total cLrcait 66*56 chains, and req airing 16 sets underground. The foregoing is a copy of the survey notes.

The stirvey was made with a 5-inch Davis dial, divided to half- dees, with a vernier reading to 3 minotea.

Tn this instance, the magnetic bearing and the horizontal distance sought, from the &ce of the heading to the intended up- cast shaft, was calculated to be N. 58° 58' K, 190*5 linka It was then determined to drive direct into the shaft, and the draft was accordingly set out at the above bearing ; and the holing proved this bearing and the calculated distance to be abeolutelj correct.

The Grabb Sight for Miners' Dials.— Sir Howard Grubb ♦ has 1 invented a new sight for miners' dials. It consists of a short brass tube ahout 3 inches long by inch square, through which the object is viewed. About midway down this tube is fixed, at an angle of 45*, a plate of glass coated with a Bemi-transparent and highly reflective film. This plate reflects the light of a lamp held on one side of the tube by means of an opening in that side, the opening containing a piece of glass on which a cross has been drawn. By this means, aided by a lens in the tube, the cross is aeen, when looking through the instrument, projected upon the object, and in the same vertical plane with the object, BO that the eye is not called upon to focus itaelf at more than one distance at the same time.

Traiw. Init. M.E., vol. iiiu., 1909, p. 118.

THK OERHiFT DIAL.

Chapter Vi I.

TuK Gebuan Dial,

Lavention of the German Dial. — Tlie continental method of sur- reymg minea coasists in suspeacLing a compass and a clinometer to a stretched cord r>presenting the line of sight. The compass and the clinometer are read, and the length of the line measured. In this way, the length, bearing, and inclination of the station- line are determined . Mine-eurveyswerecondu cted in the ma nner described by Agricola until the invention of the German dial, or hanging compass, by Balthasar Boessler, who died at Alten- berg, in Saxony, in 1673.

Heasming Station-Idiies.— The cord is 50 fathoms long. It is made of hemp, and wound round a wooden reel provided with a b&ndle (Fig. 33). This cord is stretched from station to station. The length of the portion stretched depends, of course, on the distance of the stations apart. It should, however, not exceed 8 fathoms, so as to prevent the formation of a catenary curve. The screws {Fig. 24) to which the cord is fastened are .i inches in length. They are firmly fixed into the timbering

Pig, 23.

Fig, 2*.

Kg. 25.

of the level. When the cord ia stretched between the two points, the length of the line is measured. For this purpose, the Hun- garian surveyors employ a fathom-rod j the Saxon surveyors use a hrass ENfathom chain.

For surveys at the surface, or in mines where thecQ ia uo

JIIMR-SliRVK¥llt(ik

timbering to hold the screws, a trestle of the form shown in Fig, 25 is employed. It consists of a beam 8 feet in length &nd 6 inches in diameter, with two short legs. It should be as heavy fts possible, and no iron roust be used in its construction.

In the Harz mines, instead of the cord, a thin brass chain ia oafid. It is 10 metres in length, and is provided with a hook at one end. Every metre is indicated by a brass tag. The is wound on a reel, and used in the same way as the cord. The advantages it offers are : 1, It weiglis very little ; 2, its length can be read without any delay ; 3, the best place for hanging the clinometer can easily be found ; 4, no further meosurementa are required to determine the points where offsets have to be taken. Its disadvantage is that it is liable to stretch, and must there- fore be carefully examined and adjusted every time it is used.

The Clinouieter is used for determining the inclination of the stretched cord. Xt consists of a thin bras semicircle

Fig. 2&

(Fig. 26), 9 inches in diiuneter, provided with hooks for hanging it on to the stretched cord. In the centre of the circle is a hole, through which a black human hair is passed, and fastened on the other side by mrians of wax. At the other end of the hair, a small brass plumb-bob is &8tened. The hair touches the graduation of the semicircle, and enables the angle of inclinsr tion to be deteriuined. The* hooks open towards opposite sides, and are provided with apertures through which a clamp may be in- serted when the clinometer is suspended from a highly inclined cord. The graduation begins at the centre of the semicircle — that is, perpendicularly below the centre from which the plum-

Tek Oerhan Dial.

Ha

met h&ags. It commeuceii with 0*, and goes to 90* on both idea. Each dejiee is subdivided into four equal parts, bo that hn angle caa be read direct to 15 minutes. As a rule, the quarter degrees are further divided by the eye into three equal parts, so that angles can be read accurately to 5 minutes. In order to facilitate the reading, the graduated side of the clinometer is usually silver-plated.

Use of the Clinometer. — If a cord, about 10 yards in length, is stretched horizontally, and the clinometer suspended from ita centre, the human hair, hanging vertically on account of the weight of the plummet, will coincide with the zero of the gradu* ation, provided that the cord is (tretched perfectly tight, and that the clinometer is free from defects of construction. If the cord is in- clined at an angle B A (Fig. 27), the hair will notcoincidewitbEero, but will give the angle DHE, which represents the angle of in- clination of the cord. For since AHD + DHE - a right angle, and AHD + BAO a right angle, AHD + DHE AHD -I- BAO, therefore DHE 6 A C. The clinometer thus may he used for determining the inclination of lines.

The cord when stretched forms a catenary curve, and con- sequently the angle of inclination varies at different points in the curve. There must, however, be a poipt where the cord is parallel to the line joining the two end points, and there the clinometer must be placed in order to obtain the true inclination. The weight of the clinometer being neglected, the correct point of suspension is h lightly below the centre of the cord. But the weight of the clinometer alters the inclination of the cord, as it is not uniformly divided between the two hooks. The place where the clinometer must be suspended, in order to give the correct inflirifttion of the cord, has been found by Professor A. von Miller- Haaenfels. His rule is as foUows: — The clinometer must be pended at a certain distance above the centre of the cord. for cords at an inclination of about 15°, this distance is obtained y multiplying the length of the cord by 0'004 for each degree ; for greater angles, the length must be multiplied by 0-003 for each di'gree. Thus, with a cord 12 metres in length inclined at an angle of 20°, the clinometer must be suspended at a distance of 6' 7 2 metres from the lower end. In practice it is found sufficient to suspend the clinometer at the middle of the cord, when the latter is but slightly inclined. With highly ine\m&d cot', Vvt-

Mine-Sdkvbtino.

ever, it is advisable to euspeud the clinometer litvlfa yard from the two etids, and to take the mean of the two readings, ob the correct angle of iaciiaation. The error will thus not exceed k few minutes in a cord 10 yards in length.

The Hangiilg-CompasB.The compass-box is 3 to 4 inches in diameter. It is graduated into 360°, or, more frequently, into twice 12 hours. The numbering commences at the ends of the diameter marked north and south, the 12 o'clock line, and pro- ceeds from right to left. At the 6 o'clock line, the east and west points are transposed as in the ordinary miner's dial. In the larger compasses, each hour is divided into Ki parts; in the smaller ones, into 8 parts. Further Bub-di visions may be esti- mated with the eye. The compass is, as a rule, read in hours, eighths, and sixteenths of eighths. One hour is equal to 15*, one-eighth is 1° 51' 30", and one-sixteenth of an eighth is 7'

In order that the compass shall assume a horizontal position when suspended to the cord, it is constructed on the plan of a ship's compass. When the compass ia fastened in the gimbals of the hanging instrument, and suspended to the cord, the 12 o'clock line is in tho same vertical plane as the axis of the cord, and the compass hangs level at all times.

The original construction of Rossler'a

hanging-conipaas ia shown in Fig. 28, copied

from Voigtel's Geometria Subterranea, the

first complete treatise on mine-surveying

ever written. It was published in 1066.

All improved form of hanging-compass,

made by Osterland of Freiberg, ia shown

The hanging ring of the old compass is here

In order to keep tlie centre of

gravity as low as possible, the

clamping of the magnetio-needle

is effected by a large screw

underneath the compass-box.

The compass and clinometer fit into a leather case &8tened to a lielt worn round the sur- veyor's waist. A few hairs, some wax, and a plummet must always be carried in reserve, 'g' Sunreying with the German

DiaL — Id booking a survt'v

Kg. 28.

in Fig, 29.

replaced by two movable arms.

made with the Uerman dial, the date, the name of the mine, and &

J

description of tlie startiugpoint should tirat be noted. A lixed point having been selected as a, starting-point, intermediate pointa are eo chosen that they can be connected without hindrance by cords 6 to 6 fathoms in length. These points are either in the permanent timbering of the level, or in timbers teraporarily inserted for the purpose. At these pointa, cord-screws are fixed. The loop at the end of the cord is placed over the first screw. The cord is tightly stretched to the next screw, and having been wound round it two or three times, is carried on to the next again. Six to ten station-lines are thus obtained, and the survey is commenced. A plummet is dropped from the first screw to the floor of the level, and the perpendicular distance measured. The length of the stretched cord is measured by placing the measuring rod gently along it. The clinometer is then suspended from the middle of the cord, and the rise or fall read. Lastly, the hanging- compass is suspended to the cord near the end-point of the line, care being taken that the north end of the dial is directed towards the end-point of the line. The bearing of the cord is then read. The mode of procedure is the same with the other lines.

The observations are noted in the dialling-hook. In the column for remarks sketches of portions of the level are inserted, showing the position of the ofisets measured from the stretched cord. The bearing and dip of any veins or cross-courses met, should also be noted. As the end-point of the survey, a fixed point should, if possible, be selected, and the distance from the floor of the level measured. When great accuracy is required, a reverse survey is made as a check.

When the survey is complete, the bases and perpendiculara of the inclined lines have to be determined. The cord being the bypothenuse of a right-angled triangle, its length must be multiplied by the cosine of the angle of inclination, in order to obtain the base of the triangle, that is, the plotting length of the line. The perpendicular is obtained by multiplying the inclined length by the sine of the angle of inclination.

The form of dialling-book adopted is given on next page.

In this survey, the distances were measured in metres. The hangirtg-compasB used was divided into half-degrees, which were subdivided by the eye into tenths of degrees. The olinometer was also read to tenths of degrees. The figures obtained by calculation, in the "base" and "perpendicular" columns, are usually entered in red ink. If the survey is to be plotted trigonometrically or by means of the protractor, the observed hearings are first corrected for the magnetic declination. The following is an example of the method of booking recom- mended at the Freiberg School of Mines —

vrNE-SDItVETtSO,

Carl Mine, Alsace —Survey Of Adit Level With Tub Hauqing-Compass.

r

OD right

Timber,

&t e:;triuica to Level.

Vo.

LofUl.

iBcUMllon.

h™

Rsmcrta.

OfeHmA.

Oometad.

mw

tUL

R. W-0

I'M

To +

A

Vo

240*-9

2a8*-9

B

S-41

R. ri

aKP'S

S-40

F. 1-2

igs'-a

6-S2

D

4 'Si

R. r-8

188°-6

174' -6

E

F. (r-4

202" -8

0'O4

P

4'6S

R. I'-l

173*1

iai*-i

4'6d

i-as

] To fioM oflereL

In the HsTz, where a thin wire is used instead of a cord, the Btation-line ia, if possible, made 10 metres in length. The trigonometrical calculations are thus greatly facilitated, especially if logarithuia are usfid. The form of dialling-book adopted when the compass is divided into hours, is shown on the next page.

The right-hand page of the survey-book is reserved for sketches, showing the position of the offsets taken.

Plotting the Survey. — The survey may he plotted by means of

the coiupcus that was used underground. The plotting in- strument (Pig. 30), consists of a truly rectangular plat* of brass, 10 inches long and 5 inches wide, with a raised ring in the middle for the reception of th cotnpasa-box. The diameter of the ring parallel to the long side Fig. 30. of the plate is marked on its

surface by means of two fine tines. The compass-box is placed in the ring, and clamped so that the 12-hour line coincides with

d

THB aBBMAN DIAL.

s

O

I?

2:8

Ej

M

§?

is

El

5tii

2" s

lo e e e

e rt 04

a

g

s

e o o n

H H

+ '<PQOQHbiOtD'-3tiJ

MlXE-SURTEYINa

these two lines. The uppr edges of ttae reotaugular plate are bevelled, so as to dimmish the shadow ou the paper.

The paper, on which the ptau is to be drawn, is fastened tos horizontAl table. The plottlng-instrument is then placed on the paper, and turned until the marked end of the needle points to the north. A line is then drawn along the side of the plate whieb will represent the north line of the plan. A point for commencing the plotting is selected, and the instrument turned at that point until the needle points to the bearing of the first line. A line is then drawn along the side of the instrument, and the required distance measured with a scale.

This method presents the advanlge of plotting the survey

with the actual instrument used to make it, and consequently

with the same degree of approximation. But the errors due to

magnetic influences are not eliminated, as the conditions are not

the same as they were in the min&

In a drawing office, too, there are

always iron objects that may affect the

needle. At the French collieries of

Decize in Nivre, a drawing office has

been built in which all the ironwork

has been replaced by copper, for the

purpose of employing this instrument

without inconvenience.

Surveying with the Hanging-compass in the Presence of Ifod. — Numerous attempts have been made to modify the construction of the hanging-com- pass in such a way that it can i>e used for surveying over iron. Perhaps the most successful is the adjustable hangitig-compass (Fig. 31), invented by Mr. Pen- kert* of Beuthen. It is so arranged that it can be centred under the point of junction of two cords, and thus the bearing of the two lines can be taken from the same place. The instrumeut is manufactured by A, Ott, of Kempten, Bavaria.

In all instruments constructed on this principle, there is the disadvantage, apart from the diculty of centering the mag- netic-needle with a small plumb-line, that when cords with different inclinations come together, the position of the point of uspension of the needle difitrs vertically on the two eords, and, ooniequently, the essential feature of the method is defective. Thia drawback haa been obviated by a banging-eompasa invented by Air. Oscar Langer, of Glaustbal, in which the point of sus-

Berg. H, £lg., toL xxxix., 1880, p. 8.

V\g. 31.

The Okknan Dial.

B9

pension of tbe compass, which retnains unmoved, fortuB the Apex of the angle to bo measured.

Use of the Gennan Dial. — The haaging-compass in Germany Aod France is being repl&ced bj the theodolite ; but it is still found iiseful in narrow workings. It is occoaioaally used in America. Thus, in survejriag the Longdale iron mine in Virginia, Mr. G. R. Johnson has found it a useful auxiliary. The four main adit levels of the mine having been surveyed, and their entrances connected by level and theodolite lines, it remained to survey the stopes and workings in order to make a complete map, and to test the accuracy of the foregoing work. To do this with the theodolite aad level was out of the question, both on account of the roughness of the workings, and also because they were much too small — so .mall in places that a man could scarcely crawl through them. The hanging-compass was consequently used with very satisfactory results, the ends of the survey coinciding with the corresponding points deter- mined in the theodolite survey. A modification of the stretched string method htm been used with success by Mr. F. L Burr* in surveying secondary mine openings in the Lake Superior iron ore mines, the hivtiging-compass being dispensed with and the angles between the strings measured.

' Engmtaiug atid Mininy Jottmai, vol. Ixxx., 1003, p 568.

HINK-8URTSriNa

OHAPTER VIIL Thb Thbodolitb.

Historical Sketch. — In mine-Buryea, there extreme accuncj is required, the theodolite aEonld be employed. There is, how- ever, no oocotsion for it to be used exclusively, as the in<Kieni vernier-dial is a form of theodolite, which from its simplicity &nd compactness is better adapted for underground work than tha theodolite itself, and proved by severe tests to give highly aatiafactory results. For aur&ce-snrveying the dial is, however, decidedly inferior to the theodolite.

The employment of improved matruraents for measurmg angles underground in place of the compass, dates from the end of the Ifith century, In 1T98, H, 0. W. Breithuupt, of Cassel, invented a mine-aurveying instrument, resetnbling au oitrol. This was essentially a theodolite. It had a graduated horizontal circle with verniers, a vertical arc, a sighting-tube, and a com- pass. Two sets of legs were used with the instrumeDt. In the same year, Professor Guiliani, of Klageu&irt, invented a mining theodolite, calling it a caUigeolabium. Mine-surveys, too, were made between the years 1795 and 1801 by the PoKsb General, Komarzewaki, with a graphometre stnitfrrain which he invented, Since 1832, the theodolite has been used, more or leas, in alt mine-surveys, where great accuracy is required. Theodolites specially constructed for mining purposes are now made in great numbers by the continental and American instniment-makera In Great Britain, however, the tendency has been to improvs the construction of the circnmferenter, making it more and more like the theodolite, so that with it results can be obtained ai accurate aa those made with a German mining theodolite of tlid same size.

Description of the Theodolite, — The theodolite is the moat important, but at tlie same time the most complicated, instru- ment used by the mine-surveyor. In general outline, it may described as a telescope mounted on a horizontal and a vertical axis, in such a way that the horizontal and vertical rotation of its optical axis may be measured.

d

The Theodolite.

There are many forms of theodolite, hut there are certain.

sential parts common to all. The cost of a theodolite being

considerable, the niine-aur- veyor is, as a rule, not in a position to have sevei-al of diflerent aizea. In purchas- ing an instrument, therefore, he must select one which will fulfil all his requirements. It must ho sufficiently large to give accurate results in tri- angulation, and at the same time it must be sufficiently portable to be used iii the mine. In its construction, all metal must he avoided that will affect the magnetic- needle. The horizontal circle should be 5 inches in dia- meter, divided into half- degrees, and provided with verniers reading to single minutes.

The various parts of the theodolite are shown in Fig. 32. The most important part is the horizontal circle, G, which has its edge bevelled and graduated, the degrees being numbered continuously round it towards the right up to 360°. At the centre of this circle is another cir- cular plate, the vemier-plata F, capable of rotation inde- pendently of the horizontal circle. On the vernier-plate is engraved a line, the index line, passing exactly through the centre, the end-points, or indices, extending to the graduation of the horizontal indices are provided with vernier.s, read by means

the microscopes jf, which are sometimea provided with plates

prj to reileot light on the scale. The hotuonlai

iHErSVRyEYisa,

the vernier-plate together are sooaetiutes termed the Aorteofilal| limb, in which <mse G is called the lower limb. The instrument' ' makers' names are (F) plate, and (G) limb.

On the vernier-plate are two nprighte or supports, D, D, whici support the horiioatal axis, 0, of the vertical or altitude etrele, E. The latter ia provided with two indices with verniers at the opposite ends of a horizontal bar, read by the microscopes e, i The telescope A B is fixed directly upon the horizontal axis. I

The horizontal circle is screwed by a flange to a brass verticsl axis, K, passing through the collar of a clarop, where it may be lixed or loosened by the clamp screw, L Below the collar, the vertical axis works freely on a ball and socket joint at its lowei end. The ball and socket is placed between the parallel plates, L, M, which are provided with four levelling screws, I. The vernier-plate is provided with two spirit-levels, /,/, and a longer spirit-level, e, is attached to the telescope. The whole instrument is supported on a strong tripod stand. M

The vertical circle is divided into four quadrants, the degree! in each of which are numbered from 0° to 90', as shown in Pig. 33. In the old-fiaahioned theodolite the verti- cal limb is a semicircle. This is surmoanted by an oblong flat piece of brass, the itaffe, to the ends of which are screwed the two forked rests called Y's, by which the bell-metal collars of the telescope are supported. Under the tele- scope JB a long spirit-level. A theodolite of this kind is trmed a plnne theodolite, whilst one with a complete circle as vertical limb is termed a tramil theodolite. The advantages presented by the latter form are the greater vertical sweep of the ' telescope and the greater accuracy of the readings of the vertical limb.

Connected with the horizontal circle and vernier-plate, tfaers are two screws, H, I, one of which, H, is a clamping screw and the other a slow-motion or tangent screw. When H is loose, the two plates, G and P, can be moved independently, but when the screw H is tightened they can only be moved separately by means of the tangent screw I. Beneath the horizontal plates, ther are two screws, and t, one of which, k, is a clamping screw and the other a tangent screw. When the screw k is loose, the whole of the upper part of the theodolite above the screw lean be rotated in either direction, in which case the horizontal fl circle moves upon the double conical axis upon which it rests. " On tightening the screw h, the upper part can be moved only by means of the tangent screw Two screws rofer to the vertical

Fig. 3S,

The Theodolite,

ss

eirole, a claiopiag acrew and a taiigent screw d. When the

clamping screw is loose, the

V?i . r;, vertical circle can be moved

freely; but when it la

tightened, the circle can be moved only by means of the tangent screw d.

Ab an aid to memory, the screws may be divided into three sets, each of which consists of a clamping and a tangent screw. The upper set belongs solely to the vertical circle ; the centre set, H, I, belongs to the horizontal circle F ; and the lower set, h, i, refers to the entire portion of the instrument above it.

The circular platea with their accompanying sockets are shown in section in Fig. 34. The upper plate carry-

Fig. 34.

mg the compass-box, Ac., is screwed fast to the flange of the interior spindle, the lower plate is fastened to the exterior socket, which in its turn la fitted to and turns in the hollow socket of the levelling head.

The telescope consists of two tubes, one sliding within the other, with the object glass at the further end. A, of the outer tube, and with an eye-piece at the nearer end, B, of the iiner tube. The object glass is achromatic, that is, made of two lenses, one of crown and one of flint-glass, the curvatures of which are suitably combined. The object glass forms between the eye-piece and its principal focus an inverted image of the object sighted, and the eye-piece, consisting of two condensing lenses, acta as a magnifying glass, and gives a virtual and highly magnified image of the inverted image thus obtained. Some- times, especiaUy in American instruments, the eye-piece ia made up of four plano-convex lenses. An erect image is thus obtained. An erecting eye-piece, however, causes a considerable loss of light, and is therefore not to be recommended. It requires but little practice to get accustomed to the use of an inverting eye-piece, and the brilliancy with which objects appear, owing to the amount of light gained by dispensing with two leiues, is vejy marked in comporiaon mtla tW na'ffAi

94 Hime-Sdrtbtins.

obtained with an erecting eye-piece of the same power. The telescope ra&y be focuBsed hy moving the inner tube by a rack and pinion turned by the milled head, b (Fig. 32).

The rays proceeding from the object-glass form a cone of light In order to get a line from the point of the cone straight througli the optical centre of the object-glasB, and on, without deviatiou, to the object examined, recourse must be bad to the device of eoUimation. The collimator of a theodolite telescope ia a circular brass diaphragm, with a hole about half an inch in diameter in its centre It has a rim on its edge, and in this are the colUmating screws, a, a. The hole ia crossed by three spider- weba or equally fine platinum pj„ 35

wires (see Fig. 35), one horizonl, A B, and the other two, D, EG, deviating slightly to opposite sides of a vertical plane. The point F where the wires cross each other should be exactly in the axis or line of collimation of the telescope. It ia adjusted to that position by the collimating screws.

Vatioua Forms.— (a.) Hoakold's transit-theodolite is an instm- tuent of great perfection, specially adapted for mining work. It differs from the ordinary transit-theodolite in the arrangement of the upper plate, which is made to project over the lower plate at the points where the upright supports are attached, so as to enable a larger compass to be employed. Thus, a 5<inch circle will carry a 4i-inch compass; whilst in an ordinary theodolite of the same size a 2 i -inch compass would be used. The Hoskold theodolite presents the further advantage that the compass is not obscured by the appendages of the upper plate. In order to enable short sights to be taken, a pair of folding sights, like those of a miner's dial, are fixed to the top of the telescope. The instrument is also provided with a diagonal eye-piece, which enables the telescope to be pointed vertically without any discomfort to the observer.

In this theodolite and some others, a second telescope is some- times attached below the horizontal circle. This is used like the outer pair of sights of the Henderson dial, to determine whether the circle has been disturbed during the interval between two observations.

(b.) The Everest TbeodoUte. — This instrument differs con- siderably from the ordLaary transit-theodolite, though the principles of its construction are exactly the same. It was designed by Captain Everest, and was first made by Messrs. Troughton &, Simms in 1838. Instead of the upper parallel nlate this instrument has three diverging arm& (Fig. 3G) vith

HIirE-SDBTKTIirO.

a vertical leTellmg screw aupporting the end of each. Each Bcrew has a flange at its lower end, bj means of which it la held down to the plate forming the top of the staff head. Ths chief advantage of this construction is that the three levelling screws can be adjusted with one hand, whilst the adjustment of four levelling screws requires both bands.

Fig 38.

The vernier-plate is represented in the Everest theodolite hf four radiating arms, three with verniers, the fourth with clamp- ing and tangent screws. The verniers are read with the aid of an independently moving microscope. The mean of three readings is thus obtained for each observation-

The telescope is permanently &xed to the horizontal axis by means of a collar-like expansion at the middle of the bell-metal axis, into which the telescope is fixed. Instead of a vertical circle, the Everest theodolite has two opposite sectors of about 90° each, so as to be capable of measuring elevations and depres- sions, as &r as 45*. The horizontal axis works in a Y-shaped upright The spirit-level is not attached to the telescope, bat to the index bar. The circular compass-box of the ordinary instrument ia replaced by a long compass-box placed above the telescope, reading only a few degrees east or west of the magnetic meridian. The spirit-level for the horizontal circle ia attached to a stage below the Y's.

(c) The Hoffi&an Tripod Head.— The theodolite! made by

The Theodolite,

HeBBTS. J. Davis il: Son are provided with the Hoffman tripod bead (see p. 64). Ever since the introduction of the theodolite, efforts bare been made to give it the same facility of levelling as il poBsefised bj the miner's dial. The ball and socket motion has been frequently tried. The upper part of a theodolite is, how ever, madi heavier than that of the dial, and requires more binding power than can be obtained with an onlinnry ball and ocket joint.

The great need for a tripod that can be easily manipulated is ftpparent, as it rarely happens that there is a level surface oa which to set the theodolite, and much of the time in surveying is employed in adjusting the levelling screws. It has been pointed out that it is almost impossible to level up a sensitive bubble so that it will remain in position long enough for a satis- &ctory sight to be taken, and the difficulty of centering a plummet over a station has also been shown. Tho latter defect has been obviated by the addition of the sliding-head, which permits the entire instrnnient, with its plummet, to be accurately placed over a fixed point, after the operation has been approximately per- formed by moving the legs.

The HofTman tripod head,* as modified by Professor J. H. Harden of the Univerrit of Fennaylvania, is shown in Fig 37.

Fig. 37.

On unscrewing tbt levelling screws, the plate forming part of the tocket of the small ball, the centre of which is the axis of the instrument, and the point from which the plummet is suspended, can be moved in any direction within the limits of the inside opening of the screw cap. It will be observed that besides the small ball and socket, there is an extra and larger ball and socket formed by a part of the plate to which the instrument is fastened,

Traat. Amer. Intl. Min, Eng., vol. vvi., ¥, 8ft.

98 mirB-SDKVETixo.

and the prt to which the levelling screws are attached. Thp latter part always reniains parallel to the £crw cap of the tripoJ head, on which the points of the levelling screws rest, so that whatever position the inatmment maj assume in relation to the tripod bead, the screw wjJl always act directly perpendicular to both platea.

Under all conditiona, the instrument moves apon a oommon to the two balls, this being the point to which the plummet is attached. It is therefore impossible for the plummet not to be perpendicular to the axis of the instrament.

The advantages claimed for the HoSmaa tripod hoad are follows : — 1. A saving of one-half to two-thirds of the time usually occupied witJi screwing and unscrewing as in the old plan. The instrument can be levelled approximately without the use of the screws. Less than half a turn then nece.a8ary to bring the instrument to a perfect level, the operation at the same time clamping it. 2. The levelling screws are at all times perpendi- cular to the plat-a to which they are attached, and to the plate aud screw cap on which they rest. 3. The levelling screws are reduced in length, and their duty to a minimum, the instrument being no higher nor heavier than before. 4, The shifting head for plumbing over a fixed point — an improvement common to all first-class instruments — is retained, and no extra screws are required to clamp the instrument. 6. The levelling screws are covered from dust, and at the same time are no obstruction to the working of the instrument in any position in which it can be placed.

Numerous other attempts have been made to apply the ball and socket motion for levelling theodolites rapidly, and several American devices of this kind have proved very succesafi)!. Thus, Messrs. W, h L. E. Gurley, of Troy, have patented n quick-levelling tripod, somewhat similar in principle to that ty'. Hoffman. The spherical surfaces are, in this case, concave, anti the friction of these sur&ces may be increased or diutiiiisbed at will by means of spiral springs. Messrs, C. L. Berger &. Sons, of Boston, furnish their theodolites with a quick-levelliug attachment, which does not form part of the instrument proper, but consists of a coupling, with a ball anil socket joint, which can be screwed between the instrument and the tripod.

{d,) American Theodolites. — In America, the miner's dial is very rarely used for mine-surveys. In all important work, the trauut-theodolite is alone used. This instrument is known iu Ameriea aa the traintU. The name theodolite is reserved for the Y-instrument in which the telescope cannot be revolved on its horizontal iixia, The transit ins trumeivt which h&a no vertical

Fig. ZlA.-TheodoUte of the Jlwerican type, wi* HoBmMi Vw&.

lU8E-CRTETt>-a.

circle and no spirit-level attftched to its telescope is called the plain transit.

An excellent transit- theodolite, msnufactirred by Messn. Heller & Brightly, of Philadelphia, is described by Dr. B. W. Baymond.* It is a small portable instrument specially adapted for ase in mine-surveying. The principal peculiarity is the rib- bing and flanging of the parts requiring strength, bo as to dispose the minimum amount of material where it will secure the greatest rigidity. The horizontal circle is 4J inches in diameter, and is read by two double opposite vemiera, placed outside the compais. box, the vernier openings in the plate being made very wide so as to allow the e-asy reading of the graduations. There is a 3-inch magnetic-needle, and its ring is divided to half-degrees. Tha telescope is inches long, with an erecting eye-pieca A sensi- tive level, inches long, is attached to the telescope. The tripod is famished with a shifting head for precise centering. Clamps and tangent-screw movements are supplied to the plates and vertical circle- The graduation of the compass ring suid of the horizontal circle is continuous from to 3G0'. The weight of the instrument, exclusive of the tripod, is lbs. The weight of the tripod is lbs. The height of the instrument from the tripod legs is 7 inches, the extreme dinmeter of the plates 5 inches. The instrument and tripod head are packed in a box inches square, arranged with strapi to allow its being carried over the shoulder, while the folded tripod legs serve as a walking-stick. Such compactness sad lightness are very important for underground work. This also applies to aurface-surveys, especially in a country like America, where the J urveyor has often to carry his own instrument.

Traveller' B Tian Bit- Theodolite.— A still smaller transit- theodolite is manufactured by Mr. L, OaseUa, of London, for the use of travellers. It has complete 3-inch circles, both vertical and horiiiontal, with vemiera reading to one minute. It can there- fore be used as an altajdmuth for determining time, latitude, and azimuth, as well as for ordinary surveying purposes. Its telescope is eccentric. It is provided with a diagonal eye-piece and a reflector for illuminating the cross-wires. It is thus well adapted for shaft-surveying. It ia supplied with a dark glasi for soUr observations, a finely divided level, and a compass. H packs in a mahogany case, inches by 5) inches, aiid 4 inches deep ; the whole weighing only lbs.

A light tripod stand is added. Many important surveys bava been made with the instrument with -very satisfactory results.

TVaiu, Amer, Iiul, Jfin. £ng,, vol. 1., p. S7$.

Tus Theodolite.

This inBtrument is also coastructed with the telescope in the centre, the supports being raised to allow it to revolve vertically. 67 this arrangement, whilst the height is increased, the width is reduced in proportioa.

Adjustments of the Theodolite. — Every time the instrumeat is used, the observer must make the following adjustments: —

1. Place the theodolite exactly over the station by means of a plummet hung from a hook direutly under the vertical axis. It must next be levelled, that is to say, the vertical axis must be placed truly vertical. The easiest way to do this is to make the vernier-plate truly horizontal, by means of the spirit-levels, /, / (Fig. 32), For this purpose, the vernier-plate is turned into such a position that the two spiitrle'els shall be parallel to the two diagonals of the square formed by the four levelling screws. Two opposite screws must then be turned simultaneously and equally, but in opposite directions, until the bubble is brought to the centre of the leveL The other screws are then turned in the same way, until the bubble of the second level is brought to the centre of its tube.

A more exact adjustment can be made by means of the larger and more delicate level, c, attached to the telescope. For this purpose, set the instrument approximately level, clamp the axis of the limb by k, leaving the plate free, and move the latter until the telescope is over two of the levelling screws. Then bring the bubble to the middle of its tube by the tangent screw, d. Then turn the vernier-plate, carrying with it the telescope, throgh half a revolution, and if the bubble is not in the centre of the tube, bring it half way back by the tangent screw, and the other half by the levelling screw. Repeat this until the bubble remains central with the telescope in either position. Then turn the vernier-plate through 90°, so as to place the telescope at right angles to its former position, and repeat the process until at last the bubble remains central during the complete rotation of the telescope. If the instrument is correctly con- structed, the vernier of the vertical circle should read 0° 0'.

If the hubbies are not at the centres of the vernier-plate levels, when the bubble remains central in the level attached to the telescope, the vernier-plate levels are not truly perpendicular to the vertical axis, and must be adjusted by mens of the screws at their ends. This adjustment is rarely required with a well- made theodolite.

2. When the image of the object viewed, formed by the object glass, either falls short of or beyond the place of the crosB-wires, an error arises, which is called parallax. Its existence may be detected by moving the head from side to aide l<;tVdi\%

102 Uine-Sdbtktinq.

through tlie telescope, observing whether the image appears to move. To correct this error, the eye-piece must first be adjusted bj menB of the movable eje-piece tube, until the cross-wirei are seen clearly defined. Then direct the telescope to boi clistant object, and by means of the miUed-head screw, 6 32), at the side of the telescope, move the inner tube in or oat until the proper focus is obtained. When disregarded, parallas gives rise to serious error.

3. In addition to the temporary adjustments described above, there are certain permanent adjustmenta which should be tested from time to time, but which in a well-made theodolite seldom require correction.

The adjustment of the line of eoUimation consists in placing that lute accurately at right angles to the horizontal axis. To effect this, direct the telescope to a distant object, making the cross-wires bisect the object precisely. Then carefally lift the telescope out of its bearings, and replace with the ends reversed. Revolve vertically, and again direct the telescope to the distant object. If the cross-wires still coincide with the object, the line of collimatton is perpendicular to the horizontal axis. If not, move the cross-wires one-half of the deviation bj turning the screws holding the diaphragm, and correct the other hoM by moving the tangent screw of the horizontal circle. Eeverse the telescope again, and repeat the operation until the adjustment is perfect.

In the Y-theodolite, the line of eoUimation is adjusted by bringing the intersection of the cross-wires upon some well- defined distant object. The telescope is turned round on its collars in the Y's until the level is uppermost. Then, if the cross-wires do not continue to coincide with the object, half the difference must be corrected by moving the cross-wires, and the other half by moving the tangent screw of the horiaontal circle.

4. The level attached to the telescope must be parallel to the adjusted line of eoUimation. To effect this adjustment in the transit-theodolite, the elevation or depression of a distant object is taken. The instrument is then reversed, the telescope revolved vertically, and again directed to the same object. The mean of the two readings will be the true elevation or depression of the object Set the verniers to this mean angle, and again observe the object, making the intersection by means of the screws retaining the index in its horizontal position. Then, correct the level by its own adjusting screws.

To effect the adjustment in the Y-theodolite, the clips for securing the supports that bold the telescope should be thrown open, and tlie bubble of the spirit-level brought to the centre of

The Theodolite,

the tube by means of the tangent screw attached to the vertical arc. The telescope should then be lifted out of its supports, and reversed. If the bubble does not remain central, correct half the error by the adjusting screws connecting the level with the telescope, and the other half by the tEtngent screw of the vertical arc.

5. When the telescope level has been adjusted, and the vemier- plate is truly horizontal, it is necessary to note whether the zero of the verti<ml circle coincides with the zero of its vernier. If it does, there is no index-error. If it does not, the amount of error should be noted and applied aa a constant correction to all subsequent readings,

G. The adjustment of the horizontal axis exactly perpendicular to the vertical ax.is is, as a rule, lefl to the instrumentmaker. In some theodolites, however, there are adjusting screws for the supports of the vertical axis. This is usually the case in instru- ments of Amorican make. In order to determine whether the horizontal axis is perpendicular to the vertical axi,?, direct the intersection of the cross- wires to an object, the altitude of which is considerable. Then turn the vertical limb, until the cross-wire* cut some other well-defiued point near the ground. Kevolve the telescope on its axis, and turn the vernier-plate 180*. Then if, in raising and lowering the telescope, the line of coUimatiou passes through the two objects, the adjustment is correct. If not, half the deviation is to be corrected by the tangent screw of the hori- zontal circle, and the other half by the adjusting screws of the supports. The operation must be repeated until the adjustment is correct.

The permanent adjustments described above should be made with great care. Many valuable instruments have been injured by students who were anxious to adjust them, hut were un- acquainted with the method. It is necessary to be quite certain that an adjustment is required before a screw is touched,

Heasuring Horizontal Angles. — The theodolite, having been set up so that the centre of the horizontal circle is perpendicularly abo\e or below the station-point, is carefully levelled. The horizontal vernier-plato is then clamped at zero. The position of the second vernier is noted, in case it does not read 180* exactly. The horizontal circle and vernier-plate clamped to- gftlier are turned, until the telescope is directed to the left-hand station. The horizontal circle is then clamped, and the cross- wires are made to accurately bisect the point by means of the tan- gent screw. The remier-plate is then released, and the telescope carefully moved, the lower supports only being touched, until the right-hand object is bisected. The vernier Dlate \at\vbTL(i\Bn.',

UING-aUBVETJNO.

:

&nd the crosB-wires are made to accurately coincide with the ob- ject by means of the tangent screw attached to the vernier-plate. The two vemierB have thus described an arc on the horizontal circle equal to the angle to be measured. This may be read direct from vernier I. With vernier II. it is found by taking the difference of its two readings. The mean of the results ob tained with the two verniers is taken as the correct angle.

Another method of measuring horiiontal angles is to clainp the horizontal circle in any position. Then, direct the telescope to one of the stations, clamp the vernier-plate, and turn the tan- gent screw attached until the cross-wires accurately bisect the left-hand object. Read the angles indicated by the two verniers, and note the mean of the two re-adinga. Then release the vernier-plate, and move the telescope until the right-hand object is bisected. Olamp the vernier-plate, and make the cross- wires accurately coincide with the object by means of the tangent screw. Again read the two verniers, and note the mean of the two readings. The difference between the first and second mean readings will be the horizontal angular distance between the two points, Thus, as an example ; —

The first reading . The second reading

Vprnlor I.

Its- 11' 259° 35'

VorB'Ipi- II,

353° ir 79" 34'

Correct angle,

MefcD.

173° ll'uO" 259" 34' 30"

86* 23' W

The reason for reading the two verniers is to correct any error due to eccentricity or incorrect graduation of the pj&tea.

It is advisable to measure the angle a second time with the telescope invcfTted. The errors occurring during the first measurement also occur during the me&surement with the tnle- Bcope inverted, but on the opposite side, so that the mean of the two measurements gives a result nearly free from error.

Repetition. — In measuring horizontal angles, when gret accuracy is required, the errors of graduation may be diminished by the process known as repeating, an operation invented by Tobias Mayer, of Gottingon, in 1752.

The mode of procedure is as follows :— Determine the horizontal angle between the points A and B in the usual way, the vernier plate being clamped at zero. Let the angular distance between A and B be 30' 10'. Now, leaving the vernier-plate clamped to the horizontal circle, unclamp the vertical axis, and turn the instruinent back to A Then clamp the vertical axis, release the vernier-plate, and again direct the telescope to B. In this way the reading will be repeated, beginning at 30° 10' instead of

Tue Tueodoute.

(y. Suppose the result iiow is 60° 25'. Repeat again, etart- ing this time from 60° 25', and suppose that the third result is 90' 40'. IMTidiiig this result by the number of readings, we obtain, as mean result, 30* 1 3' 20",

The operation may be repeated any number of times, care Ifeing always takon to direct the telescope towards A by turning the Tertical axis, and towards B by turning the vemier-plate. For each complete revolution of the vernier-plate, 360° must be allowed. It is advisable to perform the operation with the telescope inverted, and to take the mean of the two resulti obtained with the telescope in its two positions,

The following is an example of repetition : —

The horizontal angular distance between the two points determined in the usual way was 102* 45'. On repeating, ths following results were obtained : —

Ver. L 61* tW 49* Ver. II. 231* OO" 45"

11 Wd.

411" Off 45'

102*45' 11'

to'

Ver. I. 153* 45' 45" Ver. n. 333* 45' 45'

613* 45' la'

102* 4ft' (W

Ver, IL 7G* 31' (X)" f

816*31' 00"

102* 45' 10'

With

obtained

the

telescope inverted, the following

results were

Ver. I. 51' 00' 15* Ver. 11. 231*00' 15*

Ueau. 411*00' 15*

102° 45' 04'

to'

Ver. 1. 153* 45' W 1 Ver. II. 333° 45' .W (

513° 45' 25'

102° 45' Ob'

to'

Ver. J. 256° ai' iiy

Ver. II. 76° 30' 30'

Menn 102* 45'

616° 30' 35- 08'.

102:45' 06*

Meaanrement of Vertical Angles. — The instrument having been carefully levelled, the telescope is directed to the object, the elevation or depression of which is to be measured. The crosa- irires are made to accurately bisect the object by means of the

Uuib-Survevikq.

tangent screw attached to the vertical circle. The angle is then read from both Temiers, and the mean of the two readings taken as the correct angle. When great accuracy ia required, the determination should also he made with the telescope inverted.

The following is an example of the measurement of a vertio] angle in this way : —

It Mill ng.

With TelMoop* InttrtcJ,

Uetn.

Vernier I,

12° 45'

13' 0'2'

12° 53' 30'

Vernier II.

13" 06'

12' 40'

12" 63' 00"

Mean

12° 63' 16'

The Solar Attachment is a contrivance that is fastened to the telescope axis of xYmerican transit instruments for the purposa of determining the true meridian. The principle was enunciated by W. A. Burt, of Michigan, and applied by Mm to the compass in 1836. It has since come into gene- ral use in the surveys of the United States public lands, the principal lines of which are set-out with reference to the true meridian.*

The Burt solar compass consists mainly of three arcs of circles, by which can Iw set off the latitude of a place, the declination of the sun, and the hour of the day. Through the centre of the hour arc passes a hollow socket, containingthe spindle of the declination arc. This is termed the polar axia When this axis is parallel to the axis of the earth, the vertical plane of the terres- trial line of sight, as defined by the slits in the vertical sights of the compass, coin- cides with the meridian.

Fig. 38.

Fig. 38 represents the solar apparatus placed upon the cross-bar of the transit-theodolite. The form represented was patented by

A doliiiled history of solar sarveying inatnirocntB has ))pcn written by 3. B, I>[iviB, Traiif. Amrr. M.E., vol. iix.. 1901, j). S03.

Th£ Theooolite,

Messrs. W. ife L. E. Ourley, of Troy. The foUowing is the manu- facturers' description of this attftchment : — A small circular disc, li inch in diameter, with a short round pivot projecting above its upper surface, ia first firmly screwed to the telescope axia Upon this pivot rests the enlarged base of the polar axis, which is also firmly connected with the disc by four capstan head BcrewB passing from the under side of the disc into the enlarged bftse. These screws serve to adjust the polar axis.

The hour circle surrounding the base of the polar axis is easily movable about it, and can be fastened at any point desired by two flat-headed screws above. It is divided to 5 minutes of time. It is figured from I. to XII., and is read by a small index fixed to the declination circle moving with it. A hollow socket, fitting closely to the polar axis, moves upon it, and may be clamped at any point desired by a milled-heod screw on top. By its two expanded arms below, this furnishes a firm support for the declination arc, which is securely fastened to it by two large screws.

The declination arc is about d inches in radius. It ia divided to quarter-degrees, and reads by its vernier to single minutes of arc, the divisions of both vernier and limb being in the same plane. At each end of the declination arm is a rectangular block of brass, in which is set a small convex lens, having its focus on the surface of a small silver plate fastened by screws to the Inside of the opposite block. On the surface of the plate, two sets of lines are marked intersecting each other at right angles. The two sets are termed the hour lines and the equa- torial Unea, as having reference respectively to the hour of the day and the position of the sun in relation to the equator. The declina- tion arm is also provided with a clamp and tangent movement.

The latitude is set otf by means of a large vertical limb, below the telescope, having a radius of inches. The are is divided to 30 minutes, and is figured from the centre each way in two rows, from 0" to 80°, and from 90° to 10°, the former series being intended for reading vertical angles, the latter for setting off the latitude. It is read by its vernier to eiogle minutes. It has a mp screw inserted near its centre, by which it can be clamped

tlie telescope axis in any desired position. The vernier of the

rtical limb is made movable by the tangent screw, attached so that its zero is readily made to coincide with that of the limb when the arc is clamped to the axis in adjusting the limb to the level of the telescope.

A spirit-level on the under side of the telescope, provided with a scale, ia indispensable in the use of the solar attachment. sn the telescope is made horizoutal by ilB ftm\ANa\,\JiMi

Hine-Subveyino.

hourxircle will be in the plane of the horistm, the polar axis will point to the zenith, and the zeros of the vertical arc and its vernier will coincide. In this position of the instrument, if the arm ol the declination arc is placed at zero, and one lens directed to the Bun, its image will be seen between the lines on the silver plate of the opposite block, and will indicate its position in the heavens, on an instrument placed at the North Pole of the earth at the time of the equinoxes, or when the equator is in the plane of the horizon. K the telescope is inclined, as shown in Fig. 37, the polar axis will descend from the direction of the zenith. The angle through which it moves, being laid off on the vertical arc, and shown by its vernier to be (saj) 40°, will be the co-latitude of the place where the instrument is supposed to be used. The latitude itself is found by subtracting iO° from 90°, making it 60°. Now, if the declination arm remains at zero, and the lens is

r'n directed to the sun, its image will appear on the opposite e as before, the instrument being used at the time of the equinoxes at a latitude of 50°. When, however, the sun passes above or below the celestial equator, its declination or angular distance from it, as given in the Nautical Almanack, can bo allowed for and set off upon the arc, and the image brought into position as l>efore.

In order to do this, it is necessary that the latitude and declination be correctly set off upon their respective arcs, and that the instrument be moved in azimuth until the polar axis points to the pole of the heavens, or, in other words, is placed in the plane of the meridian. Thus the position of the sun's image will not only indicate the latitude of the place, the declinatioa of the sun for the given hour, and the apparent time, but also determine the meridian line passing through the place where the observation is made.

The latitude of a place — that is, its distance north or sont ot the equator, measured on a meridian — may be found by means of the solar attachment in the following manner : — First carefully level the instrument by means of the spirit-level of the telescope. Next clamp the vertical arc, and, by means of the tangent screw, make its zero and that of the vernier exactly coincide. Then, having the declination of the sun for 1 2 o'clock of the given day as affected by refraction carefully set out upon the declination arc, note also the equation of time. The sun is sometimes faster and sometimes slower than a clock adjusted to mean time, the difference being termed the equation of time. Fifteen or twenty minutes before noon, the telescope is directed to the north, aiul the object end lowered until, by moving the instrument on its spindle and the declination arc from side to side, the sun's

J

The Theodolite,

image is brought nearly into position lietween the equatorial lines. Then bring the declination arc directly in line with the tele- scope, clAnp the axis firmly, and with the tangent screw bring the image precisely between the lines, and keep it there with the tangent screw, raising it as long as it nms below the equatorial line — that is, as long as the aun continues to rise in the heavens.

When the sun rfoches the meridian, the image will remain stationary for an instant. The instant is, of course, apparent noon when the index of the hour-arc should indicate Xll, The latitude is determined by reading the vertical arc.

The angle through which the polar axis has moved, being measured from the zenith and not from the horizon, the angle read on the vertical limb is the complement of the latitude. The latitude may, however, be read direct from the inner row of figures on the arc, beginning with 90 at the centre and running to 10 on either side.

A very important addition to the solar attachment, patented by Messrs. W. i& L. E. Gurley, is shown in the figure. It ia an arrangement for recovering the latitude of a solar transits theodolite without referring to the vertical arc, and generally for setting the telescope at any desired angle in setting-out inclines. It consists of a spirit-level, connected by a short conical socket with the end of the telescope axis, to which it is clamped by a milled-head screw, and made adjustable by a screw and spring on opposite sides of the enlarged end of the level- tube. When the milled-head screw at the telescope axis is released, the level turns vertically upon the axis, and can thus be set at any angle with the telescope.

The latitude being set oS' upon the vertical arc, as usual, the level ia clamped, and centred. The telescope may then be released and used in running lines, until it is desired to recover the latitude again. This is accurately done with the spirit-level alone without referring to the vertical arc.

The declination of the sun given In the Nautical Almaruick from year to year is calculated for apparent noon at Greenwich. To determine it for any other hour at any other place, reference umst be mside not only to the difference of time arising firom the longitude, but also to the change of declination from day to day. Thus, supposing that the observations are being made at a pleice eight hours west of Greenwich, the declination given in the almanack for Greenwich noon of any day, will correspond to the declination at the place in question at 4 o'clock a.m,, of the same date. To this must be added algebraically the hourly change in the declination, also given in the almanack, A table may thus _be prepared giving the declination for each ho\it of tk d&'j.

CHAPTER IX. Travkksing Undebgbouwd,

Use of the Theodolite in the Mine.— In making a. surface- nrvey with the theodolite, one line may be measured, from which all the other distances may be calculated by making them sides of a series of imaginary triangles, the angles of which are deter- mined. This method obviously cannot bo employed in the narrow workings of a mine, and consequently recourse must always be had to the method of traversing, A traverse is a series of consecutive drafts, of which the lengths and bearings or azimuths are determined. When the miner's dial is used, the bearing of each course is determined by the needle inde- pendently of that of the preceding course. When the theodolite is used, the readings taken are the argles contained by each successive line and the preceding one.

When the station representing the angular point is marked on the roof of the level, the theodolite must be so placed that the centre of its horizontal circle is exactly perpendicular below that point. The accuracy of the survey depends to a very great extent upon the manner in which this operation is performed.

When the angular points are to bo permanently marked, brass or iron hooks (Fig. 39) may advantageously be used. The station- point is marked by a hole in the hook, through which a plumb-line may be passed. The hooks are driven into tho timbering of the roof, or with hard rock or masonry into wooden pegs driven into holes previ- ously drilled for the purpose. For centering, a plummet is employed, the point of which coincides with the axis of the line. When the plummet is steady, and its point is directly above the centre of the horizontal circle, the instrument is centered. A mark should be made on the spirit-level, or on the telescope, to indicate the position of the centre of the horizontal circle. In order to ascertain whether this mark is accurately in the axis of rotation of the theodolite, the mstrumont, having been care- fully levelled, is rotated under the plummet. If the mark is in

Fig. 39.

TSAT££aiNO trNSSRGROtJHD.

rertical axis of the theodolite, it will retain the some positioD tinder the point of the plummet during tlie rotation. If not, it irill describe a circle, the centre of which is the true pospt to be ospd for centering.

If the workings of the mine are so low that a tripod-stand cannot be used, recourse must be had to an icon arm screwed into the timbering or into a vertical prop, or to a thick board firmly fixed horizontally across the level, as a support for the instrument. A new theodolite stand, intended to replace the ordinary tripod, was shown at the Budapest Exhibition in 1885. It is the invention of Professor Ohrismir of the Schemnitz School of Mines. It consists of a support fixed across the level at such a height that the mine trucks can pass under- neath it, A survey can thus be made without interfering with the ordinary work of the mine. The instrument consists of two hollow wrought-iron pipes, one sliding within the other, in such a way that the length may rapidly be increased or decreased. By means of a steel wedge working in a screw, the stand may be forced against the side timbers of the level with a pressure of as as 800 lbs, without arty part of the construction being injured. The stand is prevented from rotating by providing it at one end with three steel points. These stands can be used from 35 inches up to 5 feet, and, with the lengthening bar sup- plied, up to G feet 9 inches in width. The total weight of the appaiKtus is 16 lbs. The plate for the reception of the theodolite is connected by a spindle with the outer iron pipe. This stand has been adopted in the Burveys of several of the Hungarian mines with considerable success.

In using the theodolite underground, care must be taken to avoid, as far as possible, short lines of sight. In the mine, the croBS-wircB may be made to coincide with the object, and the verniers may be read by artificial light, with the same precision as at the surface. The unfavourable atmospheric conditions, which BO often interfere with the accuracy of surveys at the sur- face, are not encountered underground. It cannot of course be denied that, in subterranean excavations, difficulties have to l)e overcome which never occur at the surface. For example, great difficulties are met with in surveying with the theodolite in very confined spaces, and particularly in shafts.

For long station-lines, a candlc-flame is the best object to sight, care being taken to shield it from draughts. With station-lines less than 30 fathoms in length, it is advisable to sight a plumb- line suspended from the angular point. This is distinctly seen OB a black line on a white ground, if a sheet of paper dipped in

lis

UIKB-StJBTETIKG.

oil is held beLind it, and illuminated from behind by the Same of n candle or lamj>. A sheet of paper rendered ti'ansparent ia tbia way is visible at a much greater distance thao a sheet simply illuminated from the front side. When the air of the mine ia quite clear, a plumb-line can be sighted in this way at a distance of 160 yards. Oare must be taken that the paper is not held ia front of the plumb<line and the light behind, as, in this case, tho telescope will be directed not to the plumb-line, but to its shadow, which also appears as a black line upon a white ground. j

Weieshach advocated the use of a plummet-lamp, the flame off which is accurately centered under the angular point. His lamp has, however, not been adopted to any great extent, as it ia found to oscillate even with a moderate air-current. In collieries, a safety-lamp suspended in the same way may be advantageously- used. A contrivance for turning the lamp on its longitudinal axis must be provided, in case one of the rods outside the glass cylinder obscures the flame. The flame of a safety-lamp burns very uniformly, and is a very good object to sight. The lamp, too, hangs very steadUy on account of its weight, M

In the anthracite mines of Pennsylvania, a plummet-lamp ia used in underground surveying. It consists of a brass lamp, suspended by two chains, and terminated below in a conical plummet It is provided with a so-called compensating ring, that is, a gimbal ring, surrounding and supporting the lamp, which swings freely within it upon an axis. The two chains are attached to this ring at the extremities of a diameter perpen- dicular to the aids. Thus the point of suspension, the centra of the lamp-Bame, and the steel point of the plummet always lie in a true vertical line, no matter how much the broaa chains may alter in length from the beating of the lamp or the wearing of the links. A shield at the top prevents the flame from burn- ing the string. These lamps are used in pairs for back aad forward observations.

The sal'ety-lamp may be supported on a truly horieontal tripod- rest, in which case it is advisable to use three tripods, a central one carrying the theodolite, and two others carrying safety-lamps in brass cups for back- and fore-sight respectively. Mr. W. F. Howard advocates the adoption of coloured glasses, red and green, for the object-lampa. Additional certainty is thus afforded from the impossibility of mistaking other mining lights for the object For the same reason, H. Haebner* employs a plummet-lamp with a red glass.

' Preuu. Zeittchr., vol. sxxii, p. 3O0. 1S8L

Tavkrs1N0 Underqhoditd.

In reading the grodnations of the theodolite, a copper or brass lunp sboold be used. The metal should be tested as to its free- dom from magnetic subiitauces. An oil lamp will bo found more agreeable to use than a candle. In fiery collieries, a small co)>per or hToaa safety-lamp must be used. Unfortunately, all safety- lamps give a poorer light than the open lamp or candle, and their construction will not permit of the flame being brought near the eorapasB graduation and the verniers. A method of increasing the illuminating power of safety-lamps, suggested by Mr. Przyborski,* a Hungarian mine-surveyor, appears, therefore, to

erit attention. To one of the rods guarding the gauze exter-

lly, a powerful condensing lens is fastened by means of a double- jointed arm. The lens can thus be brought into any position that may be desired. Safety -lamps modified in this way have been used for some time in the surveys of the Resicza collieries in Hungary, with great success. Mr. E. B. Ooxet in Penn- sylvania haa constructed a plummet-Mueseler safety-lamp for surveys in fiery mines.

An ingenious device recently suggested by Professor Brathuhn, of the Clausthal School of Mines, will proV.iably come into general use. To two of the rods outside the glass cy Under of the safety- lamp (Fig. 39a) a small plate is fastened by two screws. In the

J" i i "V

n

fi£. 39<i.

itre of this plate, opposite the flame, a tube is inserted, and into this a bored cork . Through the bored cork passes a curved glass rod, with a circular section 0'43 inch in diameter. The light which pas.'ies in at the terminal surface is totally reflected by the curved surfaces of the rod, and passes out ab

' Berg. H. Zig., vol. lUiL, p. 49, 1884. f Trant, Amer. Intt. M.E., vol ili, p. 39.

the lower which

the vernier, and umes free from

llINB-aUBV£YIN&

end in full inteDaity. The free end of the glass rod,

can eaaily be moved in ita oork-h older, is placed over

& steady adequate light is obtained. Even in

gaa it appears worth while to uae a light

Bafety-Ump for theodolite work, as the flame is so steady and so free from smoke.

A novel method of lighting has been adopted by Mr. Stanley, who has adapted the prismatic compass of the military surveyor for use underground. In this instrument the floating ring attached to the magnetic needle is made of transparent celluloid, and light is thrown under it from a small movable lamp by means of a large prism. The floating ring is divided to half- degrees, and the divisions can be very clearly read.

The electric light has been successfully applied to mine- surveying purposes, incandeaoent lamps being used as objects to be sighted, and a smaller incandescent lamp for reading the verniers. A convenient lamp, of the dry storage-battery type, weighs 8 ozs., has an H candle power bulb with silvered reflector, and furnishes light tor 6 hours.

When the theodolite is used underground, it is necessary to illuminate the cross-wires. This is best done by reflecting light into the telescope through the object-glass, in such a way that the object can, at the same time, be sighted without hindrance. For this purpose, a ring is fitted on to the object-end of the telescope. To the ring is fixed at an angle of 45° a piece of brass, silver-plated on the under side, with an elliptical hole in the centre. The optical axis of the telescope thus passes approzi- mately through the centre of (he hole in the reflector. Two forms of reflector are shown in Fig, 40. In one case there is an elliptical hole, in the other there is a small ellipse of nietaL A light held near the reflecting surfacd illuminates the cross-wires. Satisfactoiy results con be obtali)ed when the reflector is made of white cardboard. A small silver ball attached by a wire also answers well. For illuminating the cross-wires very little light is required. The elliptical hole of the one reflector must therefore not be too small, nor the small ellipse of the other too large. In the theodolites made by Messrs. Troughton and Simms, the cross-wires are iUuminated by means of a hole drilled in the supports, and a small mirror placed at an angle of 45°, in the axis of the telescope. The light is held near the supports, instead of near tb" object-glaea.

Fig. 40.

Tbater8Inc) Underobohnd.

Shades of white note-paper should be fixed to the verniep- inicroBcopea of the theodolite, and the light should be allowed to fall on the back of them. In this waj, the vernier can be read underground with great precision. In Bome theodolites, ground glass or ivory reflectors are placed above the verniers. They are useful, not only in the mine, but at the surface on a bright day when there is a diflBculty in reading the vernier owing to the glare of the silver surface.

The following is an example of the survey of a closed polygon with the theodolite ; —

So,olUat.

Hortttiotal Aijiflef.

Heridlu)

Mag. met, . .

O-Oo"

0*00'

Lint).

1 off nwg. msr.

121° 27'

121* 27'

2(iffl . . .

97' 36'

39" 03'

3 off 3 . . ,

W9' 01'

68' 04'

loe

4 off 3 . . ,

169*40'

47° 44'

S34

5 off 4 . . .

195' 32'

63° 16'

6 off 6 . . .

85' 31'

328° 47'

7 off 6 . . .

1S2* or

300° 64'

8 off 7 . . .

103* 34'

224*28'

9 off 6 . . .

104° 03'

148" 31'

10 off S . . .

262° 58'

231° 20'

1 off 10 . . .

69* C8'

121° 27'

proof line.

In traversing underground, the theodolite is set up at a station, B, and after levelling, and clamping the plates, the magnetic meridian is observed. The telescope is then directed to a line suspended down the shaft at A, The vernier-plate fa then released, and the telescope directed to the forward station at 0. The firat angle is entered in the survey-book as 0° 00', with the length of the line A B in the distance column. Tha angle indicated by the verniers is read, and noted in the cotnmn for horizontal angles. The distance, B 0, is then mesLsared., and

lit

HINE-SUfiTBttHS

noted with any remarks tliat may be neceasary. Then, remove

the inBtrument to 0, level, clamp the vernier-plate at zero, and direct the telescope to the back station, B. Release the vernier- plate, and direct the telescope to station D. Read the angle, and note it, while B is being measured. After reading the horizontal angles, the vertical angles are read if required, aad noted as angles of elevation or depression. Proceeding in thii way, the conclusion of the survey is arrived at.

Before this traverse can be laid down upon paper, the hori- zontal angles must be reduced to angles from the first line (in this case the magnetic meridian) as meridian for the whole. The rule for reducing the horizontal angles to plotting angles from one meridian is as follows : — Siile : To the first meridian angle add the next observed horizontal angle. If the sum exceeds 180°, deduct that amount from it. The remainder will be the Becond meridian angla To this, add the next observed angle and proceed as before. When the sum of the meridian angle and the next observed angle is less than 180°, it must be increased by IfiO". If, after deducting 180°, the remainder exceeds 360*, it must be diminished by that amount, to give the required meridian angle.

In the example given, the angles would be reduced to ono meridian in the following manner ; —

Meridiao 0" (W -(- Ist angle 1*21" 27' 121* 27' No. I mer, aogl*

No. 1 meridian a.ngle 121° 27' -t-2nd uigle 97° Sa'* 03' air 09' -180" 00' =3ff'03' No, 2

(39"03'-(-20901')-I8{r

(68° 04' + 159° 40'} - 180°

(47° 44' + 196* 32') - Iw

(63° 16'+ 85° 31') + 130°

(328° 47' + 152* 07') - 180*

(300° 54' + 103* 34'} - Isc

(224° 28' + 104° 03') - 180C

(148'31' -h262*58')-180°

(231' 29' + 6S1° 58') - 180°

68° 04' No. 3 47° 44' No. 4. 63°16' No. 5

328° 47' No. S =300° 54'= No. 7 224° 28' No. a 14r 31' No. 9 231'29' No. 10 121° 27'= Proof

In working a closed traverse, the angles recorded form the angles of the polygon. If the survey has been kept on the left hand these angles will be interior ones, and a means is afforded of testing the accuracy of the survey, as the interior angles of the polygon together with four right angles should he equal to twice as many right angles as the figure has sides.

The interior angles of a traverse may be found from the bear- ings or courses by the following rules : —

Tbavkbbino Usdkrgkoono,

1. When the two lines lie m the first &nd second quadrants, N.-E. and S.-E., or iu the third and fourth quadrants, S.-W. and N.-W., their sum is the interior angle.

2. When the two lines lie in the first and third quadrants, N,-E. and S.-W., or in the second and fourth quadrants, S.-K nd N.-W., their difference is the interior angle.

3. When the two lines lie in the second and third quadrants, 8.>£. and S.-W., or in the first and fourth quadrants, N.-B. and If.-W., their sum deducted from 180' is the interior angle.

4. When the two lines lie both in the same quadrant, their difference added to 180° is the interior angle.

For example. — Let line 1 bear N. 63* 16' E,, and line 2 bear 6. 59* 06' E., then the angle between the two bearings ii

63° 16' + 59° 06' 122° 22'.

There is another method of measuring angles well adapted for use in mines. It is, however, only practicable with a transit- theodolite. The mode of procedure is as follows ; — Olamp the vernier-plate at 0' 00', unclamp the vertical axta ; direct the tele- scope to the back object, and direct the line of collimation exactly towards the object by the tangent screw of the vertical axis. Revolve the telescope vertically. Unclamp the vemier-plata ; direct the telescope to the forward object; clamp the vernier- plate, and direct the line of coUiniatioo exactly towards the object by the tangent screw of the vernier-plate. Angles where the vernier has moved in the direction of the graduation are minus, or to be subtracted. When the vernier has moved in the opposite direction, the angles are plus, or to be added.

This is the method of surveying adopted in the anthracite mines of Pennsylvania. Mr. E. B. Ooxe* works with the transit- theodolite and plummet-lamps, with a single assistant, in the following manner ; — He first selects the stations, marking the places where spuds, or nails with a hole in the head, are to be driven into the timbers. This is done before any instrumental work is begun, as much labour can be spared, and very short sights can often be avoided. When the stations have been marked out, he goes to station 3 with the transitr theodolite, and by means of the plumb-bob belonging to the instrument centres hia instrument exactly under the spud. His assistant in the meantime takes the two plummet-lamps, suspends one from spud No. 1, and the other from spud No. 3, and then comes back to hold the light while the final adjustments are made and the readings taken. Mr. Ooxe sets the vernier at zero, and sights back to lamp No. 1. He then reads the compass-needle, inverts

TVan* Amer. Itui. Min. Etig., vol. i., p. 375 ; vol, U., 2W.

H 118

HiKE-enayBTiNa.

tile telescope, and iights the lamp at station 3. Having the two vemierB and the needle, he turns the telescope back,

siglits Ko. I, and turns the vernier-plate round nearly 180° until he sights No. 3, when he again reads the two vemiera. Thus ba

obtains four readings of the deflection from the verniers, and % compass reading as a check. If the readings are concordant, he ia sure that there is no mistake, and proceeds with the instrument

to No. 3. In the meantime the assistant brings the plummet-lamp from No. 1 to No. 2, and then takes the lamp &om No. 3 to

140. 4, The distAnces arc measured with a 500-foot steel band.

A survey made by Mr. Ooxe, iu the anthracite coal region of

Fennsylvania, of a closed polygon with a periphery of 66G0*19 feet gave the following results : —

Statioii.

RntiOD Anu

DlSTAfrcA

.

Lett

0=04'

+ o'fti'

FtM.

0°47'

+ O- 51'

o'sir

- 0° 01'

40S60

0'33'

+ 0° 32'

fi

179' 32-

-179'' 00'

B

3V 12'

-2J0°r2'

Ss-4S

Bi

ir39'

-229° 51'

3S9-50

B,

9° 36'

-23r27'

631 Do

B,

4° 06'

-235° 21'

3S1-25

B,

35° 65'

- 199* 26'

752'50

B,

6-r 30'

-13e°47'

294 -So

F

G

or

- 145* 48'

86*27'

- 59° 21'

484 '85

44° 17'

- 103° 38'

5' 61'

- 108' 29'

Thaversinq Dsuebg Hound.

The mode of procedure in tbe surveys of the imthracite mines of Pennsylvania varies considerably in tbe ditterent districts. The excellent method adopted In the mines of the PenoBylvama Railroad has been fuUy described by Mr, "&. van A. Norris.* The surveying party consists of a theodolite-man, 8tation*man, backsight, foresight, and chain'man, 'th a fireman to attend to the safety of the party. Three tripods are used, but the wicks of the tripod lamps, which were found too large for accurate sight- ing, are replaced by steel wire one-sixteenth of an inch in diameter and three-eighths of an inch in height. The sights are taken to the bottom of this wire, and measurements are taken along tbe Una of sight with a 300-foot steel tape, marked at every 6 feet. The station-man keeps abf ad of the party and fixes the stations by drilling a small conical hole in the roof and suspending a plumb-line from an iron rod with a notched end fitting the hole. The point is then transferred to the floor. A better method is to put a horse-shoe nail, with a hole punched in the end, into a plug of wood driven into a hole in the roof, and then to suspend ihe plumb-line from tbe ring and to set up tbe theodolite under- neat)). A still better method is to put a shoe-peg holding a small loop of copper wire iu the hole.

Continuous azimuth angles are run, and the entries in the note- book consist of the vernier reading on a continuous gradation from 0° to 360°, and the quadrant reading or course. A needle reading is taken roughly with a view to detect serious errors. At the commencement of the survey, the vernier is set to the course of the first line taken from the notes of a previous survey. The error in a closed survey of fifteen or more lines is rarely found to exceed three minutes. For levelling purposes, tbe vertical angles are read very carefully, the sight-wire being so arranged that it isjustO'5 foot below the centre of the instrument. Tho method of booking adopted is shown on the next page. T)ie error on closing this survey is one minute. The horizontal distances, elevations, and vertical distances are calculated in the office; and the column headed " staff" gives the distance from the centre of the instrument to the station in the roof. With this method of surveying, it is possible to attain great speed, from forty to fifty stations being considered a fair night's work. All main itwtions are plotted from calculated latitudes and departures (see Chapter XI.), and tbe stations in the workings are filled in with the aid of the protractor. Where the roof is bad, trouble is often experienced in markin- the survey stations. In the Ohio collieries Mr. C. M. Henretta bus employed the following

School of Mina Qnarlerly, vol. li., 1890, p. 329.

UINB-fiCKVlYINa.

n

I I I t I b I I I I

IS g

+ +

p § S 2

S S S ' e3 M oi 9

+ + +

3 a g ss

ih

us

O

?D

U5

(.'

'

'

+ 111

So fe °3 ii h

°g fc 3 °S £ fe

V3 ,-j

uO

b4

d

P5 i -f O -T?

A Co Q C4

t Is i" s. s 5c V °§ fe - h is

eiioUTis

Thatersikg Onoerorocnd. 131

'metliod ; — Plugs made out of horse-Bhoe naila flatteued at the end, with a small hole punched in them, are put into the side. FrotD three of these plugs a tri&ogular piece of thin galvanised iron, incbee long on each side, is suspended bj three brass chains. In the centre of the triangular piece there is a small bole to admit a thin wire to which the plumb-line is attached. Each of the pieces of chain is 6 feet in length, altliough in exceptional circumstances a greater length may be used. At the end of each chain is a small hook which fastens into th plug at the side of the roadway. The chains are put up, the plumb-bob suspended from the centre piece and the theodolite set up under the point of the plumb-bob.

t'oT underground stations that require to be permanently fixed, Mr. 6. A. Troye recommends that a hole 2 to 3 inches deep should be drilled into the roof, a wooden plug forced into it, and a small brass staple on which to hang the plumb-line driven into the wood. A small tin label, witb the number of the station punched on it, should be tied to the staple with copper wire.

ComparlBon of the Theodolite and Compass. — On account of the great coal of mining works, the surveys for determining the direction, in which levels or tunnels are to be set out, are of such importance that the greatest possible accuracy is demanded. For this reaaon, the mine-surveyor ought to employ the instru- ments and methods that will give the most accurate results, and to use less perfect instruments only for unimportant or prelimi- nary surveys. The compass is an imperfect instrument of this kind. It is of great value in certain cases, especially for filling in details. When, however, it ie used for large and important surveys, there is always a danger of meeting with great inaccu- racies. The daily variation of the declination of the needle is nearly 10 minutes. Disregarding the occasional irregular per- turbations of thp needle, it is obvious that errors of 10 minutes or more may occur in the period between 8 a.m. and 1 p.m., when the declination of the needle passes from its minimum to its maximum. With a radius of 100, the chord of 10' is 0'29. Therefore, from the change in the direction of the needle, there will be in a length of 100 fathoms a lateral displacement of nearly three-tentlis of a &thom.

The uncertainty of the readings of the compass is also a dis- advantage. With compasses of the ordinary size, the needle cannot be read more accurately than to one-fifth of a degree. Thus, errors of one-tenth of a degree, or 6 minutes, are unavoid- fable. In a length of 100 fathoms, this error in the bearing givei a lateral error of 0-174 fathom.

Hinb-Survbyiko.

Magnetic Rtorms and the influence of ferriferous rook masses* ixi the neighbourhood may give rise to considerable error, often difficult to detect while the survey is in progress.

With the theodolite very different resulta are obtained. With a, 6-inch instrument, the horizontal angle, even without repeat- ing, may be determined accurately to 30 seconds, The chord of this angle being 0'000145, in a length of 100 fathoms, the lateral error will not exceed 0*0145 fathom. The accuracy of the theodolite is thus 30 times as great as that of the compass.

The repetition of the angles not only ensures great accuracy, but is also a valuable check on the results. If, for example, aa angle has been repeated four tiroes, and if the second, third, and fourth observations give results closely approaching the result of the first observation multiplied by two, three, and four respec- tively, it is evident there can have been no serious error. With the compass, on the other hand, when a bearing is read re- peatedly, the conditions remain the same, and it is quite possible to have exactlv the same error each time.

In reading a bearing with the compass, the instrument must remain unmoved. The surveyor is therefore compelled to put his eye, his head, and sometimes his whole body into a particular position with reference to the instrument. With the theodobte, however, there is no necessity for such inconvenience, as the horizontal circle may be turned to any required position, without changing the ajigle indicated by the vernier. The results are therefore read with far greater precision.

The disadvantages of the compass pointed out in this coupari- son are not presented by the vernier form of that instrument. The modern vernier-compass or circumferenter is practically a theodolite, from its compactness and simplicity specially adapted to underground surveying.

The theodolite of the usual size has the disadvantage of want of portability, its weight being a great drawback to its use underground. The telescope, too, cannot be used in minei when the air is bad from powdersmoke.

See paper by Sir A. W, RUoker on "Regional Magnetic DiBturbanoe&" Five, RoytU Soc., vol. itviii., p, 505, 18' i'.

Suhface-Schvets With The Tb80D0L1Tk.

CHAPTER X. Slefack-Sdrvets with the Theodolite,

[

Triangulation. — The surface-survey of a mine royalty may be made with almost any degree of accuracy that may be requirad by haTiDg recourse to a system of tnangulatioQ. A base-Hue is meaaared with great accuracy, and, from its ends, angles are taken to distant statione. The instrument is placed at each of these new stations, and angles taken to other stations. In this way, the ground is covered with a network of imaginary tri- anglea, all the angles of which have been measured. The length of the base-line being known, the lengths of the sides of the triangles may be calculated trigonometrically.

The first operation is the measurement of the base-line, a pro iseeding requiring careful attention, as any errors will be multi- plied in proportion to the eitent of the survey. The baae-line should be measured upon a level piece of ground, and from both of its ends the principal objects in the surrounding country should be visible. The length of the base-line should be in proportion to the extent of the survey. For mine-surveying purposes, a base-line need never be longer than 300 fathoms.

The iMt triangle of the system should be selected in such a wsy that one of its sides may be measured. This line is called the hag of verijieation. One base-line can then be calculated from the other, and the calculated and measured results compared. In this way the accuracy of the survey may be tested.

The of the base-line should be marked by means of some permanent object, such as a large atone sunk in the ground, or a pile driven deep aad concealed from casual observation. In the level surface of the stone, a hole about 3 inches in depth should be bored to mark the exact end of the line, and to serve for the reception of a signal pote. Permanently marked in this way, stations could be readily found at a future period.

The triangles should be as nearly equilateral as possible. Special care must be token to avoid ill-conditioned triangles, that it, triangles with any angle less than 30° or more than 130°, as a point is not definitely defined if the lines fixing it meet at a

MtNE-BURTETINO.

verj obtuse or very acute angle. The triaagnlar points may bo marked by means of woodea pickets, 1 foot long and i inehes thick, driven into the ground. In these, holes should be bored to a depth of 4 inches for the reception of the signal poles.

In measuring the angles, the telescope is first directed to the left-hand object and then to the right-hand one, so that the verniers move in the direction in which the horizontal circle is graduated. If the telescope is directed to the right-hand object first, the angle read must be subtracted from 360' in order to giv the interior angle required.

The three angles of each triangle should be measured, so that the accuracy of the operations may be checked, by adding them together, when they should amount to 180'. In the case of the great triangles occurring in geodetic surveys, the total exceeds 180°. The so-called spherical excesi is due to the feet that the triangle is spherical on account of the curvature of the earth. Small errors made in measuring the angles may be corrected by adding to, or subtracting &om, each angle one-third of the total error.

It sometimes happens that the level ground is of limited extent, and not suited for the measurement of the whole of a base-line. In such a case the base-line is prolonged by ranging lines in continuation of it, at one or both ends, until a suitable length is obtained. The lengths of the additional lines are cal- culated from angular measurements, follows : —

When the measured base, A B (Fig. 41), can be conveniently extended in one direc- tion only, towards H, select a lateral station point, 0, Eo that the resulting triangles, ABO and B E, shall be well-conditioned, and if possible nearly equilateral. Measure all the angles of these two triangles, and radculate the length of the side B 0. Then choose a point E in the Hue ranged in continuation of A £, and by means of the side B and the angles E B, B E, calculate the length of B E. Check the result by selecting another lateral station, D, on the opposite side of the base-line, and by solving the triangles, A B D, D B E. The length of the line B E is thus calculated from independent data. E H represents a farther prolongation of the base-line, and F and G the lateral stations, which form the triangles, by means of which its length is calculated.

A comparatively short base-line may Ije connected with the sides of large triangles, without prolonging it and without

Pig. 41.

e0HrAOE-BUBVBTS WITH THE THEODOLITE.

Fig. 42.

introducing ill-conditioned triangles, by continudly increoeinj

the sides of the tri&ngle, as shown in

Fig. 42. A 6 is the measured base-line,

and D are tlio nearp.st stations.

In the triangles ABC, ABD, all the

angles and the eide AB being known,

the other sides can be readily calculated.

Then in e-ach of the triangles D A and

D B 0, two sides and the included angle

being known, the length D may be

calculated in a variety of diflernt ways which will check each

other. Taking D as a baae-line, choose a pair of stations, E

and F, at opposite sides of the base, and as far from each other

as is consistent with making U D F and ODE well-conditioned

triangles. Proceed as before to calculate the distance E P.

This will probably be sufficiently long to serve as the side oi a

pair of triangles. If not, continae the process until a distance

sufficiently long is obtained.

The triangulation-survey of a mine royalty is based on the tame principles, operations, and methods as are adopted on the trigonometrical surveys of countries. In such surveys, the spheroidal form of the earth's surface has to be taken into account, and the amonnt of accuracy required is much greater than that required for any ordinary topographical survey. Thus, on the Ordnance Survey of the United Kingdom, the average length of the sides of the Primary Triangulation was 35 mites ; the longest side was 111 miles. The angles were measured with four large theodolites, two 3 feet in diameter, one 2 feet, and one 18 inches. With the exception of the theodolite 2 feet in diameter, these instruments were constructed by Ramsden at the commencement of the trigonometrical operations in England in 1798. They are now exhibited in the South Kensington Mnseum, id are still in perfect condition.

In order to show how accurately the main triangulation was conducted, it may be mentioned that in 1836, a base-line was measored at Lough Foyle, in the north of Ireland, by means of General Colby's compensated bara, and in 1849 the old base-line on Salisbury Plain was remeaaured with the same apparatus. The length of the Salisbury Plain base was 6 '97 miles, and that of the Lough Foyle base 7-89 miles. The length of the latter base was calculated by a triangulation carried from the Salisbury Plain base, and the diflerence between the calculated and measured length of the Lough Foyle base was only 5 inches.

By means of secondary triangulation, the long sides of the principal triangulation were reduced to lengths of 5 miles. The

Mme-suBTBTiNa

lUigles were measured th a IS-incb theodolite. The stations selected were, as far as possible, permanent objects such an cborch towers.

The 6-mile sides of the secondary triangulation were reduced by means of the Parish triangulatioa to lengths of 1 mile, or less. In towns, the points were sometimes within as short a distance as 10 chains. The angles were measured with a 7-inch theodolite. Finally, the details were filled in by means of ordinary chain-surveying.

Computing the Sides of the Triangles, — For the solution of the triangles when the base and the three angles are given, th ordinary sine ratio is employed —

sin B

when, if e represents the hose,

sin A siaO'

or, using logarithura,

log a log c -(- L, sin A - L, dn 0.

The sine of an angle A is equal to 1 -r cosec A. Instead, therefore, of subtracting L. sin 0, L. cosec may be added ; the formula then is —

log a log e + Im sin A + L. cosec — 20.

In the survey of the triangles shown in Fig. 43, the base-line a/ was found on measuring to be 4009'5 links. The emgles wero as follows ; —

L/aff 35* ly ttB/l(W43' a/g 40*05' VL abg 52° 58' 603 67° 50' HI, ebg 36° 47' bgc So' 49' beg 67=2*'

IV. Cff6(r42' tegS5'0g

eeg3S' 15'

V. dee&T 20' eed53*0l

VL eg/bsrasf

tfgWlT

BUEPACE-SORVEYa WITH TBB THEODOLITE.

The sides are calculated in the following manner : — To find side a g in Triangle I. af: ag sin agf: sin a/g log a J log o/ + L sin afg L. sin a gf.

log 4009-5 + L. tin 40° 05' - L. sin 104* 43*

3'6030902 9'S0Ssi93 9'9855135

3'4263959

2669-3 links.

instead of subtracting the sine of the angle opposite to the "given side, its cosecant is added, the result will be as follows ; —

log 4009-£

3-U030B02

+ L. Bin 40° 05'

s

9'S088192

+ Ll como 104* 43'

10-0144865 M

ln(?iff

3'42G395B

To find side/j

in Triangle L

o/=/ff sina

fff-

an fag.

log 4009'6

3 '6030902

4- L ain 35° 12*

a

L. COMO 104° ti*

lO'OU-lSOS H

/9

To find side a h

in Triangle II,

logic

3-4263050 H

4- L. nn SO* 12'

9-0339729

>fL.MiMa 62° 68'

10 '0976419

3-4632107

ab

2872-3 fl

E-

To jind side bg in Triangle II.

P

1 ta the ftame "waj, the lengths of the other sides will foond to be as foUovg : —

Triangle III.

log 6 c log hg + L. sin 85' 49' + L, omea 57" 24' -M

be sees'OtiDks.

w

log c J log 6 B + L. iin 36° 47' + L. tsoaeo 5T 24' -30

ct; SSOl-OUnka.

log c e log c(f + L, sin oG" 42' + L ooec 33* 15'-20B

e e 2071 -S liiikn

H

n

log cd log e e + L. Bin 53° 01' + h. coseo 69" 39' - 30

ed 2531-7 links.

logde loger + L sin57°2n' + L,coMo69°39'-S0

de 26630 links.

p

e/ - 2SS3-3 linkt

log 3'5492413

L. tin 42* 10' 9'S2909S

L. coaeo 84° 17' 10-0021653

Is 2.389'.'i5 link*,

Bitbfaokubvets With Thk Tbeodolitk. 129

a resuH piBotically the same as that obtained in the solution, of tliangle I.

In some cases the two sides of a triangle and the angle con- tained between them may be known, and it is required to find the two other angles, and the third side. In this case, the sum of the two aides is to their difference, as the tangent of half the sum of the two unknown angina is to the tangent of half their difference. Half their difference thus found, added to half their am will be the greater of the two anglea required that is, thn angle oppoidte to the greater side.

lotenor Detail of the Triangnlation.— The toriangulation for a survey being completed, the filling-in of the interior detail prp- ents no difficulty. Roads, rivers, woods, (fee., may be surveyed by traversing with the theodolite or with the dial. For filling in details, the pri-gmatie eompasa is of great use. It ia a hand instrument consisting of a glass-covered circular brass box, inches in diameter, containing a graduated card or aluminium ring, under or across which a magnetio-needle is fixed. The card or ring is divided to half or one-third of a degree. The needle and card are accurately balanced. Sights are attached to the rim of the box. The farther sight has a fine thread stretched along its opening in the direction of its length. The near sight has a small slit below which is a reflecting magnifying triangular prism, BO placed that on looking through the slit the eye sees at the same timt the vertical wire of the farther sight and the needle- reading, the divisions on the card appearing as a continuation of the wire. The graduation of the ring begins at the south end of the needle, and proceeds towards the right, round to 360*. In this way bearings are shown to the east of north. With this instru- ment, when held in the hand, bearings may be read to within 30 minutes to 2 degrees. The instrument is thus suitable only for preliminary and unimportant work. Mounted on a stand, the instrument gives more satisfactory results,

The plane table* ia an instrument, invented in 1S90, which may be advantageously used for filling in details where minute accuracy is not required. It consists of a diuwing-board mounted on a portable tripod capable of being levelled, like the graduated limb of the theodolite. It must also have a free horizontal angular movement, and be provided with a clamp and tangent screw. The index on the board consists of a flat straight-edge, either with up- right sights at its ends or with a telescope for determining the line of sight. The use of the plane table ia similar to that of the theodolite. Instead, however, of reading off horizontal angles and afterwards plotting them on paper, the angles are at once laid down in the field on a sheet of paper strained on the top of the table,

Conaalt J. Pierce's paper on the eooDomio nM ot the V)&\, M.Vs. J've. liut. 0,£., yol. loii., JSSS, p. 187.

UlNE-gUSVBYING.

Before the introduction of the theodolite, the pl&ne table was largely used for mine-survey ing ia Sweden, where the magnetio nature of the iron ore deposits renderB tlie compass useless for lurveying purposes.

In surveying mines in that country, the surveying instrucnent used consists of a sighting-tube attached to an alidade-rule, a, b (Fig. i3a), provided with a tube, c, aod a vertical graduated circle,

E-'ii;, AM.

d, both fastened to one and the same horizontal axle, in suoh a manner that the tube can move in the vertical plane which passes through one edge of the alidade, a h.

This sighting-tube, in surveying, is placed on a plane tabla fixed to a tripod frame, which at the top consists of a round braes ring, a (Fig. 436), whose upper edge ia plane turned and polished. In the interior of the ring ia fitted a round wooden disc, h, supported by the screws c, and adjusted by the screws d, in such a manner that, when drawing-paper of somewhat amatier dimensions than the wooden disc is glued fast on the upper surface of the disc, the disc surface thus covered is close under the upper edge of the brass ring.

In surveying, at least two plane tables are always used. From each station the immediately preceding and immediately follow- ing station is sighted, as well as all the fixed points situated

BUBFACE-fiURVETS WITH THE THEODOLITE.

between these stations and the oontour-pointH in the excavation which is being surveyed.

In surveying station- points and fixed points, the lines of sight are marked on the paper on which the distance and the angle of the lines to the horizontal [tiatie are noted. The contour-pointa are marked, with the help of a scale, direct on the paper, after the distance to them from the station has been determined. The plan of the mine is then made by combining all these different observations.

This method of surveying has, according to Frofesaor Q.

Fig. 436.

NordenstrSna,* been in use in Sweden for more than 150 years. During the last thirty years many improvements have been made in these instruments, and since steel tape-measures have come into use in all more important surveys, very excellent results have been attained by this method. The instrument is alio much more convenient to use than a theodolite in excava- tions of the form which is common in Swedish mines.

If, however, the ore fields to be surveyed are of very great

Jtna-Hoi o/lKt Iron and SU<i IiutiiuU, vol. liv,, 1898 p. 62,

HINB-SUfiVETIKO.

extent, this method is not suitable to nae alone, and in such

cases recourse is had to theodolite surveying. By the help of the theodolite a number of fixed points are determined, and the survey filled in with the plane table,

American Mining ClalmB, — Prospectors are usually without suitable instruments to lay off their claims on the surface with any degree of accuracy, and consequently the methods they em- ploy are generally very crude. Before the patent or title from the United States can be obtained, a very accurate survey of the claim must be made with the theodolite by a deputy of the United States Surveyor-General of Public Lands. These officers are known as the United States Deputy Mineral Surveyors, and are required to pass an examination.

Mining claims are of ditferent dimensions according to the local laws. The length is limited by the United States laws to 1,500 feet in the direction, or along the strike, of the vein. The width varies in the different States; it is usually 300 feet on each sido of the middle of the vein at the surface. The end linea of the claims must be parallel, but the side lines need not be so. This prevents more than 1,500 feet of a vein being included in one claim.

When mineral discoveries are made on surveyed land, the sur- veys must be so connected with the public survey that there will be no difficulty in finding some fixed point or comer of that survey. When discoveries are made on unsurveyed land, the survey must be connected with permanent natural objects, such as mountain peaks or rocks.

It is frequently found that two or more claims conflict or over- lap. In such cases, priority of location determines the ownership of the area in dispute. In making the plan, the United States Deputy-Surveyors must deduct the area in conflict from the sub- sequent claim. When the survey for patent is completed, the claim must be marked by at least four stakes, one in each comer.

According to the instructions issued to the United States

L Deputy Mineral Surveyors, all mineral surveys must be made with a transit-theodolite with solar attachment, or with some other {nstrument acting independently of the magnetic meridian. All courses must be referred to the true meridian. The magnetic declination must be noted at each corner of the survey. In case the claim is situated in a district where there are no comers of the public survey within 2 miles, the surveyor must establish a permanent mineral location monument. This should couaiat of a post 8 feet long and 6 inches square, set 3 feet in the ground, and protected by a well-built conical mound of stone, 3 feet high and 6 feet in diameter at the base. All comers of

A

d

eVRPAOE-StTRVeYB WITH THB THEODOLITK. 133

Ee claim must be established in a permanent maoner, and the srner and aurvey number must be neatly chiselled on the facing the claim . In case the point for the corner is cessible, a witness-corner must be established aa near as practicable to the true corner, with which it niust be connected by course and distance.

The claimant is required by law to show that 500 dollars' worth of labour has been expended upon the claim by himself. The sur- veyor must, therefore, give full details of aU improvements made upon the claim. A preliminary plan on a scale of 200 feet to an inch must be filed with the field-notes. With the notes, too, a report must be submitted stating in detail the observations and calculation for the establishment of the meridian from which the oonrses were deflected, in cases where the solar attachment was not used. If any of the lines of the survey were determined by triangulation or traverse, full details must be given of the calculations whereby the results reported in the tield-notea were obtained.

The field-notes must be prepared in conformity with the accom- panying specimen : —

Field- Notes*

THE SuaTiT Of THE Claim of thb "Arobntitm Mnfiso Compamt"

CPoH THB Silver Kiso and Gold Qitebn Lodes, akd Silvbb KiBO Miti. Site, in Alpine Mining Distbict, Lake CotrsTT, Colorado. Surveyed by G. Liohtfoot, April 22 to 24, 1888.

I Survey No. 4226 A— Silver King iorfe.— Beginning at comer Ko. I,

MeoticKl with corner No, 1 of the location. A api-uco poat, 6 feat long 4 inches square, set 2 feot in the ground, with a mound of gtone marked (1)4225 A, whence the W. corner Section 22, Township 11 S., Range 81 W. oi the 6th principal meridian, bears S. 73" 34' W., 137S-2 feet. Corner No. I, Gottenburg lode (nnsurveyed}, bears S. 40° 29' W., 187-67 feet. A pine, 12 inches in diameter, blazed and marked B. T. (bearing-tree) (1)4225 A, bears 3. 7° 25' E., 22 leot. Mount Ouray beftra N. U° E. Hiawatha Peak bears N. 47* 45' W.

Thence 8. 24* 45' W. (variation IS" 12' E.}, 1242 feet to trail couraiog N.-W. and S,- IC., 1366-28 feot to comer No. 2. A granite stBiie, 25 by 9 by 6 inches, set 18 inches in the ground, chisel led (2) 4225 A, whence comer No. 2 of the location bears S. 24* 45' W. , 134-72 feet. Comer No. 1, survey No 2580, Coman-on lode, bears S. 3' 29' E., llC-6 feet. North end of bridge, over Columbine Creak, bears S. 65° 16' E., 660 feet.

Thence N. 65° J6' W. (variation 15° 20' E.), 152 feet intersect line 4-1, giin-ey No. 2560, at N. 38° 52' W., 231 -2 feet from corner No. 1. 3<M feot to comer No, 3. A cross at comer point, and (3) 4225 A chiselled on a granite rook in place, 20 by 14 by 6 feet above the general level, whence

k

For tx>pj of mtwe iiot, lun lodebtffd to ttaa klndnttii ot l&T.0.C4,nVKtiii&> TVTOr-OennL Colorado.

TTVjor-OennJ, Colorado.

UIMZ-BCRVETtNO.

comer No. 3 of the locatiod bears !j. '24° 45' W,, 134 '72 feet. A ipmcf 16 JQchea in diameter, blazed and marked B. T. (3} 4225 A, bean S. &6' W., IS feet.

Thence N. 24° 45' K (variation 15° 20' E J, 73-4 feet intersect line 4-1, Qney No. 25C0, at N. 38° 52'W., 396'4 feet from comer No. 1. 150 feetioter- sect line 6-7 of this survey. 237 feet to trail, coursing N.-W. and 8.-E 1000 '9 feet intersect line 2-3, Gottenbarg lode, at N. 26 56' W, 76*26 feet from comer No. 2. 1365'2S feet to comer No. 4, identical with ortier No. 4 of the location. A pins past, 4 '5 feet long, 5 iiiohea square, set 1 foot in the ground, with a mound of earth and atone, marked (4) 4*225 A, wbeno* a orosa, chisoljed on rook in place, marked B, R. (l)earing rock) (4) 4225 A, bears N. '28° 10' E., 58!) feet.

Thecce 3. 65° 15' E. (variation 16° 12' E,), 28*5 feet intersect line 1-4, Gottenburg lode, at N. 25° 56' W, , 28513 feet from corner No. 1. 65 feet intersect Une 5-6 of this aarvey. 300 feet to comer No. 1, the place of beginning.

Ootd Lode. — Beginning at comer No. 5, a pioe post, 5 feet long, 6 inches square, set 2 feet in the ground, with mound of earth luid stone, marked (5) 42*25 A, whence corner No. 1, of this survey, iiesrs S. 14* 64' G,, 37016 feet. A pine, 18 inches in diameter, bears S. 33° 15' W,, 61 feel;, and a silver spniee, 13 inchea in diameter, bears N. 60* W,, 23 feet, Botb are blazed and marked B. T. (6) 4225 A.

Theiioe S. 24° ,30' W. (vBriation 15° 14' E.), 285 feet iaterseot line 4-1 of this survey. 315 feet interaeot line 4-1, Gottenbarg lode, at N. 25° 56' W., 237*78 feet from comer No. 1, 688*3 feet intersect line 1-2, Gottenburg lode, at N, 64° 04' E., 12-23 feet from corner No, 2. U.38 feet to trai coursing N. -W. and S.-E. 1500 feet to corner No. 6, granite stone, 34 by 14 by 6 inches, set 1 foot in the gronnd to bed-rock, with mound of stone chiselled (C) 4225 A, whence a cross, chiselled on ledge cf rock, marked B. R. (0) 4225 A, bears due north 12 feet.

Thence N. 65° 30' W (variation 15° 2ff E.), 70*3 feet intersect line 3-4 of this survey, 223 37 feet interaeot line 4-1, survey No. -2560. at N. 33' 52' W. , 567*28 feet from oorner No. 1. 300 feet to corner No. 7, a cross at comer point, and (7) 4225 A chiselled on a gmnite boulder, 12 by 6 by 3 feet above

?; round, whence a cross chiselled on vertical face of cu marked B, K. 7) 4225 A, bears N. 72° W,, 56*2 feet. A pme. 14 inches in diameter, blazed and marked B. T. (7) 4225 A, bears N. 10° E. , 39 feet.

Thence N. ?4° 30' E. (variation not determined on acconnt of local attrac- tion), 38*43 feet intersect line -1-1, survey No, 2560, at N. 38° 52* W., 6.i3 feet from comer No. 1, 165 feet to trail, cotiraing N,-W. and S.-E, 1043*73 feet intersect line 2-3, Gottenburg lode, at N. 26° 56' W., STSoe feet from comer No, 3. 1432*90 feet intersect tine 4-1, 6ottenbui;g lode, at N. 25° 66' W., 6*26-94 feet from comer No. 1. 1500 feet to comer No. 8;, a spruce post 6 feet long, 5 inches square, set 2 '5 feet in the ground, with mound of atone, marked (8) 42*25 A, whence a cross chiselled on rock in place, B, li. (8) 4223 A. bears S. 0° 12' E., loS feet, A pine, 20 inches in diameter, blued and marked B. T. (8) 4225 A, boars N. &3° K, 28*5 feet

Thence S, 65 30' E (variation 15° 16' E.), 300 feet to corner No. 6, tli place of b(inising.

jirca.— 'Total area of Silver King lode, 9*403 acres. Less urea in conflict with sQr>'ey No. 2580, 0'124 acre, and in conflict with Gottenburg lode, 1 fCS aore ; total 1 '487 acres. Net nrea of Silver King lode, 7*910 aorea.

Total area of Gold Queen lode, 10 331 acres. Area in conflict with otllBF urveys, 4*022 acres, tiius, with survey- No. 2560, 0034 acre, with Gottan*

Gottaif M

SUB rA0E-8UR VETS WITH THE TBEODOLITK,

13S

borg lode, 3-676 aoras, with Silver King lode (exclnsirs of confilct of Mid Silver King lode with the Ootteabnrg locte), I '309 item. Net area of Gold Qanen lode, 6 '309 wres,

The net area of the lode claim, iaoluding the Qold Queen lode and Silver King lode, ia 14 '225 aorea,

Stuvey No, 4225 USilvtr King Mill Site, — Beginning at comer No. 1, gneiM (tone, 32 W 8 by 6 ioohea, set 2 feet in the ground, chiselled (IJ 4225 B, whence W. i ocrner section 22, TownaUp 11 S., Kaogo 81 W. of the Cth principal meridian, bears N. 80° W., 1880 feet. Corner No, 1,

AficrNTUH Mining Company

, n Atfmv MittiHa Dutiict

/ /j

Fig. 44.

survey No. 4323 A, bean N. 40° 44' W., 760 '2 feet, A cotton-wood, IS ischee in diameter, blazed and marked (l) 4225 B, beara S. 30' E, 17 feet.

Thenoe 8. 34" E., 90 feet roail to Wobasso, oouraiog N.-E. and S.-W, SI08 feet right bank of Colorabine Creek, 75 feat wide, flowing S.-W. G04'8 foet to corner No. 2, an iron bolt, IS inches long, 1 inch in diameter.

UI.HE-SUBTEYINa

place, chuelled (2) i2'25 ]1, whetiM & ootton-wood,

et 1 faot ia rock in

blazed and marked B. t. (2} 4225 B, beara doe east, !82 feet.

Thence S. 56° W,, 351 feet left bunk of Columbme Creek. 394 4 feet to corner No. H, a point in bed of creek, uniuit&ble for the eatablUhmeDt of a [lermauout comer.

Xhonoe N. 34' W., 15 foet right bank of Columbine Creek. 40 feet to witniiSB corner No. 3, a pine post, 4 '5 feet Iook, 5 inche in dtameier, let 1 foot in ground, with inound of stone, marked W. C. (3) 4552 B, wheno* a cotton- wood, 15 inches in diameter, beara N. 1 1° E., 16'5 feet, and a cotton- wood, 19 inchea in diameter, bears N, 83° W., 23 feet; both blazed aud marked B. T. W. C. (3) 4225 B. 370 feet rood to Wabasao, coureini; N.-K. and S.'W, &i7"2 feat to eorner No. 4, gneiag stone, 24 by 10 by ilnchet, et IS inches in the ground, chiselled (4) 4225 U, wbeuce a cross, chiaelled on ledge of rock, marked B. R. (4) 4225 B, bears N. 85° 10' E., 26-4 feet.

Thence N. 4S° 43' E., 1 25 '5 feet to corner No. 5, a gueiaa stone, 30 by 8 by 6 inches, set 2 feet in the ground, chiaelled (5) 4225 B.

Thence S, 34° E., 158*3 feet to corner No. 6, a pine post, 5 feet long, 6 inches sqoaro, set 2 fact in the ground, with mound of earth and atone, marked (6) 422S B, whence a pine, 12 inches in diameter, biased and marked B. T. (S) 4225 B, bears S. 33''E., 63-5 feet.

Thence N. 56° E., 270 feet to comer No. 1, the plaoe of beginning. Hie Tariation at all tbe comers is 15° 20' £. The area of the mill site ia 5 acres.

Expenditure of Five Hundred iJoMar* The value of the labour and improvements u[Kin thb claim is not leas than 50O dollars. The said im)>rovement)i consist of: —

The dbcovary shaft of the Silver King lode, 6 by 3 feet, 10 feet deep la earth and rock, which bears from eoruer So. 2, N. 6° 42' W., 2S7*5 Icet. Value 8U dollars. An iucline, 7 by 5 feet, 45 feet deep in coarse gravel and rock, timbered, course N. 58° 15 W., dip 62°, the mouth of which bears from comer No. 2, N. 15° 37' E., 908 feet. Value 550 doUara. The diacoveiy shaft of the Gold Queen lode, 5 by 5 feet, 18 feet deep iu rock, which heart from comer No. 7, N. 67° 39' E., 219'3 feet, at the bottom of which il a croas-cut, 6 '5 by 4 feet, running N. 59° 26' W,, 75 feet Value of shaft and cross-cut lOOO dollars. A Tog sbaft-bouse, 14 feet square, over the last-mentioned shaft, value 100 dollars. Two thirds interest in an adit, 6 '5 by 5 feet, riinuing due west 635 feet, timbered, the mouth of which beara from comer No. 2, N. 81° 15' E, 920 feet. This adit ia in course of construction tor the development of the Silver King and Gold Queen lodea of this claim, and survey No. 2560, Camorvou lode. The reniaininK one- third intereet baa already been iucluded in the estimate of 5O0 doUan expenditure upon tbe latter claim. Total value of adit, l.OOO dollars, A drift, 6'5 by 4 feet, on the Silver K.in lode, beginning at a point in the adit 800 feet from the mouth, and runmng N. W' W E., 195 feet; theoo* N. 54° 15' E, 40 feet to breaat. Value 2,600 dollars.

Other improvements consist of:

A log cabiu, 35 by 2S feet, tbe S.-W. comer of which bears from comer No. 7, N. 90° 44' E., 496 feet. A dam, 4 feet high, SO feet long, acrosa Columbine Creek, the south end of which bears, from comer No, 2 of the mill-site, N. 5S° 20' W.. 240 feet. An adit, 6 by 4 feet, running N. 70* 50* W., 100 feet, the mouth of which bears, from comer No. 5, S. 68* 12* W., 323 feet.

Inntrurm'nt.—The survey was made with a Youog h Sons' mountain trausit-theoiloUte with sclar attachment. The courses wera daQacted from the true meridian as detemiined by solar observations. The distances mured with a 60-foot steel tape.

BCRFAGSDBVEYS WITB THE THEODOLtTB.

The first comer of the aurvej must be coanected hy course and distouce with some comer of the survey of public lands of the United States, if the claira lies within 3 miles of such corner. The United States public lands include aU the territory north of the Ohio River and west of the Miaaisaippi River, not owned by individuaU previous to the date of cession to the United States Government. All this territory has been laid out in rectangular tracts bounded by north and south, and east and west lines, each tract having a particular name. The reference lines conaist of principal meridians and standard parallels The former may be wore than 100 miles apart. The standard parallels are 24 or 30 miles apart. In setting-out these lines, each mile ia marked by a stone, tree, or mound, and is called a sectioit corner. Every sixth mile has a different mark, and is called a lownkip comer. From 'each of these, auxiliary meridians are set-out north to the next itand&rd parallel. The territory is thus divided into ranges, which are 6 miles wide and 24 miles long. Each range is numbered east and west from the principal meridian. The ranges, being cut by east and west lines joining the corresponding township comers on the meridian, are thus divided into touuhijm each 6 miles square. Each township is divided into 36 .squares called ttetioiu, by meridians 1 mile apart, and by east and west lines at the same distance from each other. The sections are divided into half-sections and quarter-sectionB. The law requires that all excesses or deficiencies, either from erroneous measurement or &om the convergence of the meridians, shall, so far as possible, be thrown on the extreme tier of sections and half-sections con- tiguous to the north and west boundaries of towuahips.

For rapid surveys in the United States and Camida, the insenioua pocket-theodolite, patented by Mr. D. W. llrunton in' 1894, is now largely used. It measures 2j by 2 J by inches, and its weight, in an aluminium case, ia 8 ounces. It is no larger than an ordinary pocket-compass, yet it does the work of a sighting compass, a clinomet-er, a prismatic compass, and an Abney level, mi'asuring horizontal and vertical angles with a high degree of accuracy. In using this instrument the chief precaution to be observed is that it should not be turned in the hands, as is customary with an ordinary com puss ; but the hands should be held rigidly against the body, which should serve in place of a tripod, and changes of direction Bhould fa made by twisting the body to right or left.

Surveying in South Africa. — In the colony of the Cape of Good Hope the legal unit of land measure ia the Cape rood. The Cape measures are aa follows: —

JHl

UlNe-BUKVETUra.

MeAlurvf of LD0h.

Uutim of flarfju.

KUi.

RdocLi. 423 -1*4

.

luetics.

Bn rkhIi.

Bn-ta*.

In order to convert British feet into Oape roods, multiply by 0-08067, and aci-oa into morgen, multiply by '4724 6. In order to convert Gape roods into feet, multiply bj 12-396, aad morgen into acres, multiply by 2'11654.

In ordinary survey work in South Africa, measurements ol distttnces by chain or ateel tape are less frequently resorted to than in Europe. The use of the chain is limited to the measnro- ment of baee lines, from which the longer distances are derived by triangulation. Base lines should be nieaswred at least twice, and the results should agree within an inch in 100 roods. The triangulation is commenced from the base line, and the size of the triangles increased as rapidly as possible without making them ill-conditioned until their sides have an average length su6Scient to enable the surveyor to cover the area to be sur- veyed with a set of comparatively large triruigles. With thia main triangulation, all other points of the survey are connected by minor triangulation. The vertices of the triangles are shown by flftgSj the staves of which should be perpendicularly fixed in the ground. The theodolite is always used for measuring angles.

In the gold law of" the Transvaal, as set forth in Act No. 14 of 1894, the drawing and maintaining of accitrate detailed plans of the surface and of underground works was enjoined. The plana must be drawn to the true meridian, :ind must be posted every six months. All bench-marks, iixed survey poin, the strike and dip of reefs, faults and dykes must be shown. All general plans must be drawn to a scale of 1 to 5,000. Mine pltins may be on a scale of 1 to 500, or of 1 to 1,000. The present Government has gone farther, and call for information on the plan as to the nature and extent of the deposits worked. The plan 1ms to represent in colours the position and character of the deposit, and to sliow separately the work of development and that of stoping. Valuable information on carrying out Btope measurements for this purpose is contained in a paper by Mr, J. A. Wilkes communicated to the Transvaal Institute Mine Surveyors in 1904 and discussed in 1905,

te of 1

PLOTTINO THB SirSVET.

1S9

CHAPTER XL Plotting tek Survey.

Scales. — Plotting a survey coasiats in representing on paper, to s smaller scale, the lines and angles determined on the ground. The o{>eration of drawing lines, the length of which shall be some fraction of that of the lines measured on the ground, is called drawing' to teale.

A Bcal may be defined as an artificial means of representing any given dimensions. Thus, a fathom may be represented by a tiaight line 1 inch long; then 2 fathoms would be represented by a line of 3 inches, fathoms by inches, and so on. Three kinds of scales of equal parts may be distinguished — 1, simply divided scales ; 2, diagonal scales ; and 3, vernier scales.

L Simply divided scales conBist of any extent of equal divisions, ntunbered 1, 2, 3, Jcc, beginning at the second division on the left hand. The first of these primary divisions is sub-divided into 10 equal parts, and from these sub-divisions the scale is named. ThuB it is a scale of 30, when 30 of these secondary divisions are equal to 1 inch. If the primary divisions are taken as units, the secondary divisions will represent tenths.

As an illustration of the method of constructing scales, let it be required to construct a scale of 3 chains to the inch, to exhibit 18 chains. Draw a line 6 inches long, and divide it into 18 equal parts. These ore the primary divisions, each of which represents one chain. Divide the first primary division into 10 equal parts; each of these secondary divisions wiU represent 10 links. Next draw a thicker line at a short distance below the first line, and draw vertical lines between them to indicate the divisions of the first Unea. Place the zero at the line between the first and second primary divisions, and then, from left to right, place in succession the numbers 1, 2, 3, Sic,, at each primary division. Number the secondary divisions from the zero from right to left, O'l, 0'2, 03, ic. With this system of numbering, lengths are taken from the scale with greater facility. Thus, to take offS chains 23 links from the scale described, one point of the dividers

am

MINS-eCBVETINa

extended back to a place midway between the aecond and third flecondary di'isions.

In cases wliere fathoms and feet are retuired to be shown, tha first primary division is divided into 6 diviaions representing feet. If the scale is to show feet and inches, the tirst primary division must be divided into 12 equal divisions, representing inches.

A scale constructed in this way should be drawn upon every mine pJan. Paper, when exposed to atmospheric influences, is found to expand or contract to a considerable extent. This a especially the case with new paper, or newly-mounted paper, The serious errors apt to arise from this cause are, to extent, obaated by making a scale on the paper us an accurate standard of measurement. This will expand and contract with the paper, and thus afford a valuable indication of the state tt the paper.

The scales usually employed for the plana of metalliferoos mines are 4 or 8 fathoms to the inch, sometimes 5 or 10 fftthoms. For coUiery plans, scales of 2 or 3 chains to the inch, or of 25*31 inches to the mile, are the most usual.

In order to ELSsist in giving a clearer idea of the relative pro- portions of the scales used, it is desirable that they should be expressed fractionally- — that is to say, that they should be so named as to indicate the ratio the line drawn on the paper beara to the line measured on the ground. Thus, a scale of 2 fathoms to the inch is a scale of jj, or, as it may also be written, 1 ; 1 44, since 1 inch represents 2 fathoms, or 144 inches of real length, A scale of this kind is called a naluj-al scale.

In the construction of the maps of the Ordnance Survey of Great Britain, the following ecalea are used ; —

Towna, . . . 1 : 500, or 126 '73 incheg to the miK

Pttrishea, , . 1 : 25f)0, or 25-34 „ „

Countiea, , . 1 : 10560, or 6 „ „

The Kingdom, , 1 :63:C0, or 1 „ „

In the scale adopted for the parish maps, largely used for

ooUiery plans, 1 square inch represents an acre.

2. DiODal Scales. — A diagonal scale of equal parts is oonr atructed in the following manner : — Draw eleven straight lines parallel to each other and inch apart. Divide the top line into eqiial parts, these primary divisions being of nay required length. Through the points marking these primary divisions, draw perpendiculars cutting all the p&T8.\VB\a. tuinVwit '

Plotting Thk Burvev.

divisions from the left, 1,0, 1, 2, 3, &c., as in the case of the simply divided scale. Then aub-divide the top and bottom line* of the first primary division into 10 equal parts. Number the alternate divisions, 2, 4, 6, 8, from right to left along the bottom line, and number the alternate parallel lines, 2, 4, 6, 8, from the bottom upwards. Then diuw lines, as in Fig, 45, from the zero of the bottom line to the first division of the top line, from the first of the bottom to the oecoad of the top, and so on until the scale ia complete.

10 a a 4 £ o

to

Fig. 45.

The diagonal lines are all parallel. Consequently the distance betvreen any two Buccessive lines, measured up any of the eleven |)iarallel lines which they intersect, is the aame as the distance measured upon the highest and lowest of those lines. The distance between the perpendicular which passes through the zero point, and the diagonal at the same point, is on the top line, and equal to one aub-diviaioa on the bottom line. It is therefore equal {Ettdid, vi. 4) to one-tenth of a sub-division on the second line, two-tentha of a sub-division on the third, and so on. In this way, each of the diagonal lines, as it reaches each enccessive parallel, separates fartiier from the perpendicular through the aero point by one-tenth of the extent of a sub-division, or one-hundredth of the extent of a primary division. Thus, by means of a diagonal scale a distance can be taken off to two places of decimals.

The general rule for taking off any number consisting of three figures from a diagonal scale ia as follows : — On the parallel line indicated by the third figure, measure from the diagonal indicated by the second to the vertical indicated by the first.

3. Vernier Scales.— The construction of the vernier scale ia similar to that of the vernier of circumfe renters and theodolites

how tke prinile of Uie Ternier

aeale let it 1m reqnind to

hm iach to iIipw feet uid dedmtli

of feet n the ordiaAry w&y, gnb-

AboTB tlie £nt primiry

dimv m line prDel te tke eale and ulmg mt the aero point Pron tbii point eet towuda tke left elMig the line re n i Hel to the icale a dJttence eual to 11 eaVdiTisioni ud divide Ihia disUnce into 10 eqwd parte abowit m Fig. 46,

P

-in ' r" i

Fig. 4fi.

Even diTuions of tlie scale being divided into 10 equal parti on the renuer, eacli division of the Latter represents or foot , the distanoes firom the xero of the scale to tD acoeaaive divisions of the vernier represent 1 foot l-t#nth, 2 feet 2-8, 3 feet S-tenths, 4 feet 4-teQdu, 5 fnet 5-tenthA, 6 feet 6-tenths, 7 feet 7-tenthi, 8 feet S-tenth, 9 feet 9-tenth8, 10 feet IO-, and II feet.

The manner of using the scale is as follo-s ; — To tftke off distance of 16 feet 7-tenths, one point of the dividers must be plaoed on the 7th division of the vernier, and the other on tbe dth division of the scale. From to tlie 7th division of the vernier represents 7 feet 7-tetith8, and that distance snhtiacted from IC feet 7-tenths leaves 9 feet.

Plotting Scales. — The most convenient scales of equal parte for plotting are those of ivory or box-vood, which have a feather edge along which they are divided, so that distances otsa be at once marked off without the application of the dividers. In the same way, the length of a given line can be at once read off Dividers should never be used to measure distances when an edge acale is available for the purpose. An ivory scale is soon spoilt by being dug into by the dividers.

I'jach plotting scale should be provided with a shorter scale for thfi purpose of plotting offsets. The offset scale should be edge- divided like the plotting scala In plotting a survey, the plotting scale is placed along the station>Une with its zero point at the beginning of the line. The offset scale is placed at right angles to the plotting scale, and slid along the latter, until its edge comet to the distance at which an offset was taken. The length of this

PLOTTIXa TffE SUBVKY.

is then marked off from the offset scale hy means of a needle. The ciliset scale is slid along to the next distance, and the operation repeated. The poiats thus obtained are joinod by s&ight linea.

Plotting with a FrotraiCtor. — A semicircular protractor mny be sed to lay down or protract angles. It consists of a aemioircla of born, brass, or Oeriuau eiiver, divided to half-degrees. The denies are Q umbered from to 180 both ways. To lay off an KDgle at any point of a straight line, the protractor must be placed so that its straight aide, th&t is, the diameter of the fimlcircle, is on the giveu line, with the middle of tbe diameter, which is indicated by a small notch, at tbe given point. With a sharp pencil or a needle, a mark is made on the paper at the required number of degrees, and a line is drawn from that mark to the giveu poiut.

Ill using this instrument for plotting a survey, the straight side must be applied to an assumed meridian line drawn on the paper, the centre of the protractor coinciding with the point in the QieiiiJiau line selected for the commencement of the anrvey, A Uiio must then be drawn from the centre of tbe protractor passiug through the degree required. The length of this line is marked oS by means of a scale. Then at the end point of the line a second meridian line is drawn parallel to tlte &Tst, and the protractor applied to this in the same way as before. The meridians at each station muy be drawn by means of a T*aquarc, tbe north and south lines on the paper being made parallel to one of the sides of the drawing- board.

Fitted with a movable arm and a vernier, the semicircular protractor may bo read with great precision. Supposing it is required to plot a line through a given point at a certain angle with the meridian of a plan, a semicircular protractor titted with a vernier may be used, in conjuuctiou with a 60* Betrquare and a straight- eitge. The arm of the protractur is set by the vernier at the required angle, and at tbe same time the arm-line is laid on the meridian of tbe plan, The et-square is then placed against the protractor by the straight- edge, and slid along the latter until its edge passes through the given point, when tbe line drawn through that point will form the required angle with the Meridian. According to T. Weliski,* this method of plottiiig is preferred by almost all Hussion surveyors.

£eit,J. ytrmejfsungtwuen, vol. xii, p, 262, 1883,

dU

U4

Uine-Bdryeyiko.

More accurate results are obtained with a full-circle pro- tractor of brass or of vulcaniti. With this inatrumeat, not only the bearing itself but the correspondent bearing on the other side should also be marked oil* Then, if the line drawn from one point i o the other passes through the centre previously marked on the meridian line, it is evident that the bearing is accurately plotted.

Drawing meridian lines at each station is apt to give rise ta error, and always presents the inconvenience of iiaving a num- ber of lines on the plan which have to be rubbed out. With a circular protractor this uiineceasary labour is avoided by placing the instrument along a meridian line drawn near ths centre of the paper, and m:trking off in rotation the various hearings of the survey. Ooufusion may be avoided by figuring on the paper by the edge of the protractor the bearing, noi the number or letter of the draft, as is often done. Tiie bearings having been thus marked, the protractor is removed, and the lines are transferred to their projier positions on the plan by means of a rolling parallel ruLer. This instrument necessitates the use of a jierfectly true drawiug- board. It is provided with two rollers of exactly the same circumference, firmly attached to the same axis. It is made of ebony or of brass.

Elaborate circular protractors are made with a movable arm provided with a vernier. Such instruments are usually made with a glass centre, with two fine lines intersecting at the centre point. The most perfect instrument for accurate plot- ting is the folding arm protractor. This is provided with two opposite arms, each with a vernier, and a clamp and tangent motion for setting the angles. The extreme end of each arm carries a point, which by a gentle pressure may be caused to puncture a fine hole iu the plan. These instra- meuts are usually 6 inches in diameter, and divided on silver.

The most rapid method of plotting a survey is by means of a cardboard protractor, ns with thii instrument there is no occasion to figure the various bearings on the paper. The cardboard protractor, as used in the Ordnance Survey OMoe, is 12 inches in diameter. The centre portion is cut out, and the north and south line made to coiocido with the meridian oa the paper. The parallel ruler is then placed at once on the required bearing, and on the bearing directly opposite. The survey line is then drawn in the vacant space inside the circumference. Much time is thus saved, and tha

PLOTTIlfO THE SDRVET.

plan is kept clean, and not covered with peacilled bearings. The results are very accurate, on account of the large diameter of the protractor.

Mr. K. P. Percy* uses a protractor of strong thin paste- board. It is made as wide as convenient (24 inchei) from west to east, and narrow from north to south. Meridian lines are drawn on it at intervals of 2 or 3 inches, whilst

I the part within the 12-uic3i graduated circle is cut away as usual, and the plotting executed within that space. Yery few meridittua are required to be drawn on the plan, as none need be within 30 inches of another. The plan can thus be kept clean, and the necessity for confusing it with nutnerous abort pencilled meridians is obviated. At the ends of all the parallels on the left at the north edge, and on the right at the south edge, divergences of I degree and fractions of a degree may be indicated, so as to allow the protractor to be twisted for declination, so as to bring the meridian to the date of the survey. An allowance for six months' change can thus easily be mode.

iShould it be found advisable first to plot the results of a survey on tracing paper, and then to fit them into the finished plan, the following will be found a rapid method : — On the tracing paper fine parallel meridian lines are drawn in red or blue ink. Instead of placing the protractor on the paper, the loose sheet of tracing paper ia placed over a pinned 'down circular cardboard protractor, and moved with the left hand until the starting point of the traverse coincides with the centre of the protractor, and the line 0'— 180° ia parallel to one of the coloured lines. With the dividers open to the required length in the right hand, the next point is marked in the direction of the bearing required.

Plotting by Means of Chorda.— A traverse may be plotted from one meridian, without a proLractor, by means of a table of chords and a parallel ruler. For this method, all that ia required is a table of sines, or, better still, of chords, and a good rolUng 2-foot parallel roller. Since the chord of an angle is twice the sine of half the angle to a riidius of unity, ready means is atForded of protracting to any radius re- quired. The meridian angles, if they have been taken with

' the theodolite or from the outer circle of the dial, must first

' be reduced to bearings ; the rule for performing this reduction

! being as follows : —

I For angles between —

TraTu. Fed, /mJ. Mia. Eng., vol, xU., 1897, p. 5(J5.

Ul.NE-BURVETING.

0° and 90°, enter in bearing oolnmn M N.E. 9U* and 180°, subtract from ISO", uid enter result M S.B. 180* and 270". deduct 180°, ajid enter result &3 S.W. 270° iu)tl 360°, subtract from 360. and enter result as N.W,

Having tabulated the chords of the bearings, describe a cirela with a. radius of 1000 uttita (say 10 inches). This avoids the necessity of multiplying the chord by the radius ; the decimal point merely having to be moved 3 places to the right. Angle* can be laid down by this method as easily as with a SOineh protractor.

The circle is drawn in a convenient part of the plan, and tho meridian line drawn through it ; the north and south ends being marked. If the bearing is N.E., the chord is measured off from the north point, eastwards. Thus, for a bearing of N. 64* 14' E, the point at which the scale reading 1063'2 intersects the dr cumference of the circle is noted, and the number of the atatien is affixed. The north and south points on the circle are the zero points to measure from, and from these points the chordi are measured off to the east or west as the case may be.

The following sample page illustrates the method of reducing the survey notes.

Plotting by Rectangular Co-ordinates. — This is the most accurate method of plotting a survey, because the position of each station is plotted without being affected by any errors committed in plotting previous stations.

It consists in assuming two fixed axes O X and O Y, crossing at right angles at a fixed point or ortMt, O, and in calculating the perpendicular distances, or eoordinatei, of each station from those axes. When the direction of the true meridian has been ascertained, it is advisable to make one of the axes represent iL Thus, in Fig. 47, let A represent a hori- T zontal line surveyed. Through the starting

I? point 0, draw a north and south line, O T,

and at right angles to this, through the same point, an east and west line, O X, then the angle Y O A will represent the bearing of the line O A. The line Y is taken at abscissa axis, and the line X as ordinate axis. Prom the end point of the given line, O A, the two perpendiculars A a and A a' are let faU to those axes. A a is termed the latitude and A a' the ikparture of the line O A. The latitude of a point may be dedned aa its distance north or south of some parallel of latitude. The distance that one end of a line is due north or south of the other end, is called

J

H

p

PLOrriNO THB

Survbt, 147 1

StJRVBY OP LONG- WALL WORKINGS AT A SCOTTISH .J

Colliery.

No.

W Pit. FWhh centre of Bh&ft, 12 h.

X 6 fL ; long lide bearing S, 16° E.

HMldiui

Antl*.

Brlni.

StUMoa.

Amirlu.

Uakt.

A

298*00'

N. 62" Off W.

B

299° 30-

N. 60° 30' W.

10O7-5

320' W

N. 40 00' W.

315* ocy

N, 45° Off W.

7C5'3

mm

bearing only into v.r oourse*

227° 30"

S. 47" Sff W,

805 '4

ISl

into ston© drift.

S

228° 00*

S. 4S° 00' w.

F

301* Off

N. 69° Off W.

984 -S

Q

287" 30-

N. 62* Sff W.

H'

20' 00'

N. 20° Off B.

P

M'Sff

N. 14° 30' E.

*,t

42'30'

N. 42* aff E.

to fiKW lying N. 68* W.

H

819° 00'

N, 41° 00' W.

16° Off

N. 16" 00' E.

10°3ff

N. 10* 3ff E.

W

10° 15'

N. 10" 15' E.

40* Off

N. 40° 00' E.

65°3ff

N Ss-So'E

to face lying 8. SCT E.

J

313° Off

N. 47° Off W.

80° Off

N. 20° 00' E.

4i

raff

N, 9° 3ff E.

8*00'

N. 8°0ffE.

N-'

20"3ff

N. 20° 3ff E.

/ 10 links to facff, lying N.

K

304" Off

N. 66° 00' W.

13°3ff

N. 13° 30' E.

365* Off

N. 6°0ff\V.

to face rtinniDg E, Mid W.

290-00'

N, 70" 00' Vv .

1147'1

1°00'

N, 1° Off E,

348° 00'

N. 12° Off VV.

to face lying S, 65* W.

M

278° 00'

N. 82° Off W.

N

266* Off

8. 86° Off W.

136.'} 9

S4r0ff

N. 11° Off W.

H

33rOff

N. 28° Off W.

to fivwi lying N. 60* E.

i

ssroff

8, 81' Off W,

Off

N, rOffE.

So

to face lying S. 89* E,

261* 3ff

S. 8!° 30' W.

to end of level.

k

J

ua

HINB-SURTKTlKa

the difference of latitude of the ends of tlie line, or, briefly,

latitude of the ILae, or ita northing or goulhing. Similarly th

distance which one end of a line is due east or west of the other

end is called the ditlerence of longitude of the ends of the line,

or the departure of the line, or its eaglmg or westing.

On regarding the right-angled triangles O A a and O A a' ia

Fig. 47, it will at once he seen that the latitude and deprtare

may be calculated from the length O A and the bearing A O n'

or 8, Now a' A is equal to O a, and a is equal to A a ; it tsaK

A a' therefore evident that - sin j3, and couBequently A n".

O A ain jS, and Oa OA ein 0. Similarly O a' 0. COB and A a - A cos $, In other words, to find the lati

tnde of any line, multiply its length by the cosine of its

and to find its departure, multiply its length by the sine of bearing. If the foreward bearing of the line is uorthvard, i latitude is north and is regarded as positive. If the hearing of the Une is eastward, its departure is east, aad regarded as positive. West departures and south latitudes regarded as negative magnitudes.

In Fig. 47, let Y represent the meridian, and lt O A represent a mine road, the survey of which with tbc ciiva-. ferenttT gave the following results : —

He.

Aarld

neaiuf.

Dbuant.

B

(fOOf 220* 17'

79* ly

32*16'

72*32'

Iso

The Temier-angles must first be reduced to meridian ansln with the result given above. The reduced bearings tii calculated. Tliey will be found to be as follows : — A, K B. N. 72' 32' E. ; 0, N. 28* 15' W. The latitudes and departurM may tbea be obtained from the formula! —

Utitad*

Diftonoc Dirtanoa

ooa bearing in bearing

The troublesome and tedious multinltcatinn by nnt.irA: -i:;' tad cosines may be avoided by using logarithms. Th? cal. uIj lions will then be as foUows v —

Pl.OTTlNi. THE SVliVl;Y.

U'J

A.

log 170

L. sin 32" 16'

Easting

log 180

I., (in 72* 32*

log 155

Lu nn 28* 16'

Werttog

ss

j'll a;: ares.

log 176

L. cos 32* 16'

Northing

log 180

L. 00* 72* 82'

XorUiing

log 165

L. cos 28* 16'

Northing

ar

2 245512

B.

9 97M99

219U331

In making calculations with logarithms, it must be remembered that in tables of logarithmic sines and cosines, the logarithm of the assumed radius is 10-000000. Consequently in the pre- ceding calculations, the log. radius 10 is deducted in order to give the log. of the natural number sought.

The results of the calculation should be entered in four columns, for northing, southing, easting, and westing respectively.

to.

BiDiramBsABiaa.

DiiTAia.

Latitusi.

N.

E.

w.

A

N. 32* 16' a

B

N. 72* 32- E.

N. 28* 16' W.

(

Mine-Surteting.

Regarding the northing as positive and the soutMng aa negative, the algebraical sum of the latitudes ia 339-41 links. The easting being positive, and the westing negative, the algebraical sum of the departures is 266-61 - 73-36 - 192-25 links.

Before the calculated co-ordinates can be used for plotting por- posea, the total latitudes and the total departures must be csdcu- lated. This is done by taking the algebraical sum at each atation, as follows : —

No.

Total LtUludcl lra SUtloa 0,

TaUi Dp*rtare> rrani SUtton a

A

+ 148-85

+ 93-81

B

+ 202-87

+ 265-61

+ 330 41

+ 192-Ss

Having prepared this table, draw a meridian line through tho first station O, Pig. 47, Along the meridian, north latitudes are set off upwards, and south latitudes downwards. East departures are set off perpendicularly to the right, and west departures perpendicularly to the left. 3et off, therefore, along the meridian in a northerly distance the latitude 148 "85 links to the scale required. This gives the point a'. From that point, set off perpendicularly the right the departure 93-91 links. The station A is thus fixed on the plan. Join the points O and A. From O again set off upwards 202-87 links to fi', and from that point set off 265-61 links perpendicularly to the right. This gives the point B. Join the points A and R From O again set off upwards the latitude 33941 links to c', and from that point get off the departure 1 92-25 links. The last point is thus fixed.

In this way any survey may be plotted with great ease and rapidity, and with greater accuracy than is possible by any other methoti.

Tlie calculated co-ordinates are of gret value for testing tlie accuracy of a closed traverse. Obviously, when a aurreyor makes a circuitous survey returning to the starting point, he has gone exactly as far to the north as he has to the south, and as for to the east as to the west. Consequently, if his survey is correct, the sum of tho northings should be equal to that of the southings, and the sum of the eastings equal to that of the westings.

An illustration of this is afforded by the surrev of A closed

Plotting The Bdrtet.

ISl

polygon with a theodolite, the notes of which are given on p. 107. On calculnting the co-ordinates, the following results are obtained : —

LTLTITItBa.

OlUSTtlUI.

Ha.

Eietrcni Biuiikm.

Dtnixd.

North +

Soaa-

Sut +

WMt-

s. ss'syE.

Llnki.

5G9'5

N. 39" 03' B.

1B5S

158'S

N. 88° 04' E.

ISfi

N. 47* 44' E.

sai

N. 63* W E.

172S

N. 31* 13' W.

N. 59" 06' W.

l.OM

S. 44* 28' W,

S50'6

8. 31' 29' E.

Im

So-5

S. 51- 29' W.

20tll-0

If there should a slight error, the latitudes and departures must be corrected, before plotting, so that their sums shall bo equal in each case. This is done hy distributing the error among the Uiies in proportion to their length, the balancing being effected by the following proportion ; — As the sum of all the lengths is to each particular length, so is the total error in lati- tude (or departure) to the correction of the corresponding latitude (or departure). The correction has been made in the above example. It may frequeutly be made by determining the error per chain, without making the exact proportion.

The error of closure is the ratio of tlie length of the line joining the first and last points of the survey of a closed polygon, to tlie whole perimeter. Being the hypotheause of a right-angled I triangle, of which the err-ors in latitude and in departure are the other sides, the length of this line is equal to the square root of

p

H 152 Uiie-Surveyinq.

die stun of the sqiiaros of thoae two errors. This divided by the whole perimeter gives the error of cloaure. In mine-surveys. it should not be more than 1 in 1,600, or 5 links per mile. In ordi- TiHry Burface-surveys it will average 1 in 300 or 27 links per mile. A co-ordinate protractor, called a trigoiwmeter by the makers, Meaara. KeufTel and Esser of New York, has recently been intro- H duced in America. It oonaista of a plate 15 inches square (Fig. 48), divided into 100 equal squares by horizontal and verti( H lines. It ia provided with an arm fastened with its zero upon the zero

J

i_j

L.

/V

r

\-A

9, one corner oi iiiio piave. i.i> is graduated, with the same divTsion as the plate, to read distances from the centre outwards. On the sides, the plate has angular graduations, the zero joint being the centre of the quadrant. By moving the arm to the given angle, the latitude i( at once read ofi' on the vertical scale and the departure on the horizontal acale, for the given length as read

F

?

trr

J

/

J.

b

j

/I

f

y

Y

'

"

on the arm , if, for instance, B A U

Fig. 48. 13 the given angle, and A D the

given distance, D £ and D F are

the coKjrdinatea. The readings are exact to within O'l per cent

The instrument is also of use for calculating the bases and per*

pendiculars of inclined station-lines in mine-surveys.

Though described in 1886 by Mr. E. G. Gaertner* as a new invention, this instrument was known two hundred years pre- yiously. It is, I &nd, described on p. 127, and figured on plate 7 of Nicolaua Voigtel's Geormtria Sttbterranea, published at Eialeben in 1686.

Calculating Scalefl.— For ordinary practical work the oo-ordi-

nates may be determined with great rapidity by means of the

slide rule. On this rule, logarithms of numbers, sines, and

cosines are represented graphically in the form of scales. The

instrument consists of a rule, having on ita face a, groove cut

throughout its entire length, in which a second rule slides

1 smoothly. The bearing and length of a given line being known,

ft its departure is found bj setting 1 on the slide to the length on

the rule, and against the sine on the slide will be fottnd the

required departure- on the rule. Latitudes are fonnd in a

similar way, the cosines being read off by reading the sines

backwards. To avoid this operation, complementary figures may

be pencilled along the line of sines.

Plotting The Survey.

No slide rules of English make can compare in acourac and portability with those made by Gravt, of Paris. One 26 centi- metres long is accurate to one part in 500. Oo-ordinates of th lines occurring in mine-sunreys may thus be determined accurately to the first place of decimals. The back of the slide is divided for nmes, tangents, and logarithms, all of which can be read at the back through special openings without removing the slide, or the lide may be reversed. A sliding index, or cursor, is provided, -which adds materially to the power of the instrument For important theodolite surveys, the slide rule is not accurate enough. For this work, however, it saves much time in calcu- lating differences of logarithmic sines, &c. The most accurate slide rule available is of the Gravdt type with the graduations not on wood, but on celluloid, a white substance resembling ivory. Careful tests of tbia instrument show that the average error in calculating co-ordinates is 0*12 per cent. The errors are conse- quently inappreciable when the survey is plotted to any of the scales usually employed for mine-plans.

With the ceUuIoid slide rule, and other rules of the Gravfit type, the departure of a given line in the survey may be found by placing the given angle, as shown on the line of sines against the index at the back of the rule, and by reading off the number, on the scale on the face of the slide, eoiTesponding with the given distance, as shown on the upper scale. The latitude is found in A similar way, the cosine being used in place of the sine. In this way results may easily be found without calculation, accurate to the first place of decimals.*

In the Government Mining Offices on the Oontinent, cal- culating machines are extensively used for computing the co-ordinates of mine-surveys. The type of instrument generally used is that invented by M. Thomas, of Col mar, in Alsace. This instrument has recently been improved by Mr. Edmondaon and by Mr. Tate. Fitl! descriptions of the three instruments are given by Mr. 0. V. Boys.t

Traverse Tables, — Tables which show by inspection the amount of the latitude and departure for any bearing and dis- tance are termed traverse tjibles, because by their aid the resolution of traverses is eiTected without calculation.

In order to be of any use to the mine-surveyor, 'such tables must be calculated for every minute of bearing and to four pl&oea of decimals. These conditions are fulfil letl by the tables calcu- lated by H. Lotiis, J. T, Boileau, W. Crelliti, and R. L. Gur- den. There are several other tables published, which, though well arranged, are not sufficiently in detail for mine-surveying CoUieiy Ouatdian, p. 587, 1889. fJoum. Soc. Arti, vol. xxxiv., p, SM, \?a6.

UIHE-SUSTEtlKG.

purposes. For example, the tr&verse tables given in Chambera'a Mathematical Tables are calculated only for ever degree of bearing to one place of decimals. Tbough valuable for problems in navigation, they are useless for mining purposes.

The following example will illustrate the metLod of using Louis' or Boileau'fi tables, which are calculated for everv minute and to 5 decimal places for distances of 1 to 10 : — Given the bearing of a line, N, 33° 15' E., and its length 1 chain 76 links, required its latitude and departure. Seek the table headed 32', and from the section 15', take out the latitudes and departure* separately for the hundreds, tens, and units, removing the decimal point in each case as many places to the tight as the figures in each separated portion of the distance exceed those in the corre- Sponding numbers in the tabular distance columns. The distance 1 chain 76 links will be separated into 100, 70, and 6 links, and the traverses for each will be taken out separately, thus ; —

ReduCTil Be.rriag, N. 32° 15' W.

DltUscs.

The most accurate traverse tables published are those oom- puted by Mr. R. L. Gurden, Aitthoriaed Surveyor for tbe Governments of New South Wales and Victoria. These tables are calculated to four places of decimals for every minute of angle up to 100 of distance, so that the sines and cosines for a distance of 12 miles may be ascertained correctly to within half an inch.

In the example given above, the latitude and departure ac found with Gurden's tables, thus —

Itcdaood BarlDg. N. 32° 15' \V.

Dlstiiiia.

lAtltuils.

40;>547

Only one opening of the traverse tables is required- With logarithuis, on the other hand, the liook has to be opened in four places, two separate additions have to be made, and in taking out natural numbers proportional parts have to be resorted to, in order to find figures of the second place of deoimals. The advan- tage of these traverse tables over logarithms, both as rerds simplicity and economy of labour in calculation, is thus apparent. In important nndertakinga it will be found advisable to calcu- late the co-ordinates by logarithms, and repeat the calculation by the traverse tables, so as to obtain an iudependeut check and verification.

PLOTTIKG THE fiORVET,

I5S

Combined Sonreying aad Plottuig Instmment Henderson's

ntpid traverser is based on what is known as the pl&ne-tabla system of surveying. By its aid, underground or surface aiirveya cn be nttide, and the results laid down on paper with very great rapidity. Unlike the plane-table, however, it is not intended that the rapid traverser should be used for plotting the survey m the field, this being done in the drawing-offioe, with the aid of a parallel rolling ruler and scale.

The instrument consists of a circular metal table of about 10 inches diameter, mounted on an ordinary tripod stand, with the usual adjusting screws. It is provided with a brass alidade, with an ordinary sight at each end, revolving round u fixed centre pin. Upon the face of the table a disc of celluloid is screwed, and over this the alidade, by means of a groove, can travel freely. The disc is divided into five or more conoentrio rings marked on the celluloid, and the feather-edge of the alidade U ulso divided by means of a rectangular notch at each ring, for the purpose of pencilling on the disc the line observed. By means of clamping screws, similar to those of the circumferentor, the disc can be clamped to the stand, and the alidade, with attached, to the table when required.

In trarersing, the instrument is levelled and the alidade is lighted back to the starting point of the survey. Both the alidade and the table are then secured clamped. The direction of thia first line of the survey is marked with a finely pointed H H pencil on the selected ring of the disc, at two points equi- distant from the centre, and duly lettered or figured within the notch cut in the leather-edge of the alidade. Three tripods are nsed. Each of the two spare ones carries a candSe-holder with levels attached, a white card replacing the candle in surface surveys. The alidade is next unclamped, sighted to the forward tripod, and clamped, the direction of the second line being marked on the celluloid as before. The instrument is then re- moved from its tripod and fixed, with the alidade still clamped on the forward stand, and sighted back to the position it previously occupied and clamped. This having been done, the alidade is unclamped, sighted to the next forward station, again clamped, and the direction marked as before, the process being repeated for the remainder of the traverse. The magnetic meridian is taken at any convenient spot in the course of the traverse by means of a trough compass placed temporarily against the back edge of the alidade. The line thus given, pencilled on the disc, establishes the orientation of the whole of the survey, I The sights of the alidade are graduated to give angles of

I depression or elevation up to 25'. Thus, the mati\imen.t

lII?IB-St;BVBtI5&

for the majority of coUieries, for the leTela of metalliferoiu

mines, and for all ordinary surface euri'eya. Where greater accuracy in vertical angles ia required, as in inclined Bhafts, a vertical semicircle is attached to the alidade, and the anglei read as with the theodolite.

In plotting the survey, the celluloid disc is unscrewed from iti circular table and placed with the north line, that haa been marked on it, in ita proper position on the meridian line on the intended plan. A rolling parallel ruler is then applied to each line of the surrey in succession ae shown on the disc, and marked off on the plan. In a large survey, the disc may be moved to any meridian line as required. For future reference, the disc itself may be preserved with the name and date of the survey recorded on it, or, if necessary, the magnetic bearings may be read off with the aid of a protractor and booked, when the celluloid disc may be cleaned for future use.

This instrument has been successfully used by the inventor, Mr. James Henderson, in numerous surveys of Cornish mines, notably at West Wheal Frances, at Redruth. In November, 1892, it was decided to put out a cross-cut south from the 174-fathora level so as to come under the perpendicular portion of Bailey's shaft, which was perpendicular only as far as the 60-fathoni level, and then went off to the south following the underlie of the lode. After the cross-cut, which was 20 fathoms in length, had been driven, a rise had to be carried up through some 65 fathoms of ground to the bottom of the perpendicular portion of Bailey's shaft. In order to do this, the relative position of the two points was determined by surveying down 80 fathoms of the inclined portion of the shaft to the winie to the 174-fa thorn level, the total distance of levels surveyed amounting to 300 fathoms, and the number of stations required being fifty-three. The perfect holing on October 17, 1893, affords a guarantee of the adaptability of this instrument to complicated underground surveys.

An ingenious combined survey itij; and plotting instrument has been devised by Mr. T. Ferguson* in the form of a separate flat box adapted for tixing to the handle-bar of a bicycle, with which, whether ridden or trundled, the trace of the route can be made to develop as quickly an one proceeds. This cyclograph should prove of great value to the prospector, besides being useful for iilling in detail in triangulation surveys. In the flat box fixed horizontally to the handle-bar of a, bicycle is contained a sheet of drawing paper, which can be kept in constant orientation by adjusting meridian lines ruled on its surface parallel to a com. AtUomalic SuntyiTig iTUtrununte, tondon, 1904, p. 37.

Plottino The 8Urvbt.

pass-needle mounteil about 10 inches over the box. As ths b)i:> cle moTe?, the sheet of paper is gradually displaced in a backward direction, and a Btuall ink-roller pressing on the paper marks a line in a forward direction. As the course chaxiges in direction a simple manipulation maintaius parallelism between the paper-meridians and the com pass- needle, and a facsimile of the patit followed develops under the eyes of the observer.

Plotting Colliery Surveys in Scotland.— In the West of Soot- land, a method of plotting colliery surveys, which differs Irom that in vogue in other districts, is frei(uently employed. The protractor need consists of a circular brass plate, 2 feet in diameter, pivoted at the centre, so that it can rotate in a horizontal plane. It is supported in a square mahogany frame, the surfaces of the frame and of the protractor being flush. A brass or steel straight-edge ia attached to one aide of this square frame. The drawing-paper is used in circular sheets, which are fastened on the face of the protractor inside the graduated circle, A sheet of paper is permanently glued on, and sheets may be attached to this by means of wafers as required. A T-square replaces the parallel ruler used in other methods Ol plotting with the protractor. It ia brought to the diameter of the protractor, and then the required bearing is brought under the edge of the T-square by rotating the protractor. The protractor u then held steady, while the T-square is moved along the straight edge attached to the mahogany frame, in order that a line may bo drawn through a station point. In the more recent forms of this instrument, an index line is engraved on a small piece of brass fixed on the left of the mahogany frame, and the required bearing on the protractor is brought to this line by rotatidn. A day's survey having been plotted, a tracing ia made and transferred to the main plan of the colliery,

Calctilating the Co-ordinates of a Trlangnlatioo. — In South Africa, where triangulation is exclusively used for sttrveya of mine concessions, it is usual to plot by co-ordinates. For the calculations necessary, 0. L, H. Max Jurisch's " Tables of natural slues and cosines to seven decimal figures of all angles between 0' and 90° to every 10 seconds with proportional parts for single seconds" (Cape Town, 1884), are chiefly used. The problem occurring is as follows : — Given the co-ordinates of two points, P and Q, the angles of direction P Q or a; Q P, the dis- tance PQ and by observation, the angles of the triangle PQR; required the co-ordinates of R. From the given data the dis- tance P B and Q R and their angles of direction x F R and X Q B m&j he calculated.

k.

HINE-SUBVEYlUa

Consequently —

P R sin a; P R y - distanc© of R from P a y P R COS a: P R - distance of R from P Aaj Q R sin a; Q R y — distance of R from Q a'x Q R cos ac Q R .-B — distance of R frotu Q i' yofP + ily yofR;a:orP + Ax a; of R y of Q + A'y y of R ; a; of Q + A'x x of B

It is usual to calculate the oo-ordiDatea of R from botli equa- tions, in order to have a check on the calculations. In thesa equations, the co-ordinate drawn from any point parallel to the vertical or y axis is briefly called the y of that point, and the other co-ordinate is called the 31 of that point.

The following example, given by Leopold Marquard (" Co-ordi- nate Geometry," Oape Town, 1882), will illuatrate the manner in which the calculations are made : —

Given

Lines. Cape Kooila. AB 41-26

Angles.

69' 54'

Bc 37-98 D 66-46

Bcd + Ode -

134' 44' 47* 12'

De 118-30

Def -

87' 03'

Ef 167-75

Efg +

277° 13'

Fg 14Sm

Required the co-ordinates of A, B, C, D, E, F, G.

The line A B having been selected as jr axis and B as th origin, we hare —

y of A ; x of A yof B 0; ajof B

Ba

+ 41-26

Angle X B C 69* 54', to this U added B D + 134* 44',

and from the sum 180° is subtracted. When the angle of inter- sectioQ of two lines and the angle of direction of one of them is known, the angle of direction of the other is found thus : — When the two angles have the same vertex, their algebraical sum is the required anglo of direction, and when they have different vertices, their algebraical sura, either diminished or increaaed by 180', as may be most convenient, will be the required angle of direction. Consequently —

Angle X C D -Ji' 38'

Add C D E - 47' 12' and add 180'.

Then X D E 157° 2(1'

Add E F - 87° 03' and add ISO".

Then X E F 250° 23'

Add E F G + 277° 13' and subtract 180°.

log B 0=1-5795550 log cos XBC 9 5361286

1-5522642 yofC - + 35-67 jcof C

M 166836

Similarly tho eo-ordinatea of the other points will bo found to aa follows : —

+ 13-05

y

D

+ 63-37

+ 73-46

E

+ 108-77

F

O

- 81-U

+ 62-flS

ConTonient formB for keeping the field-book and for noting the calculations have beeti drawn up by Mr. G. A. Troye,*

" Tratu. Iiist. Mining and Metallurgy, vol. Si., 1901, p. V2&.

HINK-SUItTKTINO.

CHAPTER XII. Calculation of Areas.

Ueasures of Area. — The area of mine-royalties and of ootJ wrought is usually expressed in acres. The statute acre is equal to 10 square chains or 100,000 square links. It is sub-diride either decimally or into 4 roods of 1,210 square yards, and 160 ferchet of 30J square yards. One square mile is equal to 640 acres.

In order to reduce square links to acros, roods, and perchei, divide by 100,000 by cutting off five figures to the right hand The figures remaining to the left will be ares. Multiply the re- mainder by 4 ; the whole-number remaining will represent rood*. Multiply the remaining fraction by 40 ; the figures beyond th* decimal point will be perches. The nearest round number ii usually taken ; fractions less than half a perch being disregarded.

The metric unit of land measure is the hectare of 10,000 square metres. This is equal to 2*4711 acres.

Three methods of measuring areas are employed : the method of triangles, the method of ordi- nates, and the mechanical method,

1, Method of Triangles.— The survey of the ground having been plotted, lines are drawn on the plan so as to divide it into a number of triangles, the area of each of which is calculated, Tlius, in order to calculate the area of the polygon A B D E F O (Fig. 49 ), measure all the sides of the figure, and the diagonals A 0, A D, A E. and A F. Then if the lengths of the three aides of the triangl? ABO are denoted by a, h, and c, the area of the triangle is given by the formula-

in which f represents the half sum of the lengths of the sides of] the triangle.

Calculation Of Arbab.

Assuming that the side BO is 120 links in length, AO 13& iks, and A B 90 links, the area of the triangle is —

yi725 X 52-5 St 37-5 x 82-5,

or fi293'18 square links.

If logarithms are employed, the formula is —

In the same way, the area of the remaining four triangles in Fig. 49 are calculated. By taking the sum of the areas of the five triangles, the area of the whole polygon is obtained. As a check on the calculations, the lengths of the diagonals B Z), B £, B F, and B O may be determined. Five new triangles would ihuB be obtained. The sum of these five areas should be the same as the result of the first calculation. If there is a small diSereace, the meaiU of the two results is taken as the correct area. If the difference is considerable, the measurement must be repeated.

Another useful formula for calculating the area of triangles is the following : —

Area

in which a u any one of the sides of the tri angle, and p a perpendicular let fall upon that side from the opposite angle. When two sides and the included angle are known, the area is iven by the formula —

a b sin

Area

a and b representing the two sides, and the included angle.

When one side of a triangle and the adjacent angles are given,

it8 area is equal to — ty> my

2 sin (B + 0)

The areas of figures with curved outlines may be found by the method of triangles preceded by a process termed tqticMtviig or giving and taking. This consists in drawing through the boundary a straight line, leaving as much space outside the straight line as there is inside it, oa nearly as the eye con estimate.

It is sometimes advisable to reduce a polygon to a single triangle egnivaJent in area, aa in the foWo'wma fexa.'in'Ve \'n.

W

Wl

11Ine-B0Bvetlng.

the poSygon A B D E in Fig, 50, draw a line from A to 0, and with a parallel niler draw a line B F parallel to A cutting C D produced in F. Join A F, Then the area of the quadrilateral figure A F D E is equal to that of the original figure. Tho

Fig.fia

triangles A B P, B F being on the same base, B F, and between the same parallels, are equaL Take away from each the common triangle B H F, H being the point at which the lines A F and B intersect ; the remaining triangles A B H, F H are equaL But in the alteration of the figure, F H has been substituted for A B H j therefore, the area of the quadrilateral is equal to that of the original figure. Similarly, by drawing E G parallel to A D, intersecting D produced in G, and by joining A O, the area of the triangle A F G may be made equal to that of the quadrilateral figure A F D E, and consequently to the original figure. Whatever may be the number of sides of the polygon, a similar process will reduce it to a triangle having the same area. 2, Method of Ordinates. — An axis A X is measured along the greatest length of the track to be measured (Fig. 51). Otisets are measured at right angles to that axis, sufficiently close together to make the spaces between them approximate to trapezoids. Let d be the distance along the axis between two adjacent ofiaets or ordinates, and b, the breadths of the figure at those ordinates. The area of the trapezoid is then

„ ' , and the area of the whole figure is the sum of the

areas of the trapezoids into which it is dinded.

For eaxvmpU. — Let A X in Fig. 51 represent the chain from which ofiaets were taken to a curved fence. The lengths of the

Calculation Of Arbas.

oCsets measured in links, were aa follows;— 5 30, 6j 38, 6, 61, 6s =50, 6, 85, 80, 6. 40, b, 60, Jg 69, 48, and 615 19- The area iacluded between the ohoin And the fence is —

(30

+

38)

3,400

So

(38

+

61)

4,050

so

(61

+

60t

6,550

Co

(50

+

85)

e,760

M

(S5

+

So)

8,260

(80

+

40)

6,000

(40

+

60)

6,000

(60

+

60)

6,450

(69

+

48)

6,850

Co

X (48

Total

+

19)

—

3,350

55,&50

]f this total, that is, 27,775, is the area in square linka When the intervals between the ofiBeta are all equal, as in the aboTo example, the calculation may be coneiderablj eimplified. the values of d being equal, the formula becomes

that is to say, the area is equal to the sum of all the intermedito offsets, and of one half the end olfsets multiplied by the constant interval between them. Applying this formula to the above example —

When the line determined by the offsets is curved, the area may be calculated with greater accuracy by Simpson's formula. This assumes that the lateral boundaries of the figure consist of short parabolic arcs. An even number of equal distances must be measured along the axis, when the formula is

Area

j 6, + fc, + 2(6j + + itc) + 4{i, + 6, + <fec) t s;

that is, the area is equal to one-third of the constuit interval tween the offsets multiplied by the sum of the &c&t keA

Hine-Survetiho.

ofTsets, twice tlie sum of the even oflseta, and four timeB the sum of the odd otfsets. Applying this formula to the example giyea,

Area-(30 + 19 + 510 x 1104) 277 1 6f square links.

In calculating the area of a surveyed piece of land, it ii advisable to use exclusively the dimensions given in the Geld- book. The process is, however, very laborious, and nay frequently be dispensed with by equalising boundaries and taking measurements on the plan.

By means of rectangular co-ordinates, the area of a. piece of land may be accurately calculated without necessitating the preparation of a plan. The general rule for finding areas by this method is as foUows : — Multiply the total latitude of each station by the sum of the departures of the two adjacent ooursei The algebraical half sum of these products is the area.

The total latitude of each station is found by adding the latj- todeof the preceding course to the total latitude of the preceding station. To find the adjacent departures, add the departures of the two courses, one on each side of the station. The following is an example of this method of calculation : —

liAT]TU]>l:

Sirunu.

Ha. A

BwlDC

UUtadft

Stputum.

Am*.

N.+

S.-

E.+

w.-

N. 51' 33' E.

CluUlu.

29' 18

22 -So

B

a TS-OfB.

+ 1814

-H34 62

S. 20°37'W.

+ 6'32

¥ 771

D

S. 78°45'W.

49&

-31 '96

-1- SOi

E

H. 23''28'W.

7-B3

3 '36

+S12']

99S1

The double area of the polygon is thus 908'53 square chains, The area, therefore, is 499-26 square chains, or 49-926 acres.

3. Mechanical Metbod.Instrumeuts for measuring areas on plans are termed planinteUrt, The form moat generally used

Calculation Of Aseas,

is the [tolftr plani meter of Amgler, of which the general principle shown in Mg. 52. This is an inatruniRnt for measuring the

area of any figure, however irregular, by the mere passage of a tracer round I about its perimeter. It consists essen- '. tially of three parts, the adjustable H arm D, the polar arm BO of fixed length, and the rolling wheel F, which rests upon the plan. The wheel is graduated and provided with a ver- nier. The two arms of the instrument are hinged together by a hardened steel axis 0, and permit of an angular motion of nearly 180°. The rolling wheel is mounted on a steel axis parallel to the adjustable arm O D, that is, parallel to the imaginary line joining the tracing point at D and the axil C of the polar arm. The number of complete revolutions of the rolling wheel are shown by a record disc driven by an endlesa screw on the shaft E. At the end of the arm B is a loaded disc which rests upon the table, and serves as a fixed support for the instrument. In its centre at B is an upright pin forming the turning point or pole of the whole instrument. At the end of the adjustable arm, at the same distance from it as the axis E, the tracing point D is screwed in vertically.

When the tracing point D is carried round the outline of any figure, such as G H I, io as to return to the point from which it started, it can be proved* that the distance rolled by the edge of the wheel F is equal to the area of the figure divided by D, and consequently that the area of the figure is equal to D multiplied by the distance rolled by the wheel F. In Great Britain and the United States, the graduations on the circle usually represent square inches of area on the plan.

This planimeter gives results sufficiently accurate for mining purposes, and its cheapness and simplicity render it of great value. When, however, a very high degree of accuracy is required it is found that the planimeter is seriously affected by the papei on which the measuring- wheel revolves. This is partjoularly noticeable with old plans that have been folded up for a length of time. It is also noticeable when the operation takes place near the edge of the paper, necessitating the wheel passing over that edge.

In cases where the use of the polar planimeter appears imprac-

For proaf, consult tbe report on this instrument by Sir Frederick Bramwetj in Rfp. of Forln-tecoHti Mtti'mg of the Brit, Asioe,,. ttV. VTL

Minkscrtetino.

ticable, recourse must be had to the precieioa planimeters mads by G. Ooradi, of Zurich. In these instrumenta, the so-called tiupsnded planimeters and linear rolling planimeters, the meASor- ing wheel does not travel on the plan itaelf but on a disc, which is an integral part of the instrument.

The suspended pl&nimeter is easentiallj a polar planlmeter ; it gives, however, results ten times more accurate than those given hy Amaler's instrument. The linear rolling planimeter is the moat accurate instrument of its kind yet invented. Instui of revolving round about a pole, the rolling planimeter moves in a straight line, on either side of which the area is determined.

The following table showing the mean error in planimeter readings haa been drawn up from the results of a series of experi- menta made by Professor Lorber of Leoben, in Austria : —

iU4.

TBI Mm Kiusi IK 1 Puaioi or tet Tuen uiocn* n TBI niLtriiriiio rukCTToii or rm Auu :—

iDSqiun OntlmttnL

laSqout

WlththiPullU' Fluilmettr.

CnltofVgrBiv iota. mtn. laoirtq. Id.)

with tlie Siu-

ponilnl

P]iniinetr.

UnltDrVemlir

1 *q. nam.

(0 cci H). Id.)

witii iht

Rnlllni

PUDlmetsr.

Cult of Yen ler

(0-M??li.)

WiUitb*

Rolitac

Piituiiiwur.

nnltofVenhv

lU

3U0

1 in 75 1 in 148 1 in 356 1 in 682

1 in 1.274

1 in 62.T 1 in 1,111 1 in 2,5011 I in 4,167 lio 7.143 1 in 9.375

1 in e,25 1 in 1.000 1 in 2,000 1 in 3.333

1 in ,5,128 1 in 8,000

1 in 1,000 I in 2,000 I in 3.000 1 in 6,000 1 in 7.093 t io 10,000

The aLmpleat of all area-measurers is the hatchet-planimeter.t This ia merely a trammel of fixed length, with at one end, a traciug pointer, and at the other end, in the aame plane, a curved knife-edge ealled the hatchet. The boundary of the fignre, whose area is to be ascertained, is traced continuously in one direction, while the hatchet deacribes a from which the area of the figure can be directly measured.

Produce of Coal-seams. — The area of coal wrought in any par ticular seam may be estimated by dividing the plan into squares of 10 acres each. It will be found useful to liave a sheet of tracing cloth, divided into l-acre squares, drawn to the aama scale as the plan with which it is to be used. The aide of a square, of which the area is 1 acre, measures 316-228 links. The squares should be drawn in black lines, and a\ib-dirided into quarter- acre a by means offkint red lines. The area of coal

BjKjijuering, vol. Mi., 1894, p, 697. See also O. Uonrioi't monograph, Jie/i, Bril. Asioc.. 1S94, pp. 496-522.

Calculatioit Of Areas. 167

wrought can be estimated with considerable accaracy by merely placing the sheet of tracing cloth over the plan, and by counting the squares covering the space on the plan representitig that area.

The area of the coal wrought and the thicfcneM of the seam being known, the tonnage may easily be calculated, as the tpeciiio gravity of the coal (1,250 to 1,500), with that of water taken as 1,000 for standard, is equal to the number of ounces in a cubio foot

The produce of coal-seams depends not only upon the speoifio gvity of the coal (1*35 to 1'50), but also upon the ay stem of working, and the number of faults. According to Professor J. H. Merivale, at a Durham colliery working the Harvey seam 3 feet 6 inches in thickness, 9,185 tons per acre were obtained when working by the long wall system, and 5,052 tons when working by the bord and pillar system. The yield per acre per foot thick of the South Staffordshire thick coal by the various methods of working is calculated by Mr. H. W. Hughes to be AS follows; — Square work, 1243 tons ; longwaU (two divisions), 1398 tons; longwall (one division), 1166 tons.

A roagb rule is to calculate the produce at 100 tons per inch per aoro, which leaves an ample allowance of some 25 per cent. for loss of every kind. Another role frequently used is to calcu- late the produce at 18 cwt, to the cubic yard. This gives tons per inch per acre or 1,450 tons ]>er foot per acre.

The CoIcoIatiOQ of Ore-Beserres. — Having finished the survey of a metalliferous mine, the surveyor is sometimes called upon to calculate the quantity of ore-reserves in that mine. Various methods are employed for this purpose. Indeed different sur- veyors will not agree within wide limits aa to the amount of ore- reserves in the same mine. Sometimes the amount of ore in sight will be considered to be a rectangular block limited by the out- 4xrop of the vein, the depth of the shaft, and the extreme points of the levels, diminished by the amount extracted. Other sur- veyors would avoid so excessive an estimate and take hut one- third of that amount.

The following method is recommended by Mr, J. G. Murphy, an experienced American mining-engineer, as the fairest and most trustworthy : — Let it be required to calculate the ore- reserves in a mine opened up on a. vein with a mean cross-section of 6 feet; a cubic foot of the vein matter in place weighing 150 lbs. The ore stopes are generally very irregular. In this case, however, it may be supposed that the stope faces are 1 1 feet apart and 8 feet high. There is an inclined shaft, 10 feet by

The TAiek Coal <)f South Slaff<>rdkire, Sheffield, 1885, p. 17.

UlNB-BDHVETIFa.

6 feet, following the dip of the vein, and 6 levels, each 7 feat bj 6 feet, 100 feet apart. The lengths of the levels are —

n.

200 feet wet ;

too

3fi0

ISO fet cut.

140 „

Iso

The longest level west ie 350 feet and the shortest Assume the bounding line of the area of available ore to b eg & distance west of the shaft,

350 - 100

- 225 ft.

J

The longest level east is 400 feet, and the shortest 100 feeC The bounding line in this direction calculated in a similar wa| will be at a distance of 250 feet from the shaft.

The inclined abaft has opened up the vein for 670 feete Deducting say 16 feet for the irregularity of the sur&ce, thf quantity of ore in sight will be a rectangular block 655 feet deep> 225 + 250 or 475 feet long, and 6 feet wide, that is, 1,866,7BC cubic feet.

From this quantity, however, must be deducted the quandig of ore extracted, namely —

CuMe Pl.

Inalined abaft.

39,300

Level I.,

14,700

Level IL,

10,020

Level III.,

2i,aio

Level IV.,

10,080

Level v.,

14,490

Level VL,

21,000

Level L, Btoped east (roagb estimate), 3,400

Level I., Btnped west, L.evel IL, atoped west. Level IIL, atoped east. Level VL, stoped wett,

Total, . Or ia rouod namberi,

6,500

7,000

20,000

12,000

. li>l,230

. )82,(W0

Calgdlaxiom Of Askab.

19

lis qu&ntity, deducted from l,866,7oQ cubic feet, leaves S84,760 cubic feet. DiWded by 13 J, the nuiuber of cubic Bt required for a ton (of 2,000 lbs.), tliia gives 124,797 tons of in sight.

The quantity of ore diBcovered in a mine may be estimattid om its specific gravity and the average size of the vein. The ecifio gravity of the ore, with that of water taken at 1,000 for tndard, is equal to the number of ounces in a cubic foot. Great ittton IB necesaary to determine the proportion of the vein y<!h may considered solid ore.

A vein 6 feet square and 1 inch thick contains 3 cubic feet ; erefore, in order to find the number of cubic feet per square >hom of a vein, it is merely necessary to multiply the thickness inches by three.

!rbe following example illustrates the method of finding the light of any ore per square fathom in a vein :Wbat quantity gsleoa wUl be produced per square fathom from a mineral LQ 6 inches in width One quarter of the vein consists of Lena, the remainder of zinc-blende. One-twentieth must be owed for cavities in the vein.

The specific gravity of galena la 7*5, and a cubic foot of irater lighs 1,000 ounces ; therefore, a cubic foot of galena weighs 00 ounces. The vein being 6 inches thick, there are 18 cubic it tu a square fathom. One quarter of that amount, or 4-5 bic feet, consists of galena. The weight of galena in ounce* therefore

vm

7,600 4-6 33,750 3109-375 lbs.

this, one-twentieth, or 105 '468 lbs., must be deducted, ,ving 2003-907 lbs., or 17 cwt 3 qrs. 15 lbs., as the weight of id ore per square fathom.

For recording the value of ore-reserves, Mr. J. 0. Little inta out that, on the vertical section of a mine, contour Hues m level to level may be plotted exhibiting the number of its of value of ore existing, provided that sufEcient details of le width and assay values are available. Surface cost and leral charges are usually expressed per unit of weight of ore lied ; but by the aid of an ingenious slide-rule inventeJ by Little, these costs can be distributed over the area worked, d thetoial cost per square inch recorded. In the Transvaal i stopes are surveyed every month ; the surveys being some- les plotted on the reef plane and the areas worked out oom- ted with the planimetor. The calculation of ore-reserves haustively dealt with by Mr. A. 0. Oharleton.t

\/oiir/ia/ a/ the Jirititk Socitlt/ of Mining Slttdciits, T(o\. tx. , V'i'sa , Si. jjmC. Jfim Met., vol. ix., 1901, p. 203.

UIllB4DBVSril((k

Chapter .

Lbve:i.limo. '

Definitions and Principles. — Xievellisg is the art of detrmli the relative distances of points from tlie centre of the One point is said to be &bove another when it is farther from] the centre of the earth, and the difference of distance from thAt) centre is called the difference of level between the two points! The operation of finding how mach one point is higher or lower than a.tioth(ir may lie trigonotnetrical, geometrical, or physical.

Trigonometrical levelling uecasitates the meajsurecavnt lengths and angles. As an illustration, the simplest o&ae nuj

be tAfeen. In order to determine thi dit!V>rencte of lerel A and (Fig. 53), or in other words the line A B, the A B, and one of the two lines A G and B must bo mc The height required is then found by trigonometrioal calcukit irom the two magnitudes measured.

In geometrical levelling, a horizontal line or plaun is coc structed, and the distance of th two points A an' from tliis is measured directly by settiiigup v .vr

The difference of the two readiugs on the stavea is uie aiutr in level between the two points.

Physical levelling is based on the chaiije of tDMwphefi<~ pressure at different altitudes. The most important iaxtniDant_ for this mf'tliod of kwellitt;; is the barometer.

The Mason's Level and Boning- staves. — For geomntriol Uf ling, there may Ite employed the mason's leTel, boning-atiiv or th spirit-level.

The muson's level is baai-d on the priii It Lb only used for levelling, when no f>t

Letellino.

Fig. 65.

obtained. To use the instrument, two pickets are driveo iato the ground and adjusted antU the plumb-line of the mason's leTel shows that their heads are truly level.

The same operation ia more rapidly performed by means of

boning-taves, which are simply 3-foot staves having a T-head.

Both these methods are very rough and inaccurate, and only

niteble for very short distances.

Thfi Spirit-level is the instrument commonly used. The

sptrit-le'vel proper is a glass tube B 0,

A Fig. 55, hermetically sealed at both

" - '~yi ends, partially filled with liquid. By giving the tube a alight arched curva-

ture, the bubble may be made to rest firmly in the middle, and by regulat- ing the curvature, the travelling of the bubble may measure mall angular deviations from the horizontal line. The tubes vs ground on the inside so as to give a similar curvature to th of the tube under which the bubble travels.

(a,) The Dumpy Level — The term spirit-level is also applied the levelling instrument, of which the spirit-level proper is 0e Msential part. The instrument most generally used in Great Britain is the dumpy level, invented by W. Gravatt. It is **pre8ented in Fig, 56. A is the spirit-level attached by screws

at a, a, to the telescope B 0. The small circle near the object end B of the telescope represents a small transverse spirit-level used to show whether the cross-wire of the tele- scope is truly horizontal. D D is a flat bar or oblong plate fixed on the top of the vertical axis £. To this bar the telescope is attacbtd

IlfTvjHbojif by adjusting screws d, d. The

Jiq) fi/"j>L hollow vertical axis turns upon a

ml spindle fixed to the upper parallel

A.// (jfj plate F, the spindle being oon-

\/j y tinned downwards and being at-

tached to the lower parallel plate Q ' — by a ball and socket joint. There

p. go are four levelling-acrewfl/*, by which

' the vertical axis is set truly vertical ,

The lower plate ia screwed on the tripod head H. The tripod oonsistB of three wooden legs like those of tho theodolite. In some instruments, a compass is carried on the top of the plate d, d for taking the bearings of lines of trial sectvous.

3a

Uise-Sdrvetino.

The telescope of the level is similar to that of the theodolite except that the diaphragRi contains one horizontal wire emd two parallel verticftl crosa-wire, as shown in Fig. 57. This lerelling inatrument derives its name from its dumpy appearance, due to the large aperture and short focal length of the telescope. The latter is usually 9 to 14 inches in length.

(6.) The Y-Level.— Of the different varietieB of lerelling Instrument, that termed the Y-level is preferred hy Ameriraw engineers. In this instrument the telescope is monnted on Y'l, like those of the Y-theodolite.

A recent form of American Y-level, made by Messrs. Hellr k Brightly, of Philadelphia, is shown in Fig. 58. The telesMp* rests on Y's, and is conhned in them by clips fastened by binding- pins. The telescope is 17 to 20 inches long. It bos at eacli

mmm

Fig-fiS.

a ring of bell-metal ; by these it revolves in the agate beamg> of the Y's, and can be clamped in any position. The spirit-lefel is attached to the under side of the telescope, and is provided at its ends with screws for horizontal and vertical adjustnieat. The level scale extends over the whole length, and is graduated into tenths of an inch, A clamp and tangent screw are connected with the axis for moving the bar and telescope.

(e.) Thi Tronghtoa LeveL— In the Troughton and Simml' pattern of fixed telescope level, the brass case of the spirit-level 18 embedded in the top of the outer telescope tube. There are no adjusting screws. These levels are made with telescopes of 10 to 26 inches in length.

The Adjustments of the Level are the same as those of the theodolite. They are as follows; — Temporary Adfjtiatmenlt : 1 For parallax. 2, To place the vertical axis truly rertical hj

Lbvbllimo. 173

tueaiu of the leTelling-Bcrews. I'erumnmU Adjustmenls : 3. For coUimation. 4. To make the spirit-level parallel to the line of collinifttion. 5. To place the telescope and spirit-level perpendi- cular to the vertical axis.

The adjttstment of the line of coUiiofttion in the Y-level ia obtained by rotating the telescope on ita collars. The parallelism of the level to the line of colUmation is obtained by reversing the telescope end for end on its Y's,

The odjastments of the levelling-instrumenta with fixed tele- scopes are not so simple, but they are much more permanent. In the dumpy level, the adjustment for collimation is made by the instrument-maker before soldering the telescope tube to the two blocks that support it. In this case, the adjusting-screws of the diaphragm should never afterwards be disturbed. To make the level and line of collimation parallel, a level piece of ground is selected, and after levelling the instrument by means of the levelling-Bcrews, it is directed to a stad' held by an assistant at a distAnce of about 10 chains. The difference between the height Kad and that of the centre of the telescope above the ground is noted. The instrument and the statf are then made to change p!acs, and the observation repeated. If the results agree, thd level and the line of collimation are parallel. If they do not, the inclination of the telescope must be altered by means of the jevelling-Bcrews, and the bubble then brought to the middle of tube by means of the adjnsting-SL-rews a, a (Fig. 56).

id.) CoBhing'B Reversible Level. — On account of the inconveni- ence attending the adjustment for collimation in levfilling-instru- nients where the telescope ia fixed, it occurred to Mr. Gushing,* Inspector of Scientific Instruments to the India Ofiice, to make the eye-end and object-end of the telescope interchangeable. For this purpose he fixes to the internal tube of the telescope a pin-metal socket, which ia turned and ground with a short conical fitting and wide flange to receive the eye-end, with its eye-piece and diaphragm. On the opposite end of the outer tube, a precisely similar fitting receives the cell containing the object-glass. Both ends are identical as regards the fitting, though the object-end is necessarily rather longer than the eye- end on account of its having to carry on the outside the cover or dew-cap. The line of collimation is adjusted by reversing the collimation stop, which in this level is a glass disc with lines engraved upon it by a fine diamond, insteEui of the ordinary cross- wires.

The Levelling- staff serves to measure the vertical distance firom the horizontal line formed by the axis of the telescope down Min. Prat. Irtat. C.S,, vol. lix., 1880, p, 278.

Iiine-Surtetixq.

CO the station on the grouaJ. Formerly the levelliiig-fltaff con- sisted of a wooden rod, furnished with a Bliding vane or tart, which was raised or lowered by the -holder in response to signals from the observer. Such staves are now mrely uaei The principal objection to which they are liable is that ths oViserver must depend on the stafi'-holder to read the height observed, or if the latter is not sufficiently intelligent to perform so important a duty, must himself go and read off the beigittof the vane. In this way great loss of time is caused, and there ii uncertainty Ln the results, as the vane may possibly have shift in the meantime.

A very perfect staff of this kind, known as the New Tork target rod, is largely used in the United States. It is graduated to hundredths of a foot. To indicate where the horiiontal line cuts the staff, a target is used, the face of which is divided into quadrants painted with two alternate colours. In the face, there is an opuning a tenth of a foot long, through which the figuiw can be seen on the &ce of the rod. The right edge of the opening is provided with a vernier, by means of which the staff can be read to thousandths of a foot.

In order to avoid entrusting the reading of the staff to m attendant, Mr. W. Gravatt invented a staff, the lace of which was graduated distinctly enough for the observer himself to read off the figures through the telescope of his instrument. The sliding vane is thus dispensed with, and the staffoholder hu nothing to do but to hold the staff vertical.

The levelling-staff usually consists of three parts, sUdiiig one within the other, and, when opened out for use, forms a staff U to 1 6 feet in length. It is made of mahogany soaked in lxii!i?d oil, and painted with several coats of oU paint. The whole length is divided into hundredths of a foot, coloured alternately black and white, and occupying half the breadth of the staff. The patterns of levelling-etaves are very various. The form shown in Fig. 59, invented by T. Sopwith. F.R.S,, ia that mo st frequently used. In this the feet are represented by large red figures, the tenths are shown by odd black figures, and the hundredths are coloured alternately

L black and white. Between the odd figures represent- ing tenths, a black diamond is painted to indicate the alternate five-hundredths. The top of every figure represents its value. Of the black and white divisions, the bottom of each black space represents odd hun- dredths, the top even hundredths. The staff is usu&Uy 14 feet in length, and divided into 3 parts, which, when drawn out, are held in position by a spring clip

At the 1>ack. When closed, they fonn a. staff about 6 feet 3 inches m length, 3 inches wide, and inch deep.

An important modification has been introduced in the gradua- tion by Mr, A. G. Thornton, of Manchester. It consists in the repetition at each 3 inches of the number of feet in small red figures on the left of the staff. This improvement will be found 'Very advantageous, especially with short lines of sight, as an exact reading can be taken on any part of the stafi' where the cross-wire fells, without the necessity of raising or lowering the staff It is important that the staff be held truly vertical while it is being read. To help the staff-holder in this, a small plummet is suspended in a groove out in the side of the stat!', by tneana of which its verticality can be determined in one direction. The observer himself can detect by means of the two vertical "wires of the telescope whether it inclines in the other direction. The plummet may be replaced by a round spirit-level, the tangential plane of which is perpendicular to the hack of the

.

The error caused by the staff being inclined is considerabla let h be the reading on the staff when it is held vertical, and h' the reading when the staff is inclined at an angle of i from the

-g Thus, if a 2*, and

vesical. Then=cosd,andA'.-A 4 COS

4 feet, then A' 4-002 feet

If necessity should compel the staff to be used without a plnmmet or round spirit-level, it should be moved backwards tod forwards by the staff-holder ; the lowest reading will be the most correct one.

A triangular piece of sheet iron, about one- tenth of an inch in thickness, having the comers tamed down, is used to rest the staff on. The comers are pressed into the ground. By means of this iron plate, the staff is kept on the same spot, and at the same height from the ground, while the observer is reading the back- and fore-aight. A chain and ring are attached to the plate for the convenience of the staff-holder in lifting it from the ground, and in carrying it from station to station.

Hiiie LeveUing-Stavea.— For levelling undergronnd, staves may be employed similar in construction to those used at the surface. They must, of course, be shorter. The best sizes are a 9-foot Sopwith staff to close down to 3 feet 6 inches, or a 6'foot Sopwith staff to close down to 2 feet 6 inches. The staff is illuminated by means of a miner's candle or a safety-lamp, Mr. Stanley has designed a staff, made in lengths of 18 inches, like a folding rule

ire

MISE-SCBVETIira,

Mr. O. J. Jee has designed a useful stod' for colliery work. It consiits of three lengths, sliding one into the other. Tbt bottom length ia graduated upwards in the ordinary way, and ii

3 feet in length. At the top of the first division of the statf ia attached a 2-inch band, which is graduated upwards, and fonni an accurate continuation of the scale on the lower division of tbe staff. The band passes over a brass roller attached to the (cp division of the staff, and thence ia carried down and wound round a brass drum, fixed just below the roller, to the top of the same length of the staff, the band being kept in tension bj means of a box-spring attached on one side to the axis of fkt cylinder. It is thus evident that when the second length of the staff is drawn out, the band unwinds and gives a con- tinuous reading up to 6 feet 8 inches, or to any intermediate distance that the height of the roof will allow. In the sffle way when the third length is drawn out, a continnous reading may be obtained up to 9 feet, or to any intermediate diitwu* required. The weight of the staff is 6 lbs. It is manufectored by Messrs. J , Davis & Son, of Derby.

The clumsy contrivances used in the St. Gothard tuaflfl induced Professor M. Schmidt,! of the Freiberg School of Mines, to devise a staff specially adapted for levelling in niiiw* It consists of two staves, each 5 feet in length. The front on* is graduated, whilst the second acts aa a pedestal. The two joined together by two clatnps and screws, in such a way th&t the graduated staff may slide along the pedestal for a distuice of

4 feet. The graduated staff is backed with an iron plate driU' with small holes, corresponding to its graduation. Into the* steel pin on the pedestal works automatically with a spring, whenever tbe graduated staff is drawn in or out. A pointer is attached to the pedestal at a given height (e.g., 4 feet), when the graduated staff is pushed home. When the latter is drawn oi% the reading, less the difference between the foot and the pointer, added to the constant height, denotes the height of the line of sight above the foot of the staff.

Attached to the side of the staff, is a portable reflector Ucnp for illuminating the scale. It can be raised or lowered at will, and its reflector is so placed that as much light as possible fall' upon the scale, whilst the flame itself is kept out of sight. In mines where the ground is stony or soft, a cast-iron shoe with hemispherical steel head is placed under the staff.

For rough levelling in metalliferous mines, a levelling instru'

'OoUUri/ Guardian, vol iixvili., p. 676, 1879. + Outerr. ZdUekr, vol. ixii., p. 295, 1881.

Lxvzlliko.

meat may be made out of an ordinary carpenter's level, fitted with sights, and made to fit on the dial tripod. The stalT used in cOQJUQctioa with this instrument may be made out of a piece of planed deal, 3 inches in width, marked into lines representing feet and Laches by means of a piece of red-hot hoop iron. The numbers of the feet may also be burst-in in bold Roman figures, every half foot being indicated by a longer line. The level having no telescope, the reading of the staff has to be entrusted to the staff-holder.

For very accurate levelling, Borchera' vane-rod is generaUy oted in the Continental mines. To enable thiscontrivan;;e to ba ued, the station-points must be marked by small hooks fixed into the roof of the underground road. The contrivance consiBti of A steel rod, rectangular in section, 5 feet 5 inches in length, provided at its upper end with a movable hook. The rod is graduated into inches, the graduation proceeding from the inside of the hook to the lower end of the rod. Up and down the rod ilides a sheet-iron circular vane or target, 8 inches in diameter, which may be clamped at any height. At right angles to the longitudinal axis of the rod, a line is scratched through the centre of the vane. With their centres truly on this line, three circular apertures are cut, two t>-4 inch in diameter, and one 0-07 inch in diameter. In front of One of the larger openings ft piece of ground glass is fastened. To the back of the vane a vernier is fastened with its zero coinciding with the horiisontal line scratched on the vane.

In levelling, the rod is hung from a hook in the roof of the mine-road, and the vane placed at right angles to the line of sight. For very short station-lines, the flame of a miner's lamp is held behind the small hole, and the vane moved up or down tmtil the horizontal cross-wire of the telescope coincides with the point of light sighted. For greater distances of 60 to 200 yards, the aperture covered vith ground glass is used if the air is clear; with still greater distances the uncovered aperture is used. Very long station-lines are not to be recommended, on account of the difficulty of communicating with the assistant.

This levelling-rod is exceedingly simple. It hangs perpendi- cularly by its own weight, and, unlike wooden staves, it is not affected by the water and dirt in the mine. At the same tims it presents the advantages of fine adjustment, exact readiag, and groat rapidity.

Practice of Levelling.— If it is required to determine the differ- ence of level between two points not very far apart, this may bo done by wmpfe leveling. For this purpose, the le veiling-instru- ment ia set up midway between the two stations A aad B, Fi.

Hine-Burv£Vino.

Fig. 60.

€0. With the bubble remaining unmoved in the niddk of itt ; tube, the telescope is directed towards B staff held Tertically at A, and the reading h noted. The staff is then held Terticallj at B, and the telescope di- rected towards it, the reading A' being noted. The difference of level between the two points A and B is then A - h', and B IB higher than A when h is greater than A'. The diffisrence of level is thos determined hj two readings on the etaff, one with the teleacopa directed backwards towards the staff at A, and the other nith the telescope directed forewards to the staff at B, or, in other words, by means of a back-tight and a,/ore-sight.

In order bo obtain the greatest accuracy, the instrument ii Mt up as nearly as possible midway between the two stations A uxi B. The advantage of thus placing the instrument is that tbe instrumental errors and the errors due to the curvature of tha earth and to refraction are neutralised.

Let the instrument be set up at m, Fig. 61, so tJiat via m&i ' and let afc be a horizontal line. Then if all the sources of emr act in such a way that the optic axis of the telescope directed towards the staff at A giTes an angle, amd, with the horizon- tal line, the cross-wires of the tatesoope will not coincide with the point a, but with the point d, and on directing the telescope to the staff at B, the cross-wires will coincide not with point h, but with e. The same causes being at work in both positions of the the angles o m cj and must be equaL BecauM Ma ad 6 c. The difference in level is equal to A - A', that is (A a 4- 1 ad) - + be), It is here assumed that the oonditioo of atmosphere is the same with the fore-sight aa with tbe sight, and thus the refraction is the same in both cases.

The influence of the curvature of the earth's surfiu is i dent on the radius of the earth, r, and on the length of station-line /. Imagine an arc of a circle to be described pMsinJ through the telescope axis A, Fig. 62, and with the centre of the earth as ,8ntre. The arc will intersect the 'ttUff set up at B in the point 0. The curvature in tbe figure is of course rrry much exaggerated. The hori- toutal line pauing through A, inter

Fig. 01.

fl(. fiSL

LEYELLINa, 179

riecU the staff at the point D. Thui, A is the true horizontal iine, A D the apparent horizontal line, and D the depression of the true below the apparent horizontal line. Then the cor- r*:cticm ibr curvature is - CD, a third proportional to the earth's diameter and diatauce between the level and the staff.

D is thus equal to-r- . For a distance of 1 mile this correction

IS 8 inches, or two-thirds of a foot. Two-thirds of the square ol

the distance in miles will be the amount of the correction in feet.

The error D is diminished by the refracting action of the air,

the real line of sight is a curved line, in which light proceeds.

The curve being concave downwards, the point D is not seen at

the cToes-wirea of the telescope, but the point E, With a calm

J I'

Mear atmosphere, D E is equal to 0-1348 OD, or 01 348 -5-.

Tiip ooefiBcicnt 0-1348 is the mean of the determinations of ?Teral physicists.

The total error due to the curvature of the earth and to

'fraction IS thus ,i 0-1348=— . The earths diar

2r 2r r

iQeter being equal to 41,778,000 feet, the correction for curvature

Jid refraction per mUe would be

0-4326 K 6280* 20,889,000 0-577 foot 6-92 inches.

At distances up to 10 chains, the errors produced by curvature nd refraction are so small that they may be neglected.

In crossing over a deep valley it is sometimes advisable to set Qp the level at one of the points A and the atalF at the other point B, in which case the height of the centre of the instrument sbove the ground must be measured. The difference of level d vUl then be equal to the height of the instrument i above the ground, leas the reading on the staff A — that is, d i — A. If the correction c for curvature and refraction has to be taken into account the formula becomes

rf -(A-c) t— A + e.

If the instrument is placed at B, and the staffat A, the ditferenoe .of level is

The mean of these two values gives the difference oi level independently of all torrection —

xiantBURVETiira.

When the distanoe ta too great or the ground too much inclined for the difference of leTel to be detenniiii hj one operation, recourse must be had to compound kmUiig, a process consisting of several simple levelling operations. The differ- ence of level of each two succfla- sive points is determined in the way described. Fig, 63 gives Fig. 63.

an example of compound level- ling. By setting up the leveUing-instrument at the stations, the following values were obtained : —

-81(111. Fnt.

FtrL

Am.

Ad

671

Be

3-92

Rise from A to B 2-7B

n.

Cf

7-86

Cg

2-tl

Riae ftom B to C 8-*5

m

Hc

2 '84

Di

WL S'se

FftU from C to D 3-58

RlBe=4-e9

If the back-sight is greater than the fore-sight, the gron. rises. If the fore-sight is greater than the back-sight, ground falls. The rises being regarded as positive, and t, falls as negative, the algebraical sum gives as the result of tl .g levelling that D is 4' 69 feet higher than A. The same resic:* is obtained when the sums of the back-sights and of the fo t—? sights are taken, and the smaller sura subtracted from larger. Thus 17-41 - 12-72 4-69, The difference obtaineS is difference in level between the end points. It indicates a when the sum of the back-sights is the greater, and a fall whe* that of the fore-sights is the greater.

This is the method of conducting a Jhfing-kvel — that is, ' levelling operation merely to determine how much one point above or below another. for example, it is required to dete*"- mine what thickness of strata there is, at a certain point A 9.t the surface, above the present workings in the mine below it, the depth of the shaft is measured, and levelling commenced at the bottom of the shait and continued to the point under- ground directly below A. A flying-level is then maA at the surface from the shaft to A, The depth of the shaft being known, the thickness of the strata at A can be calculated firom the rise or fall determined at the suHace and underground. Thus, if the shaft is 300 feet deep, and the polot underground is found to be 5 feet lower than the bottom of the shaft, whilst the point

the sutface ia foimd to be 40 feet higher tlian tlie top of tha

Ut, the thickness of the stmfA &t A will be 300 + 5 + 40

1 feet.

Section-levelling. — When a section of the ground is to be drawn,

B distances between the several stations must be caret'tilt;

liored. The level ting-instrument should be placed as near as

Bible midwaj between the two stations, and the levelling is

b conducted in the manner described. To facilitate the H

tting of the section, the vertical distances of the points are H

mUted above an assumed level-line called the datwn-litte. H

lie observations are recorded in the levelling-book in th H

owing manner ; —

Form Of Record 1

'

SlthL

FfvTB-

eiKht.

RlH.

Fall.

IMutu

fiUOU,

Cjgtinea,

BinurkL

OtlltDI.

'

S-43

&6 43

t

2-0*

6'S8

64-a9

60-)8

em

'

4 'S3

3'efi

0'22

6 '98

r

3 Os

9' 18

71'49

:

'

5 Os

.%-30

[

6'01

40 -es

76 '76

47 To

.„

J

HINE-SDRTSYINa

r

The starting-point m 60 feet above the dattim-luie, which in Uiii

case was tbt; level of the high- water mark at Londoa Brid.

H The column headed " Height above Datum " contains the abio-

H lute height of each forward station above the horizontal liD

H passing through the high-water mark. The numbers are ob-

H tained by taking the algebraical sum of the rises and faUs, tlit

H former being considered positive, and the latter negative.

H As a test of the accuracy of the arithmetical work, the colmnnj

H of back- and fore-sights should be added up, and the i mailer mm

I subtracted from the larger. The result should agree with the 1-

H culated height above datum. Another test is a&>rded by adding

H up the rise and fall columns, when if, upon subtracting the smalleF

sum from the greater, the remainder is the same as that obtiiiicKl

by the two other operations, there can be no doubt that the lTeli

hove been correctly calculated. Thus, in the example givea, tin

height of N above the starting-point is 79a5 - 50'0O 2915

feet. The sum of the back-sights being 76*75, and that of tti<

fore-sights 47 -60, the difference also gives 29 -IS feet as the heiglt

of N above the starting-point. Lastly, the sum of the risei it

41-30, and that of the falls 12-15, the difference being 29-15 M

as before.

In order to make a correct section of a continuous surface, tbe levels of a series of points may be determined with the instrom*!'' at one station. The first and last observations are then the principal back- and fore-sights respectively. Thus, in Fig.

Fig, 64.

A is a station where the instrument is set up, and 6 A e is the line of sight. The first back-sight is taken with the staff at th* starting-point B, of which the height above the datum-line is known. The reading on the staff is B 6, or 2-95 feet. The first fore-sight is taken with the staff at 0, giving the reading e, or 0-58 foot. Between the points B and 0, several intermediate sights are taken. The first intermediate-sight, taken with the staff at the point marked 1, is at the same time a fore-sight to B, and a back-sight to the point marked 2; 3 is a fore-sight to 2 and a back-sight to 4, and so on with the other points. When the level is carried on to a new station D, the assistant holds the

Kff steadily at 0, at exantlj the same point as it was for tha foresight from A- The first bak-aight Oc ja taken, and tha prooesa repeated until the fore-aight £e, or 1*01 foot, ia taken. staff is then held stationary until the lerelling-instrument is

moved on to the next station. The readings are recorded and reduced in the manner shown

in the following example :—

Form Of Record Ii.

m

V*.

Bmfik-

Fon- SJfliL

SKl

FtU.

Baltht mtKlTO dklum IWW.

Dillun.

HwBUkM-

2-9S

LiDki.

S

Otil

IfiS

101 '8S

S

24S

S

s-oo

5 '52

97 '43

mVT2

1'23

a

S'Su

7-ffl)

O-Oo

46S

j!15

S-60

2'Os

m

2'08

(!36

l-Ol

.i

S9'50

-lOOW

The first back-sight and last fore-sight of each line of sight are the moBt important in point of accuracy. Any error made in taking

J

Minb-Btjrvktino.

an interuiediate sight affects that Ime only, whilst any error ia the back-sight or fore-aight is carried on throughout the section. In order to correct for curvature and refraction, the first lack- sight and last fore-aight of each line should be at points at as practicable equidistant from the instrument.

In recording the readings in the levelling-book, a separtte column may be used for the intermediate sights. The readiDgt tm reduced, and the computations checked in the manner shown in the following example : —

Form Of Record Ui.

Ma

Back-

Blglit.

tstemitdliUi.

etiht.

RLh.

Fall.

Hstetit ibon oAtat]]

Mil

Lloki

4S0

l£i

3-oa

S

2!

S

m

5W

29S

0'S2

1*23

O-fiS

O'Sb

O'Qo

45S

6 -So

4 '42

U

1'8]

le

O'So

109-6fl

n-ie

l'fi9

,.,

0-S6

9S

.„

:J

tETXLLlN'a.

In thja way a large amount of unnecessary addition is avoided.

There is a third method, known as the collimation method, of Tftducing levels. It saves one column of figures, and is easier to work out, as the distinotion between rises and falls is not con- sidered The following is the form of record ; —

Form Of Record Iv.

ncdUd

SlihU.

Height of Line ai

Ueliht of 8lirUcfl ftfacrfA

Dilum.

DliUDCta

ToUl DlttaDCM.

S'49

3'So

S-00

206 -O*

Outu.

lOO

i-m

I'Oo

CImUii.

40 Oo 43 Oo 44 -Oq

5'64 12W

""

A modification of this fomi of booking will be found advan- tageous for levelling in mines. Only two columns are used for entering the heights observed on the staff. The intermediate and fore-sights aro placed in one column, the latter being dis- tinguished by being underlined. The reduced levels for the " height above datum " column are obtained ia the following way: — Add the back-sight to the reduced height for collima- tion and subtract intermediate and fore-sights. On reaching a fore-sight, the next back-sight is added to the reduced height at that point, when the intermediate and fore-sights are subtracted as before.

Should it be required to work out the levels backwards, the rule is : — Add the fore-sight to the reduced height for coUiroation and subtract intermediate and back-sights.

On reaching the bottom of a page in the levelling-book, if there is no necessity to move the instrument, the last intermediate sight is booked as a fore-sight at the bottom of the page, and

Hine-Suhveyixo.

again as a bock-aight at the top of the following page. By to doing, the same number is added to, and subtracted ttom di collimatioQ height, and conaequetitly the reduced beigli; an not afl'ected. The accuracy of the calculations is aacertainwi in the ordinary way, by adding all the back-sights and all tbt fo( sights, and subtracting the smaller total from the larger one.

Tlie adrantages of this method, especially tor undeiround levelling, are apparent, as it necesitetea the writing of f"*er figures. The form of record for this system, reco:

Mr. H, W. Hughes, is shown by the extract from i. .;

book of a South Staffordshire colliery. (Ret-ord V.)

Bench Marks.— When a. seotion has b*eu complpt<>d, it ii generally necessary to cheek its accuracy by repetition. To do thifl, it is advisable in levelling to follow the shortest route, uiwl to level at intervals to some known points on the exact lin of section. The points thus selected we usually baneh mark- These are fixed points of reference, the levels of which are known In the Ordnance Survey of Great Britain, the bench raarki generally chiselled on some permanent stone slab, pillar, or will-

The form of mark for them is the broad arrow

7f

Ung on long lines of section, a bench mark is generally mad every quarter of a mile, so any error in the operation tuj aot involve re-levelling the whole line. By referring to the ta.j* of the Ordnance Survey, the heights may be tbund of beuJi marks above the datum-line (the level of mean tide at Liverpool)' In collieries it is the general practice to record the levels m (the works from some fixed datam near the shaft, as, for example, the flat sheets at the top or bottom of the shaft, the delivery d water from the high set of pumps, or some other fixed poiat Mr, J, A, Ramsay proposes to take or continue the Ordnance levels into the workings. In the Ordnance bench mark the broad arrow points upwards to a horizontal line. To make distinction, it is suggested that as soon as the levels become lower than the datum Ime or sea-level, the brood arrow ahould Iw reversed. The levels obt&iaecl in this way may be writt<>o tipoo [tite plan in plain figures at particular points o:

'nd, when necessary, may be continUKO into li. off-

workings,

Mr. Ramsay gives the accompanying extract from hi Irret ling-book to illustrate the method he proposes of c ;

Ordnance levels into Hits workim of a collierr. 'I

'Tran4. A'. Kwj, JttU il.£., vol U., I&70, p. 73.

FOftW OF RKCORD V. 18;

r

fkmuid

latar-

nadtole

Uelfbu.

IMltUlH,

Bcmu-ki.

To

rnt. 6,446

f Datitm 100 feet below inset, dwtanoe 1 meAsiirGd from pit ihofb Section ) of coal.— Cwa. 3' 9' ; dirt, 0" 5' ; ( coal, 3' 2'; floor composed of clay.

6,S00

floor of coaL

Ib

6,644

upooaL

2H

5,600 6,671 5,700

floor of coaL

m

S3$

4'96

5,761

up ccwL

5' below coal.

Do

S2-S2

5,823

5,900

floor of coaL

foot of fault, rise about 9 yards, fault hadea 15*.

to eo

(H8

Ooi

9rS2 93-S6

lW-89

5,966 6,015 6,018 6,078 6,111

crouing meaium below coal.

n

6,136

6,251

floor of seam.

'

6,348

r 0' above hottom of mwL

Ib

2-7fi

6,40:2 6,617

Soor of eeam, road to left.

3;64

6,623

6,781

2' above bottom of coaL floor of coal.

113'5S

6,803

6,921

,1 ,1

G-30

7,017

3' below coal.

J

Vod/.— Total (ore-iiights 38 6fl L, rise) 9-61, which, added b 112-33, tb redDCd height at

j total back-sights 48 30. Difference 102-72, th reduced height at 5,4 7,017.

—

Form Of Record Vx,

No.

Buk-

FoFe-

Xliii,

Full.

Ditom.

THit.

Bcmwto

t OrdDBQue B M. on Dortti. I east corner of houie

60S

2m

Tlieentsbeetoonlipoftt-

Take Depth of the Pit with

100 feet Chiiip.

Depth, 618 (L 11 in. =61391.

Less Burfatoe height ibon

datnm.

5Is-B1

1 1'Ut sheets at bottom ofnt; ) reversed Ordnwos BJl 1 cut iuto stone williot, side of pit.

Level down Cmsa-ou t to iniks Section for Engine F1m

e-65

5iM

go

7-9 ft. high— nard jjost oovw.

S

5 m

76 do. do. fl

5'M

80 da do.

63 do. do. timbcrei

2'53

/ Od ttie brow of large daD- J throw troiiHle, raeiunre dowut with straight edge and platub-liiie- Dist.-eft.+.Hft.+SJft. + 6ft. + tift.= 27ft.

t Down.4-33+4 45+3-39+3-3J t +.5 20 200.

1 4 ft. Iiieh -Roof very jointy I and bad— topcoalleftoo.

&

..,

f 4*3 full height of seam, bad i roof, eloseljr timbered.

2S9

ase

4-6 do. do. do.

2-oe

S-43

f 5-0 better roof, timbered in 1 places only.

la'i

4-S2

2S7

Coo

5 ordinary height of team I —good root

Wfis

-.31fi

5 do. do.

0-m

.'iO do. do.

3i 1-70

6-0 do. do.

S-Si . ..

S-O do. do.

"

8S5

6-0 do. do.

11 —

G162 87*5 8Se

34-So

25iH ..- 25-94

Lkvellino. 189

The Reflecting Level — For rough surface laTelling, the redeeting level maj be aaed. It consists of a small sighting- tube, with a, bubble-tube set above it. It is so arranged that the bubble is seen, through the bottom of its tube, and reflected by a mirror into the sighting-tube. An instrument of this kind, invented by Abney, is also useful as a clinometer. In this iDStrument, the bubble-tube is fastened to an arc 2i inches in diameter. In taking a level, the vernier, fastened to a bar at right angles to the spirit-level, is set to the zero of the vertical arc. On looking through the tube, the object observed will be level with the eye when it is intersected by the bubble, The rieafalts obtained are very satisfactory. Like all reflecting instni- ttietitg, this level is usekss in the bad light of a mine.

Sonices of Error in Spirit-Levelling.— There are four sources of error in levelling — 1, Errors of observation j 2, instrumental errors; 3, errors from unstable supports j 4, atmospherio errors.

Errors of observation are mostly unavoidable, and arise chiefly from the bubble not being carefully centred. Instrumental Arrors are doe to the instrument not being in adjustment, and to the staff not being vertical. Errors from unstable supports Can only be eliminated by duplicating the levelling in the opposite direction, and by taking the mean of the results. At- inospheric errors arise from wind, tremulousness of the air in clear sunny weather, and variable refraction due to sudden bursta of sunshine on the line.

A waterproof cloth should be thrown over the level in case of rain. Staves should be wiped dry after being exposed to the rain, placed horizontally to prevent warping, and occasionally compared with a standard length.

Accuracy Attainable in Spirit-levelling.— Mr. W. Seibt arrive* at some interesting results, calculated from observations made under ordinary conditions. His telescope of 18-inch focal length hod a magnifying power of 43, and an object glass of l|-inoh aperture, besides a very sensitive spirit-level. The instrument was always set up between the bu;k and forward staves, and the observations taken by one central cross- wire ; both ends of the pirit-level being read at each observation. Observations were only made in still clear weather; the back- and fore-sights being taken us soon as possible after one another. Each complete observation occupied S minutes, and 24 pairs of observations were taken at each station. Although the mine-surveyor is rarely in a position to use 'an instrument as delicate as that described, the results arrived at are of interest for the sake of comparison.

P

HtNE-StIit?8TIII<k

The mean error m, in an observation consisting of a hack- and fore-reading, was found to be as follows : —

At 60 metres (16i feet) ±

,,100 „ (328 „ ) ±

„ 160 „ (492 „ ) ±

„ 200 „ (66* „ ) +

0"2S mUlimetre (0-011 inch), 0'62 „ {0-024 „ ). 0-71 „ (0-028 „ ). 91 „ (0035 „ ).

7be distance for obaerring sbould be limited hj the capacity of the observer and of his instrument. It will always be rigbtif chosen when it is extended as far aa the nature of the groand to be levelled wiU allow, and on the other h&ud, when it is so timfi that no trace of air movement is noticeable through the tele- scope, and the graduation of the staff is presented as a perfecilf stationary and aharply-deiiued image. If this principle is &sAd on, it is asserted that the mean error per kilometre should tuA exceed 0-64 millimetre, as in extensive levelling operations tlw line of sight doea not usually exceed 100 metres. 1

At the second International Geodetic Conference it was I cided that the probable error in the difference of level between ' two points, 1 kilometre apart, must not, as a rule, exceed 3 milli- metres, and in no case exceed 5 millimetrea According to the report of the United States Coast and Geodetic Survey, on th line from Sandy Hook to St, Louis, 1009 mUes in length, tbe probable error per kilometre was 1 -2 miHimetre.

Plotting SectiOEB. — In order to plot a section from the reduced I levels as entered in the levelling- book, it is first necessary to rule a straight line to represent the datum-line from which the heights art calculated. Along this line the horizontal distances hetM'cen the points are marked off, and at each point a line is drawn at right angles to the datum-line. Along the lines thai obtained, the vertical heights are marked off, the figures given. in the "height above datum " column being used for this purpose. In marking off on the datum -line each distance separately, any error made is carried forwards. To remove this source of error, it will be found advisable to add the measured lengths together so as to obtain the absolute distance of each station from the starting point

As a rule, in plotting a section two scales are used, one for the horizontal distances, and the other for the vertical heights and depths. An exaggerated representation of the section is thus obtained. By making the vertical scale much greater than the horizontal one, the depths of cutting and embankment uired are shown with greater clearness than if both scales.

scales;

Levellino. 191

are the same. The section shown in Fig. 64 is plotted on a liorizontol scale of 3 chains to the inch, and a vertical scale of 30 feet to the inch.

Sections of the main ways in collieries are usually plotted on horizontal scale of 2 chains to the inch, and a vertical scale of H '0 feet to the inch. As a rule, thp scale for the horizontal m distances should be the same as that of the plan with which it

Lorresponds.

I Sections inaj be plotted with great rapidity by means of

-Marquois scales. These consist of a right-angled triangle, the brpothennie of which is three times the length of the shorter side, and two rectangular scales of equal parts, each with two scales, a so-called artificial scale placed close to the edge, and a natural ste immediately within this. The divisions on the artificial scale are three times the size of those on the natural scale. The latter is a simply divided scale of equal parts, with the divisions numbered from left to right. In the artificial scale the zero is placed in the middle of the edge of thofule, and the divisions are numbered both ways from that point to the two ends of the rule. A pair of Marquois sc-ales usuaUy has scales of 30, 60, 25, 50, 35, 45, '20, and 40. The triangle has a short line drawn perpendicular to the hypothenuse near the middle to lerve as an index.

To draw a line parallel to euiother, one of the rulers ia laid on the paper, and the short side of the triangle placed against it, when parallel lines may be drawn by sliding the triangle up or down.

To draw a line perpendicular to a given line from a given point in it, the shortest side of the triangle is made to coincide with the given line, and the ruler placed against the hypothenuse. The triangle is then slid along the rule, until a line drawn along the longest side of the triangle passes through the given point.

With these scales the sight is assisted by the divisions on the artificial scale facing so much larger than those of the natural scale to which the section is drawn, and any error on the setting of the index produces an error of but one-third the amount in I the SM;tion.

For the purpose of receiving the plotting of sections, a special kind of paper is prepared, on which faint tines are printed, dividing it horizontally and vertically into one-twentieths of an inch. By the use of this section-paper, much time is saved, as no Bcate is required.

(/.) The Water- Level is a very simple instrnment which, when necessary, may take the place of a more elaborate levelling-

instrument. It requires no adjustment ; it may be made by anj intelligent workrnan at very slight expense ; and in sliort di*- tanccB no serious error can be mode when using it. It ootuiitt of a horizontal tube made of tin-plate or brass, terminated il each end by a vertical glMs tube in which the surface of a liquid give-s a horizontal line. By means of this line, the veiae of levelling-staH' is adjusted to the right height. The tube is toad* so fis to revolve on a light portable stand.

A water-level {chorobate is described by Vitruviua (de Archi- iKtura, vlii. 6), as used in the construction of the Eonv) aqueducts. It consisted, not of a tube, but of an open trescli 5 feet long, 1 inch wide, and H inch deep, cut in a 2!) feet in length. It was adjusted until the water was at the Mma height from the top at each end. The plank was provided witi legs accurately at right angles to it. They were of equal length, and rested on the line to be levelled.

The water-level was in common use in the Derbyshire lead- mines in the 17th century. The method of levelling then em- ployed is described by Thomas Houghton, writing in 1681, follows: —

" The Instrument for this purpose may be like the following— viz,, a Water Stand, with one or more Channels, which th Miner may make himself, upon an old eeason'd Joyce, cutting* Mortess therein, a yard long, or more, as his own Discretion directs, plaining the same very well and even."

The observer sights through a hole above the water chaimelr at a staS* 6 yards long ; the atalT being moved until the top ol it can be seen. The instrument is then moved to the plM< occupied by the staff, and the operation repeated, " till you haw finished the whole, and come to the Place where you intend to begin your Sough [adit level] : then reducing your Poles into Fathoms, compare tnem with the depth of your Mine, and tiitis you may know whether it will lay it dry or no."

A modification of the water-level has recently been employed with success by Dr. Luigi Aita, of Padua. His instrumenv consists of two levelling-staves, in front of each of which a glau tube, 7'87 inches long and 0-79 inch in diameter, slides up and down. The two glass tubes are connected by an india-rubber pipe, 30 yards in length. At one end of the india-rubber tul)s is a stopcock, by means of which the connection between the two glass tubes may be interrupted. When in use, one glass tubs and the india-rubber pipe are filled with a coloured liquid, the staves are set up at the two stations, and the glass tubes raised approximately to the same height at both staves. The stopcock ii then carefully opened, the fluid will stand at the same level

Lp.Vellino,

in both glass tubes, and its pogition can be read at both staves. With this inatrument a mile may be levelled in 6 hours. For levelling in narrow, crooked, and partially fallen-in workings, this instrument offers great advantages.

In mines where the seams are thin and inclined, the use of tbe teleseope-level is attended with great inconvenience. For this work, Mr. T. L. Galloway and Mr, C, Z. Bunning* have introduced a modification of Aita's water-level. The apparatus consists of two glass tubes connected by an india-rubber pipe, which reay be of any convenient length from 10 yards upwards. Bach glass tube is attached to a scale graduated into feet, tenths and hundredths in the same way as the ordinary levelling-staff. The tubes are filled up to the centre of each scale with coloured water. The scales being held vertically upon any sloping surface and at any distance apart that the lent;th of pipe will admit, the difference of level between the stations at which the scales are held will be represented by the difference of the readings denoting the position of the coloured liquid in each tnbe.

In order to remove the source of error arising from the tiresence of air-bubbles in the liquid, a stopcock is fitted at each end of the india-rubber pipe. These stopcocks being closed ttnder water prevent all oscillation while the apparatus is being carried from station to station, so that there can be no possibility of the intrusion of air-bubbles. Falls of stnne, sudden I tends in the road, or timbering, obstacles so frequently interruptiug the line of sight in levelling underground, present no difficulty with this apparatus, as it is obviously as easy to proceed over or around any obstacle as to advance in a straight line. The instrument has been used in mines under the most difficult oircurastances, and has been found to answer in all cases exceedingly well, the saving in time being very considerable.

Trigonometrical LeTelling. — The trigonometrical method of veiling is based on the solution of a right-angled triangle ABC (Fig. 53), of which the base BO and the angle BOA are known. The difference of level B A of the points A and C will be equal to the base B multiplied by the tangent of the angle B C A. This method is less exact than spirit-levelling, because ft small error in the angle may give rise to a considerable error in the difference of level.

Any inatrument with a vertical limb may be employed for levelling trtgonometri<lly. A series of angles of depression and

h.

3VrM, JIT, Engl. Itut, M.S., Tol, xxm,, t,.

elevation are taken along the line of section, the Instrameiii being sighted to a Bt&ff with a vane or a croBS-piece fixed to it exactly the aame height from the ground as the centre of tiit axis of the telescope is. The staff must be held vertically whiie the observer measures the vertical angle which the line of makes with the horizon. The inatrument and staff are &ti made to change places, and the vertical angle determined. Ths mean of the two readings is token as the correct result. Tl distance must then be measured. As the distance it tie hypothenuse of a right-angled triangle of which the perpettdicnlr is the difference of level, the latter is obtained by mttltipljiii( the measured distance by the sine of the angle observed. The following is an example of the field record : —

Levelling Bt Vertical Angles With The Theodolite— 1.

From

To

Inclined

iBllgUn

lotset.

VttWeM

KDglU.

SlM.

Fall.

liclghl tbOTr dttam MM,

BorlioB14l leQgtbft.

Tottl

s

S

r2i'a

SMl'R

l'47'F

2*18'F

28 '6S

3)218 3H9-83

1311-ffl 167S-96

M-00

-Woo

When the line to be levelled is marked out on the ground by stakes set at a horizontal distance apart of 100 feet, the height will be found by multiplying the horizontal distance by the tangent of the angle of inclination. The form of record in thii case will be seen on next page.

In this section, in six stations a height of 146 feet has been ascended in equal distances of 100 feet. With a spirit-level and a 12-foot staff, the number of stations would have been doubled. In order to simplify the calculations with this method of lerelling, Mr. A. Faul, of Baltimore, haa computed a table of

Levelunq.

Lbvpilling By Vertical Angles With The

Theodolite-2.

rm

BwUoDC*)

Luniithi

Vertlen) Aggla.

Hlae.

Ditum IGO 00.

Kgmarki

S'-iS'R

117'18

7°16'R

?

10° 16' R

E

a'so'p

1G8-59

s

8"43'R

lUO

9'30'R

10"00'R

n°i6*R

212-45

1*46' P

m

1M74

Is

- toouo

eights* for all angles froin 0° to 334°> minutes, for buj iatance required. His object is to bring levelling by vertical tigles into more general use, and save the many stations re- uired in spirit-lerelling. The latter method is very tedious in [llj countries where extreme accuracy is immaterial, especially in all preliminary surveys. The method of levelling by artical angles gives approximate results in the shortest possible me.

Levelling may be performed by the theodolite by setting up instrument at the foot of a steep incline, with the line of

A Short TrtaiUt an LevtlUng by F<rtkat Angla with Tabta nf lU*. New York, 1886.

m

Uine-Survstivg.

oolliinatioa set at a known angle of mcUnation. Sights are ihta taken, aa if with a spirit-level. ThuH, suppose tLat the theodolite ii placed at A, Fig. 65, and that 6 A represents the inclined line of sight. Then B b, c, and the other vertical lines will re- present the heights read off the staff. The requisite data for drawing the section are thus ob- tained. This method saves time in taking the levels of steeply inclined ground.

When a proper levelling-inatrument ia not av&ifable, the Qs of eoUimation may be placed horizontal, and the theodolite ased in the same way as the spirit-level.

The Clinometer, — For exploratory work, where great accaracj is not required, the clinometer is of great value, on of its portability. It resembles a jointed foot-rule, with inlaid spirit-level and sights on one arm, and a divided an: the hinge to indicate the angular degree of opening. It ia i level on a stand, and the hinge is opened until the object it i through the sights. The angle of inclination is then read.

Fig. 6S.

E. 6SA. The best instmmentt of this kind are provided with a S-ine

LEVELLINa,

19T

I attached on pivots to the lower arm. The clinometer h&ve a spirit-level attached to each arm, and folding b, ajid should screw oa to a portable tripod, provided with u-and-socket joint. In this form, the instrument is practically tiler's dial, on account of its portability well adapted for i(>ecting purposea.

h the clinometer, manufactured by Messrs. J. Davis & Son, improvements have been introduced by Prof. H. Louis. The comfiaSB pivots are carried on a brass arc capable of revolving in the lower por- tion of the clinometer frame, so that the compass can be placed horizontally and read without regard to the position of the lower limb. In this way, the dip and strikeof strata maybe read simultaneously. The compass, too, may be reversed so that the same end of the needle may be used for all dial readings in running linos up and down hill. A further improve- ment consists in mounting the Bj>irit-level of the lower limb on a swivel, bo that the instrument may be levelled both ways without being reversed. The clinometer (Fig. 65a) is 6J inches in length, inch in width, and 3 inches in depth, It weighs [ 2 oz., and is mounted on a tripod (Fig. (j5b), which ia pro- Id with a ball-and- socket joint, and which is 3 feet 10 inches tugth and 1 lb. S uz. in weight.

simple and efficient iusirumeut lur exploratory work is the {St alt&simuth made by Mr. L. Casella, of London, In this, (linometer consists of a graduated weighted disc. There is an azimuth compass with an aluminium disc. Both discs beld by catches, and, when released, arc read by a micro- An excellent telescope ia provided for sighting, the foment being held vertically for altitudes, and horizontally pimuths.

tyslcal Levelling. — The application of the barometer to the iurement of heights is based on the fact that for a constant terature, the density of the air is proportional to the pressure it a u stains. Since the atmospheric pressure decreases aa cend, it is obvious that the barometer will keep on falling is taken to a greater aud greater huight, ke mouiUain barometer is an ordinary barometer tube, made rtable as possible, and protected against external injury, in use, it Ia mounted on a portable tripod and when not

Mine-Surveyino.

in use, it is packed in a leather case. The mercury ia coBtained in ft wooden cistern at the lower part of the inatrument. A Bcrew compresses the mercury and forces it, when required, ap to the upper portion of the graduated tube, fiy means of vernier, the height of the column of mercury may be read to the one-thousandth part of au inch. Attached to the barometer is a thermometer, enabiing a correction to be made for temper ature, This correction is n;essary because the air and tha mercury are unequally expanded by heat.

The simplest barometric rule ia as follows : — Obserre the height of the barometer in inches at two stations. Then, as BUni of the two readings is to their difference, so is 55,000 to tifl difference between the height of the stations stated i& feet.

For exumple. — What is the difference In level between two points at which the barometers read 30*014 inches, and 29'S70 inches respectively 7 The thermometers read the same at both stations,

0'144

Difference hi level 55,000 x ir-soi 1 32 3 feet

0s)'Bo4

To correct for temperature, add of the reault for eicli

degree, that the mean temperature of the air at the two stations exceeds 55°. Subtract the same amount if the mWi temperature ia below 56'. When the upper thermometer readi higher than the lower, of the result must be subtracted wtep the me&n temperature of the air exceeds 66*, and added when it is below 55°.

On the United States Geological Survey, a simple and dire** method of hypsometry is in use. In this method, proposed 1>J Mr. G. K. Gilbert,* three barometers are used instead of two. Two of these are placed at points whose heights are known, tin third being read at the point to be determined. From the reading of the two barometers at the points of known height, the weight of the intervening air column is deduced, and, bot the weight and height of the column being known, its density a computable. The density thus derived is then used in the computation of the height of a second column of air between one of the known points and the point to be determined.

Levelling by the barometer may be occasionally used for taking flying levels in exploring a district. An approximation, however, is all that can be obtained, even if the most elaborate formulse are employed. The mountain barometer is a cumbrous

' Srcoiid Amitial fffport of tht U.S. Oriyl. Surv., 1882, p. 405. In thi* vnlaabEe monogrnpli all the priooipftl methodn that have hitherto beea empinyed are fully doacribed,

LEVELLtlfO.

instrunieiit. It must be more than 30 mches long, esuiusire of the cistern, and the mercury is always troubleiome to transport. On account of these diaad vantages, for engineering parpOHea the Tnercurial barometer haa been to a great extent replaced by the aneroid haroniter invented by Vidi, and p;itented in Great BriUuu in iti41. It conaiita of a circular box, the face of wMcb IB made of thin metal, rendered more elastic by being stamped into concentric circular wave-like corrugations. The box is nearly exhausted of air, and its elastic face supports the pressure of the atmosphere, yielding to it with elastic resistance in proportion to the amount of pressure. The movement is com- municated to an index, and registered upon the dial. Aneroid barometers are made of pocke1>size, carefully compensated so as not to be affected by changes of temperature, and with double ccales, one a barometrical scale of inches, the other a scale of altitudes; that is to say, a scale of differences of altitudes for one given pressure.

When specially constructed for mining use, the instrument is graduated to represent 6 inches of the mercurial column, from 27 inches to 33 inches. This scale enables observations to lia made from 2,000 feet belov? sea-level to 4,000 feet above. The finest divisions of the altitude scale represent 10 feet measurement, which can be divided by a vernier, moved by rackwork adjust- ment, to single feet. A lens, which rotates on the outer circum- ference, enables the vernier to be read with facility. Tha instrument ia inches in diameter, and is provided with a l<>ather sling case. In order to retain the sensitiveness of action of the aneroid, it should be cleaned and adjusted every two or three years by an instrument-maker.

The principle that the boiling-point of water varies with the atmospheric pressure is sometimes applied for the measurement of heights. The instrument used for this purpose, the kypsomster, consists of a thermometer, surrounded by a double-telescopic chamber, and suspended so that its bulb is above the surface of some water in a metal boiler, heated by a spirit-lamp. It is thus enveloped in steam when the water hoils. This cheap and port- able instrument for measuring heights is to be preferred, for its simplicity and certainty, to the mountain barometer. Tables are published by the maker, Mr. L. Oosella, of London, giving infitructiona for using the hypsometer.

Determination of the Depths of Shafts.— In connection with levelling operations underground, it is fifequently necessary to measure the depths of shafts. For this purpose, a wire with weights at the end, or the winding-rope with the cage or the kibble, is let down, and the length of the wire or rope measured

Uike-Survetino.

0"

by means of rods. Or the depth of the shaft may be maumt direct hj applying rods, chains, or stel bands to the timberiai of the shaft Good results have been obtained by both meiUkodt It is, however, evident that the direct measuremeat is trustworthy, though more difficult and tedious, thau the indirtt<;( method. TLe meiisureiiient muet be so contrived thai starting- and end-points can be easily vonnected with Use siulav and underground levellings.

The measurement by means of a wire is usually effected by changing the vertical into horizontal measurement in the fblloinr. ing manner: — From a small windlass (Fig. 66) erected at suitable distance from the shaft, the steel wire (piano vitn) unwound, and passed over a pulley, which is placed over mouth of the shaft in such a way that the wire weighted wifcfcj 10 to 30 lbs. can without hindrance sink to the bottom of

shaft The starting- and end itotn are distinguished by threads tied of*-' The depth is meaanred on lottinS down and hauling up the win?, is done most oonvenientiy with Ib' horizontal portion between tho putlog and the windlass. The wire is Ici'p'* in suAicient tension by the weight- The i>longation of the wire, uaowd by its own weight and the weight, does not interfere with th# accuracy of the result, as the win> ii measured in its stretched oondttion. The method is very rapid ; at Firniiny, nrar St. Etienne, a depth of 280 yards has been measured in half an hoar. ExperimentB made at Firniiny show

that the error with this method does not exceed of

an inch per hundred yards of depth. Accurate i also been obtained at Scheniuitz, in Hungary, In i Chrisuiir, who measured in aii hour a depth of 'J 10 yaidk accurately to within tjow "f the measured length.

Local conditionB may render it necessary to apply the mMWiiiv the vertical part of tho wire, in which i it

Bmi' more inconvenient, but in other i :he

prt-ceding.

Instend of the wire, th' winditifropic mav bf ni?d. In thial

1. oC

Fi. 06.

obttitiu-d with thn wire. Thus, ijorcbors mraaured ona nnd theil

Vme ihhtt o

Retelling,

iTOe ihhtt once -with the wire and once with the winding- rope ; the results being 129 fathoms 3 feet inches and 129 fathoms 3 feet 3-54 inches respectively.

For the direct measurement of shafta, iron anrveying-chains, teel hands, or specially constructed meaau ring-rods are employed. Tiie chain employed for measuring the depth a of shafts must tiret be carefiiUy tested. It is then let down tjie shaft at a suifc- iible point, and suspended by the upper handle to a nail. A second n&il is driven within the lower handle, and touching it. The chain is then removed, the lower handle being hung to the second nail, and the process repeated as before. The depth thus obtained must be diminished by the thickness of the nails included in the measurement. It is therefore desirable to employ round ttails of uniform diameter. The chain, of course, must be allowed to hang perpendicularly, and all obstacles, such as platforms, in the shaft must be removed or bored through, Sometiraea it is impossible to measure the shaft in one straight line; a suitable point must then be found in a line at right angles to the chsin, uid the measurement continued.

With the steel hand, shafts are measured in a similar manner.

Tills method has been employed with success by Mr, Graefe* in

the Staasfurt salt-mines for measuring shafts of considerable

depth. For this purpose, at a measured distance above the roof

of the cage, a seat is fastened to the winding-rope in such a way

that a miner can sit in it without tlanger, and apply the upper

nd of the steel band to the guides. The mine-surveyor stands

On the roof of the cage, and carries the lower end of the band,

Reside him stands a second workman, whose duty it is to give

the signal for raising or lowering the cage. In this way, after all

the preparations had been made, the Leopoldshall shaft was

sured three times in six hours with the following results ; —

First meunremeiit, . . . l,09fi feet S'SOiachH. Second „ ... 1,00S „ 5'S4 ,,

Third „ ... 1,095 „ 5*81 ,,

Xn this case, the heights of 8 levels entering the shaft had also obc determined.

In almost as short a time the Von der Heydt shaft, at Stass- Vrt, was measured four times ; the heights of 7 levels entering the shaft being determined at the same time. The results were —

f iist meoctirement, . , . 1,152 feet 2'16 inohea,

Second „ . , , 1,152 ,, 2-07 „

Third „ . . 1,152 ,, 2-23 „

Fourth „ . , 1,152 „ 211 „

Merff. H. Ztg., vol. xlii., l3S3,xi. 4.

the p

r

302 HINE-SURTETIKn.

The most accurate meOinB of meaauring the depths of shafts is ftffordflLl by the meaaurtng-roda conatructed for thia purpose by Borchers, which are frer|uent!yftm ployed in the continental mines. The rodfl conaist of a number of round eteel bars 016 to 0-24 incl in diameter, and 1 to -1 yarda in length. The enda are screweJ and may be connected by braas double screws, ao that a, measuring- rod of any required length may be conatructed. The true eal surfaces of the separate rods must be exuctly at right angles to tha longitudinal ax.is, and tbe brass caps are provided with an opening;' on both sidts, ao that the contact of the end planes of ttro rods can be aeon. The first rod ia provided with a hook, from the inner surface of which the counting commences. On using these rods, the influence of temperature has to be taken into account.

For measuring the depth of vertical sbafta, tapes of severaB hundred yards in length are now largely used. As, however, the absolute length of auch tapea cannot easily be ascertained, ihe reauUa obtained are not faultleaa. Nevertheless, when number of vertical shafts are all measured with the same tajie their relative depths can be determined with sufficient accunuiy for practical purposes. In mining districts where there are both vertical and inclined shafts, which are measured with diflFerenfr appliances, the determination of the absolute depth is a matter of importance. In the TJp(ier Harz, inclined shafts are always measured by means of Borohera' iron rods, and vertical shaf means of a suspended wire. Both methods have given factory results. Measuring the wire being a tedious operation, Mr. 0. Brathuhn haa employed a measuring wheel for the purpose. The brass wheel used had a diameter. of 3§ inches and a thickness of Q-'S inch, the rim being provided with a rounded groove for the reception of the wire. The periphery of th wheel is divided into a hundred divisions, and with the aid of a pointer and scale a ten-thousandth part of the circumference can be determined. A counter is attached to the axle to register the number of complete revolutions. On the cast-iron bed-plate of the wheel there is a small spirit level, so that the plane of the wheel may he placed vertically. In tbe plane of the wheel there is a ratchet winch for lowering and raising the wire passing over the wheel. Befort- the measurement is begun the wire, weighted with a plumb-bob, ia passed over the wheel into the shaft, and allowed to hang for several hours until it has stretched to it* full extents For the measurement two levelling iustrumente are required, one at the surface and the other at the shaft bottom. With the latter the height of a fixed point on the wire ia ascertained, and this is marked by tying on a piece of thread. The leveHiiig lastrumeQt at tlae aurface aiiiwaVftd to ufht tbo

LEVELtmo.

wire. The counter 13 set at zero, and when the thread at the tiottom of the shaft has been tied on, the position of the pointer read, and the wire carefully hauled up. "When the thread tied on to the wire ia intersected by the cross hairs of the lTelling instrument, the wheel is clamped, and the number of fevoltitiona noted. The difference between the initial and final reading tnultipHed by the value of one revolution gives the required depth. The coefficient of revolution was determined by repeated niea.surenients of s shaft of knotvn depth. Experi- oenta showed that the meaauriog wheel was a convenient and sufficiently accurate appliance for measuring shafts. lis coat, liowever, is considerable. The wheel, with winch and guide rollers, costs about £15.

The me-asurenient of the depths of inclined shafts presents the greatett difficulties. In such shafts, Fig. 67, a plumb-line ia

used, the points of suspension being found by means of a spirit-level. Such shafts are frequently tortuous in

jr A inclination and in direction, in which case .K- they must he surveyed in the same way

as levels, the vertical arc of the dial being employed in conjunction with a plumb- line. It is an operation of great difficulty, and one which in former times has given rise to serious errors in the surveys of the mines of Cornwall, Derbyshire, and the Harz.

In aurveying and levelling in the shafts of the Lehigh Vidley Coal Company, in the United States, a new form of plummet has recently been adopted. It consists of a vertical core 12 inches long, with eight radiating flanges 9 inches high by 3 inches wide of j-inch metal. At the bottom there is a circular

disc acting as a web. This plumb-

— - — bob weighs 20 lbs., and has a surface

area of abnut 630 square inches. A n

iff — ordinary bob of equal weight would

I f / i vVvN have a surface of 90 square inches.

- In a dry shaft, 500 feet deep, this form of plumb-bob will settle, under ordinary conditions, in about one hour instead of in five or six houra, as i-s the case with the older form,

Contoar Lines on the earth's aur- faoeare lines traversingall the points on the ground which are at a given Fig. 68. constant heig\it aXiove tV* iftX'o.Tfi.

UlNE-SUBVKTING.

level. A contour line may also be described as % homoatal sectiou of the earth's surface, or aa the liae where the earth') surfaoe ia oat by a given horizontal surface, or as the outline of an imaginary slieet of water covering the sirounrl uji to a eertui height. Fig. OS repreaenta the contours of a hill,

'i'rauing contuur UnuB consists iu determining equidistant leriu of points satisfying these conditions. The TertioaJ distance between successive contour lines on a plan depends on the figme of the ground, and oa the scale of tlie plan. Two methtM of tracing contour lines are employed — (1) The regular method, consisting in tracing the lines on the ground, and then surveying them ; (2) the irregular method, which consists in collecting, on the ground, data to enable the lines to be constructed on the pla.

On the Ordnance maps of Great Britain, on tlie scale of 6 inclw to the mile, contour lines are drawn at each 25 feet of height) with principal contour lines, deteiTuined with greater precisiimi at every GO feet in the tlattor parts of the country, and at eveij 100 feet in tlie hilly parts.

Mr. W. F. Howard advocates that colliery plans should eihiWt contour lines at regular and fi-equent intervals. In this wiy the vertical throw of each fault, excluding the mere bending up or down of the adjacent strata, which has often a tendency to mislead, would be continuously shown though the fault should be rarely penetrated. Contour lines are generally shown on the plans of the anthracite mines of Pennsylvania,

ApplicatiOBS of LBvellimg.— A branch of engineering, in which the application of levelling is of great importance, is the setting out of aerial wire ropeways. The importance of thia mode of transport in the development of mineral resources is known to every mining engineer. As a case in point, the rich iron orei of the Sierra de Bedar, in southern Spain, would probably have remained untouched to this day but for an aerial wire ropeway, 9f mile.s in length, which connects the mines with the shore of the Mediterranean, near the town of Garruclia, and which affords cheap tran.sport to the point of shipment, An ordinary railway would have cost 100,000, whilst an aerial ropeway could built for about one-quarter of that sum, an outlay which left a satisfactory mar'in for profits on the sale of ore.

In the older systems of ropeways, one endless rope is employed, serving both as carrying rope and hauling rope for the bucketa. Alany examples of lines of this class can be seen in the Bilbao iron ore district. The chai-acteristic of the modem or Otto system consists in the employment of two ropes — a heavy fixed carrying rope and a light ti-avelling hauling rope, the buckets being fitted with special devices for gripping the latter, W:'

LEVELLtNO. 205

ropevaa of this class toads of 20 . a&n be carried, so that as

much OB 800 tons mav be transported ia a day of ten hours.

i'lie moat iniportant Otto ropowiiy yet constructed is that for

the transport of iron ore at the Auiuetz ntinea in Lormiue. It

is 6*67 miles long, with a fall of 475 foet, and transports 500,000

I tons of ore annually. The longest wire ropeway in America is

K tint at Grand Enciimpjaeiit, Wyoming, which is 16 miles long.

W The highest support is 69 feet high, and there are three wide

r Spans ranging from 1,800 to 2,300 feet. At Garrucha, Spain,

I Che line is divided into four independent aectiona, the two tirat

hieing driven by a 30 horse-power engine, and the two last by a

j 70 horae-power engine. The greatest span of the line is 918 feet,

the heigiit above the ralley being 164 to 196 fent. The steepesti

gradient Is 1 in 2, and the taliest standard is 118 feet.

In making the preliminary surrey for an Otto wire ropeway, there are several points to which attention should be paid. The terminal fKiints of the line should, whenever possible, be ho placed that the ropeway joining them shall be in a sti'aight line, as each turn increases not only the amount of construction neces- sary, but also the cost of working, as it necessitates the erection of a complete station. For lines of more than miles in length, one or more intermediate stations must be erected, as greater ; lengths than this cannot be worked with one hauling rope. At the stations the line can form any desired angle. The points aelected for the supports for the bearing-rope should be marked on the ground by wooden pegs distinctly numbered, and should be shown tu the section drawn. The supports should be 50 yards apart, when 50 to 100 tuns are transported in 10 hours, 40 yards apart for 100 to 600 tons, and 35 yards apart for amounts above I 600 tons in 10 hours. This rule may be neglected in crossing roads, in which case one support should be at the side of the road, and it may be neglected when this rule would necessitate the support being platKd in a narrow valley or hollow, in which case, in order to avoid unnecessary height, the post may be moved. For crossing valleys and rivers, spans of 350 yards may exceptionally be employed, when supports are impossible or woald exceed 35 yards in height. In crossing roads, cross- sections must be made in order to give the requisite data for the erection of a protecting bridge, and oross-seotions must be taken at every point selected for a station.

Marshy sites must be avoided as far as possible ; but in caaea where this is out of the question, the surveyor must Utiteriinjae the depth of the solid ground.

The hydraulic mining ditches of California afford some inter-

Kting examples of levelling succeasfully conducted in the h£

UlNE BUBVEYIKO.

of great difficulties. Hydraulic mininK consists in the disio- tegration of auriferous gravel deposits by propelling a heavy jet of water under pressure upon the bank, and in wa.'itiiug off tlie gravel in sluices in which mercury is distributed. The jold forms an amalgam, and remains caught. This method of mining was introduced in California in 1856, although Pliny describes* system of hydraulic mining in Bpftin, -which resembled in rnanj respects the modern method. Hydraulic mining has given rise to an extensive system of artificial reservoirs in the Siem Nevada for the storage of water, and to the construction of artificial water-courses to convey the water thus stored to tiie scene of mining operations. The setting out of these canali it a grade of from 4 to 20 feet per mile, over deep gorges anrl aloaj precipitous cliffs, presents problems of great difficulty to the mine surveyor. In many places it is impossible to find room along the sides of the great cafions for miles, to excavate a cantl or to rest a conduit or " flume," as it is locally termed. The bracket fiume of the Miocene mine is a marvellous example of engineering skill. Hero, in order to obviate the erection of i trestle 180 feet in height, the water is conveyed in a wooden flume — 4 feet wide and 3 feet deepround a cliff 350 feet in height The flume is suspended upon brackets made of T-rul fixed into holes previously drilled in the vertical cliff. In another place, in the line of this ditch, is a piece of breastwork 1,088 feet long and 80 feet high. Again, the Blue Tent Mina has a ditch running for a distance of six miles along the face of a clififj over which the surveyors had to be auspejided by ropei 1,000 feet above the bottom of the gorge, in order to estabUah the line of the flume.

In other places deep gorges are crossed by means of inverted

siphons. The Cherokee ditch crosses a deep canon in this wsy,

the pipe sustaining a columnar pressure equal to 800 feet in

perpendicular height. In making the crossing, 13,000 feet of

38-inch pipes, J-inch in thickness, were used. A few years ft;;o

there were in California 6,000 miles of mining ditches, their

estimated total cost being X3,000,000, Some of them have been

built at a cost of £5,000 per mile. The cost, too, of keeping

them in rejmir is very considerable, b;b the hydraulic miner has

constantly to contend with the elements — frost and flood, ictt

and snow, wind and rain.

In the preliminary survey, to determine the beat sitaation for

ft long ditch, comparative observations should be made with aneroid barometers, care being taken to determine the eleva* tions, not only of the end points, but also of intermediate pointa, wkich diflerent surveying parties cau start on the subse-

uent setting out of the line. The necessary points being stablisbed. the line is staked out, all stations being properly lUmbered and pegs driven in to indicate the gradient. Accord- ng to Mr. Bowie, the author of the standard work on this ubject, stations may be from 50 to 100 feet apart on ordinary Otmd ; but very irregtllur country obviously demands shorter ntervals. Bencb-marks should be placed every i or A mile for nnvenient reference. All details of tunnels, cuttings, and lepressions, which require pipes or flumes, should be worked )ut in full, a work in which the hand-level can often be advan- tageously employed. Complete notes should be made of the :haracter of the ground along the whole line.

In laying out mining ditches iu Oatifornia it is usual to imploy a light frame shaped like the letter A, made of J by IJ inch wood, and provided with a heavy plummet hanging on a fine wire from a notch at the apex. The height of the fime is ttsually 6 feet, and the base 10 feet. To commence, one end is placed on a level piece of ground, and the other end is raised or lowered untU )>oth ends are level, and the plumb-line marks the ame position on the cross-bar, if turned completely round. The grade for the proposed mining ditch being decided , say inch in 10 feet, a inch piece of wood is placed under the rear end of the frame, and the point indicated by the plumb-line is marked on the oross-pieco. One raan then holds the frame, whUe another lifts the front end until the plummet coincides with the mark, he then drives in a peg in front. The rear end of the firame is then placed exactly where the front end was, and the process ia repeated. In this way the ditch can he set out with great rapidity. The only danger lies in getting the wrong end foremost.

On the survey of the Manmad-Uhuba Railway in India, F, R, Jolmson (J/in, Proc. Inst. C.E., vol. cxv., 1894, p. 343) found that theodolite levelling by angles of Lnclinatiou proved accurate under very unfavourable conditions, and he is convinced that the theodolite is the best instrument for rapidly exploring rough ground, and for taking a section by angles of inclination. This method gives sU the information required in the shorteat poflfiible time.

IIINE-aUBY£TINa,

Chapter Xiv.

OONKECnOH or the UnDSRGRODND- and SURFACE-gtrRTETK

Methods Employed. — A correct survey of the imdergroimd workings of a mine, and of the surface or royalty having been made, it is necessary to determine accui'ately the besmg o( a line underground with a view to connect the two Borreyj. For this purpose the following methods have been employed ',— (1) By means of on adib-level or incliaed shaft; (2) by mauis of two shafts; (3) by means of one shaft with two auapendfd plomb-Hnes; (i) by means of the transit-instrument; (5) by nieana of the transit*theodolite; (6) by means of the magnetio- need! a

L By Means of an Adit-level. — When the mine is connectei with the surface by means of an adit-level, the connection of the surveys is easily effected by continuing the underground trftver through the adit-level to the nearest aide of the triangle of tl" Burface-survey.

2. By Means of two Shafts. — If both the shafts are vertial. the connection of the underground- and surface-surveys is mad*

by means of two plumb-liiw'S, one suspended in each shaft' The points of suspension are joined to the siirfa<;e-triaiigii' lation by means of careful measurements. In this way the length and bearing of the line joining the two plumb- lines may be calculated by means of rectangular co-ordi- nates. A traverse is then made underground from one plumb- line to the other, and from the data thus obtained the length and bearing of the line joining the two plumb-lines is again calculated by means of co-ordinates.

EsMmph. — In two perpendicular shafts, plumb-lines are hung at the points A and 6 (Fig. 69). From the surface- tri&ngu- lation it is found that the length of the line A B is 56*29 chains, and ita bearing 118' 36'. In the mine, a traverse was made with the following results: —

Pig.

NDERGROUND- AKD SURFAOE-SUBVETa.

To

Uuitb.

AutklBi-

daudtiiaiie

Maridtui.

X.JkT[TODI.

DxTAmTCru.

K,

B

w.

(Too'

O-Oo'

177" 33'

337° 33'

ni.

2S*" 67'

102° 30'

177" 5e'

100° W

lfi-47

180' 62"

101* 18*

158° 3;t'

79° 51'

l-4fi

184* 63'

84' 44'

3'72

vm.

S32

184*20'

89*10'

93*63'

3*03'

B.

136* 11'

Sir 14'

0'83

14-se

Tm

o-ee

ith the ccKtrdinates 7 '20 chat as N., and 56-61 chaitia £,, tbs h and direction of the hypothenuae may be calctilated from irmula: base + perpendicular* hypothenuae'', or tangent

jtle of bearing — — i— , and the distance latitude x " latitude

t of angle of bearing. The hypothenuae ia the above

uwiU then be found as foUows : —

log 55-81 log 7-20

'6673325

L.tiBAC 10-8893795 BAG

log 7-20

0'8673325 10-8930271

Miwe-Scrtsting.

From this angle — that is, the angle formed by the hypothennso A B and the first line of the underground-survey A 1, and from the bearing of the line A B determined at the surface (118*36'), the beariag of the first station-line underground may be deter- mined. In the above example, this is done by subtracttoii, 11 8° 36' - 82° 38' 35*58'. From this may be deduced tlio bearing of the other linos of the traverse. In the example, thii ie done by increasing the reduced meridian angles by 35* 58' in each case. With the aid of these bearingB, the co-ordinaUs of the underground-traverse should be recalculated, &nd (be reaoltt balanced.

For suspending the plummet, a thin wire of iron or brass used Hemp cords are useless for the purpose ; because of tlieir torsion and contracting when wet. They present a greater surface to the action of air-currents and water than thin wire, ind do not admit of such precise sighting. Thi' plurauiet weighs 5 to 8 lbs. It should not be hung on when the wire is Jet down dw shaft in case of accident from the wire breaking. A smaller wdt may be used when the wire is being let down, and at the bottom of the shaft it can easily be changed for the required weight. The plumb-line must, of course, hang perfectly free, without coiiiing in contact witli the sides of the shaft. To ensure this being the case, a lamp is slowly passed round the wire at the bottom of the shaft. If, in whatever position it is placed, tht light can be seen from the top, the wire is clear.

The plumb-lines may be sighted without any difficulty in thj Burface-snrvey, as the upper part of each wire does not move. In the mine, however, the plumb-line has to be sighted at i*i lower end, which continues to vibrate like a pendulum. The motion may be reduced by allowing the plummet to dip into bucket of water, and by shielding the wire from air-currenta ana falling water as far as possible. It is, however, impossible itop the vibrations altogether.

To lessen the motion of the plumb-lines, Mr. H, D. Hoskolo proposes the adoption of iron chains made from wire thre sixteenths of an inch in diameter. The method would, however, be inapplicable in a shaft of considerable depth.

In sighting a plumb-line with the theodolite, it is beet to follow it by means of the tangent-screw to the end of its vibra- tion. There is then sufficient time to read the vernier before i'' reaches the other end of its course, as well as to intersect it that position with the cross-wires. This operation is repeate" several times, and the mean taken of all the results. Wheu tba arc is very small, the mean may be estimated, and the cross-wire* get At that angle direct. The "pWrnVfeiea leTiAciTad. visible bf

UXOEUQItOUlID- AND SUilPACE-eliaVEYB.

lining Ijehiad them a sheet of oiled paper illuminated by a lamp behind This method of sighting a plumb-line is very kiguing, anrj necegaitates great skill to read the vernier and lct the telescope to the next extremity of the course, in the paratively short time in which the plummet completes its

These difficulties have been overcome by Professor SeUraidt,*

tlie Freiberg School of Mines. The plummets he uses are

ig to thick vrire (0-04 inch in diameter), and their weight is

iddemble, being as much as 50 lbs. They do not dip into

Iter, but are allowed to swing freely. At a short distance

ive the bottom of the shaft, a horizontal finely-divided scale is

Ked perpendicular to the line of sight of the telescope. The

i&ging plumb-line is then observed with the telescope, and the

sceuive extreme positionB are read and noted, the plumb-line

big purposely made to swing parallel to the plane of the scale.

W latter is illuminated by means of an ordinary miner's lamp

candle.

from one or more series of double observationB, the mean ntion of rest of the plummet on the scale is calculated, and for subsequent survey the cross-wires of the telescope are made coincide with that calculated point. The calculation of the lition of rest ia a very exact one. From two trials, one made a depth of 657 feet under favourable conditions, the other at inpth of 1,722 feet under unfavourable conditions, Professor Jimidt found that the mean error of one series of observations 1 ± 0-12 inch, and the mean error of the result of a double isa was ± 08 inch. Under unfavourable conditions the fon were 0-17 inch and 0*12 inch respectively. Iti cases where it is required to connect the surface-survey fth the underground survey at several levels at different heighl the shaft, it is desirable to fix the plumb-line. For this pur- e, Professor Schmidt t has invented a simple centering appara- On a perforated cast-iron plate, a prismatic centre-piece 'y be slid in two directions at right angles to one another by of four centering screws. Above the latter are two scales angles. The iron plate is placed so that one pair of teriag screws is in the line of sight of the theodolite-telescope, pair being in the line of sight of a second small tele- of low power. With this small telescope and with that of theodolite, the swingings of the plumV)-line are observed, and tion of rest calculated. The weight is then removed

Stitch. Ja/irbueh., 1882, p, 145.

t Bern, fl. Ztg., vol. lUii,, p. 217.

Sis

HtRK-StrRTBTINa.

{rom the plumb-line, and a. capscvew [tlaced on ths wirkt lb* ▼eight is then replaced, nrl screwed into the centre-piee* of (be apparatus. With the aid of the two telescopes, and the ceotemi; ecrewa, the centre-piece can be brought into such a position thai the plumb-line is in its calculated position of rest.

If either of the shafts used for connecting the undergroand' and surface-suFTeys is inclined, or if both ire, the method tin same, except that the shaft is surveyed by traversing instsad of by suspending a phimb-Iine.

The two methods of connecting underground- and sari** surveys by swinging plumb-lines and by plummets proTidri with wings and dipped into a, vessel filled with wAter or oil, have been combined hy Mr. 0. Brathuhn, wlio etches plate, in addition to the ordinary cros.<s lines, a scale mAtd with short lines, the divisions having an angular vulue of W seconds. For lighting the plumb-line, u sheet of while papsri* held behind it illuniiiiateU by a lamp. Trials of Ukb VJ- piece scale have given surprisingly accurate results.

In connecting underground- aud surface-surveys witii iho ui of plumb-lines, iron plumb-boba with wings of sheet-imm largely used. Such plump-faoba may, however, in some droia- stances, give rise to erroneous results. In plumbing a slisl 130 yards deep, the error was found by Mr. O, Brathuhn considerable. In a south-westerly direction from the shaft cross-cut hod been driven, in which, in addition to the ordi>uu7 rails laid down, a large number of spare rails wer* stored close to the shaft that one plumb-line hung in close proximity to the northern end of the rails. By the induced insgDettsn of the raUs the plumbline was drawn from its pRrpeadtoaUr position to such an extent that the distance between the two plumb-lines was 7*5 millimetres greater underground thaa ftt the surface, and that the line connecting the plumb-lines at tb* points of suspension formed an angle of 6 minutes with (hat the bottom of the shaft. The enMr was eliminated by tha employment of brass plumb-bobs.

3. By Means of One Shaft.— Wlien there is only one perpen- dicular shaft, the underground- aud surface-surveys may connected by transferring a short line from the sarfnoe to th" mine by meaos of two plumb-lines suspended bearing and length of this short line may L' fiu£Bcient aecuraoy by connecting it with the sorfsoe-? tion. Then, if the underground-survey also iadade? formed at the l>ottom of the shad by tiio two *- hanging vertically, the ootincction can be made from tlir bearing of that hue. Thus, the survey is made at the

Ondkroroeind- Akd Subfacescrvets.

and in the mine in the aarne way, by constructing a triangle of whicli the litiL* joining the plumb-line is a side.

The following detfiils of tlie connection of the underground- axul surf&oe-surveys effected in this way may serve as an exAtupie : — Fig. 70 is a plan of a portion of mine, in which D G represents n line at tb sarfaee, connected with the triangnla- tion, and E F a line of the transverse of the IS-fathnni level of the mine. In order to eonxtct these two lines, two plumb-linea A and B were suspended in the perpendicular hafi, as far apart aa circumstances would allow. The distance in this case was 0-9316 tathom. Tlie two wires were sighted froni the point Q in the doorway of the mine- huusu, and the angles BOD and AGD and the distances G H and G A accurately tueaaured. llie triangle Q A B was in libia way completely solved, the potiition of the line A B formed by the two plumb-lines was determined with referaoco to G X>, The theodolite was thetn Mi up at C in the ci-oss-cut at the 135-(kil)oni level, and with it were cure- full j mewured the angles B C A 33° 08', A C E - 159' 21', and B F 26'J' 31' ;ia , and the horizontal distances B l-63T3> C A 1-7 169, and E 1 5'6563 fathoms. Since in the triangle B A the three sides were determined, it was unnecessary to measure the angle B C A. This was, however, done as a check. On calculation, the au<lu BOA was found to be 32* a' 10". A B 60° 13' 15", and B A 78' 38' 37'. Of the measured and calculated values of the angle BOA, the inetui S2* 8' 6" was taken. The two other angles of the triangle

A B were balanced so as to make the sum of the three angles <)aa] to 180". In this way the point O at the surface and the point E in the mine are oonnectd by known horLzontal distances. Y*-. 1,. wliich the line D G at the surface makes with the line

1 mine may then be easily determined.

i 11.' nil.- D being taken as the meridian, the line A B was (bond from the surface-survey to form an angle of 23* 12' 10' with that meridian. Underground the angles formed by the uicri'liuii and the various lines were

A U eO* 13' la"

CK ir.sr-Ji'W EF urivr,i,-'

- 23' 12" 10" 48° 01' 05"

- 4tr01'a5" 1'55'

H

914 Mikk-Slhvkvixg.

Ill some cases tb(f cbeodolit tuay be set up and centred xt th pointB A and B at the surfaoe, but nndeirotuid this cannot be doae with sufficient accunkcy.

The accuracy of the connection depends on the correct deter mination of the angles A and B in the triangle A B C. Tbew angteB usually have to be calculated irom the known leugtb AB and from the sides AO and B measured underground, ae w?U aa from the angle O. Thia may be done by the ordinary sin rule —

„. . a sin O . „ 6 sin

Bm A -, Bin .

c e

In thii form a la, sin A is dependent upon the three magnitndM 0, e, and a. The length e and the angle may be measored underground with great accuracy, if Schmidt's method it eDt- ployed.

The influence of an error in the length a on the angle A varirt considerably according to the form of the triangle. It is greit when the aides a and b are of equal length — that is, when tlw triangle ABC is an isosceles one. It is least when the triugls has a very acute-angled form. The sines of angles near 0" and 180° do not increase or decrease in proportion to a slight increswe or decrease of the angle. Conversely a small ohange in the nioe has an inappreciable influence on the corresponding aogk Oonsequently a small error in the length a has uo edect on th determination of the angle A, when the triangle is an ncute- angled one. If possible, then, the ordinary well-conditioni'd triangle must in this case be avoided, and the theoilolite pliced u nearly as possible in the continuation of the base-line.

By means of two plumb-lines, the connection between the underground- and surtace-surveys has been ejected with con- siderable success by Mr. E. Olark in the brown hsmatite miuM belonging to the Glendoo Iron Oo. of Pennsylvania. The shaft* are usually 4 feet square, but, where an extensive plant of pumping machinery is required, the site is increased to 8 feet Iiy 6 feet. The depth of the shafts varies from 75 to 200 feet. Tlie principal difficulty in the survey of these mines has always been the trouble experienced in connecting the underground-survey with the surface-survey, on account of the small size of the shafts, and the gradual movement of the ground pushing the shaft out of the perpend ieular.

The method adopted by Mr. Clark has been to establish a line at the surface, and, by means of a straight-edge, wire, and plurab-

nSDERGIlOUHD- AND 8URFACB-8URVETB.

ob, to project that Hue to the bottom of the shaft, and there use it OS a iMSe-line for the underground-survey. The line across the ahaft La marked in the timbera by nails, woicb may be permanent &nd used in future surveys, if the earth about the shaft is suffi- ciently Qrui. A straight-dge is placed against the nails, and tbp assist&nt above lowers the plumb-bob by means of a reel and umealed-iroQ wire of sufficient strength to hold the plumb-bob, which in of cast-iron, and weighs 10 lbs. The two plumb-bobs are each received into a bucket filled with water at the bottom of the shaft. Yibration may be lessened by mud thrown into the bucket. When the plummets hare become nearly stationary, a theodolite is set up in line with the wires. This is done by moving the instrument until the nearer wire coincides with the vertical hair, and the second wire is concealed by the first ; or the transit will be in line when the extent of the vibration of the second wire to one side of the first is equal to the ectent of the vibration to the other side. The ereater the distance between the wires, and the farther the theodolite is from them, the more Accurately can it be placed iu line. The average distance in 16 shafts surveyed in this way was IS to 6 inches, this distance being the base-line upon which the mine-survey was based. In the coal-mines of Pennsylvania very good results have been obtained by this method, with a base-line of 9 feet in length. i

For vnpidly connecting surface and underground surveys Mr, T. H. 6. Wayne* uses a collapsible triangular frame fitted with levels and legs so that it can be supported horizontally. A. telescope and vernier are placed at the apex, and the two legs are recessed at their ends to fit loosely round the two plumb lines. If the telescope is clamped to a sight at one level, the frame may be transferred to another level where the telescope will give the same direction. An elaborate mechanical device, termed an underlay-table, has been invented by Mr. S. J. Pollitzer,t and used by him with considerable success in sur- veying zig-zag shafts in New South Wales, the principle being to carry a short horizontal base-line from the surface down to the bottom of the shaft.

The necessity for measuring the relative heights of the various points iu a shaft, with a view to pi-eparing vertical sections, induced Mr. PollitzerJ to construct a measuring wire 3,000 feet long. The steel wire used weighed about 2 ozs. [ler 100 feet, ooe end is attached a 9-lb, brass detachable plummet, on

Sfimng JouiiinJ, vol. Ixxii., 1902, p. 911. + Trann. ffiM. M.E., vol. xxv,, 1903, p. 24. t Hid. , p. 17.

2ie

HlNESrRVEYlNQ,

which additional weights may be placed if aecessarj. The wire is marked at each length of 10 feet, and is wound upon a cedar wheel 18 inches in diameter and inches thick. The keel can be stopped at any single inch tnroughout the depth of the shaft. With the aid of this measuring wire Mr. Pollitzer mad a survey at a gold mine in Kew South Wales with a view l-i making the connection at the 800-foot level between two Tertical shafts about 1,000 feet apart. The intervening rock was bard diorite, and in seven months the connection was accurately completed.

In the Missouri lead and zinc mines, where the shafts &r

frequently out of repair or bent into a curved form, Mr. W, E. Gordon effects the connection by tying the plumb-lines together BO as to hang as far apart as possible and yet be clear of the shaft. At the top they led outwardly to posts planted in firm ground, and at the bottom they are tied to the end of a stretcher- bar. This bar accordingly swings into the line of the post*.

tn plumbing the very deep shafts at the Tamarack Dune, Lake Superior, considerable difficulty has been experienceii- The lines were of No. 24 piano- wire, and were lowered carryin!! a doubly conical wooden frame to prevent catching on obstruc- tions, and 60-lb. plumb bobs were substituted at the bottoiu. In one shaft, i,250 feet in depth, the wires were found to he 17 '58 feet apart at the surface, and 17 '65 feet apart at ths bottom, a difference of 0*84: inch. In another and miich shallower shaft the difference was 1'2 inch. This divergeuce was ascribed to the fact that there is an unbalanced sidewitjs puU on the wires and bobs owing to the missing mass of rocit in the shaft. Careful experiments have shown, however, that the phenomena are due to the effect of air currents. 4. By Means of a Tranait- instrument .—The most accurate H method of effecting the connection between the uadergrouad- H and surface-surveys is by means of the transit-instrument. H The transit-instrument is the standard instrument in every

H astronomical observatory. It consists of a telescope formed of H two parts connected by a spherical centre-piece, into which are H fitted the larger ends of two cones, the common axis of which H is placed at right angles to the axis of the telescope, to serve as H the horizontal axis of the instrument. The two small ends of H the cones are ground into two equal cylinders or pivots, which H rest xipon angular bearings or Y's, supported upoii staudarJs, H Une of the pivots is pierced, and allows the light from a lamp to H fall upon a plane mirror, fixed in the spliericai centre-piece, on the axis of the tek'scope, and inclined to that axis at on angle of

lUonil

Htron

vumn

UXDEitG&ODND- AND SrJRPACE-SCRVBTa.

Light IS thus thrown directly down the telescope, uid illoiumabes the cross-wires.

The transtt-inBtrumi-nt was first used to obtain the counectioii

tween the uaderground- and surface-surveys by Mr. A. Bean-

ia,* in 1856. 'ftie first method he proposed was a pui-ely

onoinical one. Having set up the tranait-instrunient with

phute considerably out of the meridian and its telescope

ited upwards, he observed the passage of several known, stars

Veross the Mires of the diaphragm in the usual manner. It was found that at the surface the deviation of the plane of the inairiusent firom the meridian could thus be approximately lietermined. Underground, however, with the telescope pointed up a vertical shaft, it waa found that the operation was attended with such difficulty that it had to be abandoned. Instead of observing stars, reoourae was had to lights fixed at the top of I shaft The experiments were perfectly successful, and led to method identified with Mr. Beanlands' name. As a matter of convenienue is has been found advisable to fix the trauKit-instrument at the top of the shaft, and to place illuminated marks at the bottom as nearly as possible in the same vertical plane as the instrument. The marks are illumin- jed by th light of a lamp reflected upwards. They ate placed K n position that they can iiJso be flighted by a. theodolite placed ia a line with them at the bottom of the shaft. If now the croa8*wire3 of the transit-telesco[ie coincicle with each of then two points, it ig evident tliat the horizontal line represented by the marks coincides with the vertical plane of the instrument, aod is therefore parallel to the jxisition of the telescope when directed horizontally. Id this way two lines ure obtained, one the top of the shaft represenU'd by the optical axis of the lescope pointed horizontally, the other at the bottom of the

represented by the line joining the centres of the nsarks.

If the two marks cannot be ) wrought exactly to the centre of

jescope, the apparent distance of each mark from the

<wui*-wire8 is measured by a micrometer, and the angular

ion of the base-line from the plane of the transit calculated.

.tearing of the baae-line is then deduced from that of the

Btrument, and the connection between the underground- and

rfaer-siirveyB effected as in the previous case. By this method

! bearing of a line underground may be determined with a degree

PBocumcy that has never been obtained with any other method-

' TW.tr .V, Engl. Imt. M.B., vol. iv., p 207 ; vol X3t., p. 85. See also n. LiveJDg, Tram. . M.i!..vo\. xvliL, 1899, p. fl6, and by .son, Ibid., vol. nil., ItKVi, p. 519.

n

As iliastntioiisof theseTere prctical tests to which this tnethod has betn subjected, the following examples may be given : —

In 1S57, Mr. Beanl&nds made a surrey at Etherley Colliery for the parpose of setting out a drift between the working! of the Geoi;ge Fit, and a new unking, the Dean Pit, half a mile to the e*Bt. There was no connection underground between the ahaits, and it was therefore necessary to make a surface-surrey, and to cotmect it with the workings at both shafts. At the Oeorgt? Pit, the connection was made by means of a very itcep and narrow day-driit, whilst at the Dean Pit, the trutsii- instrumont was employed, marks being left in each caae for tlie purpose of setting out the drifL The latter was worked from both ends ; the length being 700 yards. At entl of lii months a very accurate hoUng was effected, the deviatton between the two ends being 6 inches. If this deyiation hid been due solely to the bearing, it would imply an error of minute. It is, howeTer, evident that it represents not onlj the error of the bearing above and underground, but also of setting out and working the drift. A more convincing proof of the accuracy of this method of connecting the underground- smJ surface-surveys could hardly be given.

The Pelton Colliery, near Cheater-le-Street was worked, in 1664, by two adjacent shafts, 50 fathoms in depth. At a dis- tance of 50 yards from the bottom of these shafts, an undergrovind sinking had been made to explore a lower coal-seam. It vm afterwards thought desirable that a shaft should be sunk from the Bur&ce immediately above that already existing undergTound. Mr. Beanlands itiade a survey for setting out the centro of this Ehaftv The measurements were made with great care with levelting-stafT, and the connection between the tmderground- and surface-anrveya was effected with the transitinstrumenL Th shaft was set out from Beanlands' plan, and was found to corret- pond with the lower &haft within 2 inches.

In shafts of very great depth the method has been employed invariably with successful results. For example, in the Rybope Oolltery, where the shaft is 253 &thoms deep, the bearing was determined twice in different months, the difference between kho two results being only 1' lO'.

As the method requires only one shaft with a clear view firom top to bottom, it can obviously be adopted in nearly every colliery . Though a considerable time is necessarily spent in erecting a platform for the transit, a bearing sufficiently accurate for practical purposes may be obtained in a few hours,

4a. The Severn Tunnel Method, — On account of the length of the heading, the incessant jar of tte % nes, and the

UN DE KG ROUND- AHU i;UltPACE-8VRV£78. 219

trema wetnR<s of the sliaft, a |)lumt>-liiie metliod was Dot applicable in driving the Severn Tunnel. The leagth of thu proposed heading was 2 miles, and that of the available base- line 12 feet doaaequently ao error of of an inch would become 45 inches at the end of the two miles. To overcome the difficulty, Mr. Richardson,* the engineer, devised the following method : — A large transit-instrument was firmly set up over the shaft, and accurately in the vertical line passing through the centre of the tunnel. This line was determined by two staves, one on each side of the river. The heading having been driven a short distance, a horizontal wire, 100 yards long, was stretched at the bottom of the shaft. One end, A, waa attached to the side of the shaft furthest from the heading, the other, B, at a point 100 yards along the heading. A length of 14 feet of wire 'w&B visible from the top of the shaft when illuminated by an electric light. The ends of the wire were passed over the V- threads of horizontal screws, and stretched by means of weights Muspended from the ends. Thus, by turning either screw, a "WTJ slight lateral motion could be imparted to the corresponding end. The transit having been carefully levelled, the end A was first sighted, and the corresponding screw turned until this end was brought truly into the centre line. The telescope was then directed towards the farthest point of the wire visible on the other side of the shaft, and thi.s point also brought into the centre hne by turning the screw at the end B, 100 yards distant. The whole length of the wire thus was accurately directed into the line of the tunnel. A base-liue 100 yards in length, and practically free from error, was thus obtained. Proof of the accuracy of the method was afforded by the results obtained in driving the tunnel. The headings were found to meet exactly.

5, By Means of the Transit-theodolite. — In cases where the haft is of limited depth, and where a large and powerful tranait- instruroent it not available, the connection between the under- ground- and surface-surveys may conveniently I J be etfected by means of the transit-theodolite.

I I I The instrument is set up at the bottom of the

I I shaft. To enable its telescope to be pointed ver*

tically upwards, a diagonal eye piece must be

I employed. This consists of a small right-angled

NH glass prism (Fig. 71), placed at the eye-end of the

N telescope, in which the line of sight is reflected

Fig. 71, from the plane of the hypothenuse vertically

upwards.

The mode of procedure is as follows: — Having set up the transit-theodolite at the centre of the shaft A (Fig. 72), it is ' Eitffineering, vol. xxxiii., 1882, 44.

in

k

iloTelled, and the telescope directed to a small bright light ptaoed

the peg at B. Great cm

Mink Sdrveyihg.

must be taken to eoaure the in- strument being in perfest adjiut- ment so that the telesoope sh&U revolve Id a vertical plane. Th vertical circle is then undamped, and the telescope pointed up tk shaft in the same vertical pluut in the direction of the point a', where a lamp-flame or a hite peg iB brought exactly into tli9 line of sight. A permanent muk is placed at a'. The teleacqx is then directed towards the otbM side of the shaft, and a niuk placed at fi'. In this way two y2_ points are obtained at tlie etl

ikce in the samn vertical plane as the line A B underground. The latter is carefully meaanred, and the distance thus found is measured off from A' to Oby stretching a cord through the centres of the marks a and b. An iron peg should be driven into the ground at 0, with a hole nisd in its centre for future reference. Thia hole is directly otbi the centre of the peg previously driven into the floor of the level at B,

With this method, Mr. H. D. Hoskold has obtained, with tis miner's transit-theodolite, very satisfactory results in the Dean Forest mines. The method is well adapted for use in tninw where the ebafc is of limited depth, and the workings not nfj extensive. The shaft must obvioualy be of average width, tM not subject to any considerable dropping of water.

Ukdbrobound

aURFACE-SUHVEYS.

For coimeoting the underground- and snrface-aurveya, mining tr*nsit-theodolitea with eccentric telescopes are frequently em- ployed ia America and on the Continent. In these iastriiments

Fig. T2 auxiliary telescope is attai;hed outside the standards to the prolongation of the horizontal axis of the principal telescope, or that telescope itself is permanently mounted in a similar position. Bometitnes the theodolite is made with an extra telescope attached to the top of the central telescope, by means of coupling nuts, which fasten it directly over the centre of the inatrnment, and allow its ready removal without disturhing the adjustments.

This method of arranging the supplementary telescope ia shown in lig. 72a. This form is that generally used in oon- jimotion with the American theodolite, shown in dg. 37a, The auxiliary telescope ia attached to the main telescope by two pillars, which project beyond the edge of the horizontal plate when the telescope is placed vertically. The method of placing the auxiliary telescope eccentrically is shown in fig. 72b. In this case, a counterpoise ia fastened to the prolongation of the axis. In both these attachments, the extra telescope is parallel to the principal telaacope.

The objection to the aide-telesoope is that a correction must he applied to each reading of a horizontal angle equal to the tangent of the angle, which is formed by the distance from the side- teletoope to the centre of the inHtntment, and the horizontal distance between the stations.

mE-SURVBYJflG.

In a new form of aaxiliary telMoops designed by Mr. D. Bcott, the telescope is interchaneable, nnd may used ettJittr Ha a Bide ur top telescope; the ecceutricity being the samu in both positions, and only one oounterweigbt beiug neceaouy. The attachment of the auxiliary to the main telescope ia e0ect<ed by means of a single central pLllir, which is permanently imatened to the main telescope. If used at the side, the auxiliary teleaoope is screwed to the tiiid of the horizontal axia.

In place of the diagonal eye-piece for sighting vertically up- wards, an artificial horizon may be used, No special constructtoci of the telescope is than required, as it is merely necessary to sight the image of the flame (Fig. 73). The image and the flame itself are in the same vertical plane, and the image ia seen at an angle of depression a equal to the angle of elevation fi that would have been observed had the diagonal eye-piece been employed.

The artificial horizon may be made of oil mixed with lamp-black. The fluid is filtered through linen, and carried into the mine in a small bottle. When required for use, it is poured into a cylindrical brass vessel, ra,re being taken to protect the surface of the litjuid from air-cu;

The artificial horizon will be fountl more convenient than diagonal eye-piece for surveying in highly-inclined shafts.

e. By Means of the MagneUc-Neeole. — When the miim hu only one shaft, the underground- and surface-aurveye tray Iw connected by means of the magnetic-needle, provide! that the hftit ia not sunk in magnetic strata. If the shaft vertical, a pltin)b-line is suspended in the sliaU, -.Mii (\osu this th indr- ground-survey starts. If the shaft is inclined, a traverse is niada down the shaft.

The method of employing the magnetic-needle ooasists in determiaing the angle made by one of the nidcs of a triangie of the surface-survey, as well as that matie by one of tbo littea oC the undergi-ound traverse, with the mngnetic mcridlatu Tb lines are then connected by a survey matle with the I )iv accuracy of the method in<.'ri'Aed by oV netic bearings of two or more lines at the sui ground.

As the whole of the underground d'fM-iids on thn accuracy of the det!ruiintJon of th' lines, it is advisable to use the ;

Th thcodolito is provided with a magnetic-need ie, which serri

UXDEEQRODfD- ASD SURFACE-aURVETB.

223 B

ineridUn.

direction

sary that

bring the telescope into the direction of tbe magnetic ineri Ala rule, in theodolites, the diameter 0'-180° is in the !.tlje telescope. It is, however, not aVisolutely necessary I optical axis of the telescope should accurately coincide with

that diameter, nor is a com- pass with a complete gradu- ated circle necessary. A long narrow box, provided with an index-iine, Fig. 74, sulfices ; indeed, it has the advantage of being less in the way. The needle should ' M light as possible with thin points, and its centre of gravity >Het not be too low down below the point on which it rests. A itiifying-glass is used to see when the needle exactly coincides 'ith the index-line,

lie tubular eompms m very convenient for mine-surveying poses. It consists of a tubular case, the north end of which Bosed with ground glass, on which a fine scale is marked. By of a lens at the south end of the tube, this scale appears *ghtly magnified. In front of the scale, swings the north- Peking point of the needle, which is bent upwards, so that it can Isily be read with precision in the mine. This compass can Isily be adapted to any form of theodolite, as it is not necessary k read it from above, but by looking through it in the same way I a telescope.

With this compass, only one end of the needle is seen. To bviate this disadvantage, Mr. Hildebrand ♦ has devised a new irro of tubular compass (Fig. 65). In this, both ends oi th

P Fig. 76.

$edle are seen at once, magnified ten times, the graduation also tpearing magnified to the same degree. The compass can easily read to a singli minute in the mine, the light of a candle at a stance of a yard being suflicieat. The tube is rectangular, and . it a magnetic-needle, 4*32 inches long, swings on a steel point, lose by the south end of the needle is a glass micrometer, and I front of that is a micrometer eye-piece magnifying ton times.

Ethe south end and the centre of the needle is a small object- glass. By means of the eye-piece, the glass *)din. Proc. lii>t. C.E., vol. xxxvi., I8B, p. 459,

Minb-Surveying,

micrometer and the eoiitb end of the needle a.re seen maffnified tea times, the magnified inverted optical image of the aorta end, formed bj the ol>je(3t-glass, being also viaible. In other words, by means of the eje-piece both the north and Bouth ends of the needle are seen passing before the glass micrometer. The latter IB divided into tenths of a millimetre, one division as seen through the eye-piece consequently appearing equal to one milli- metre. The middle line of the Bcaie, the zero line, is lengthened in both directions. When the needle is projterly adjusted, th (Images of the south end and of the inverted north and will appear on that line. But if the needle gets out of adjustment, its centre and its north and south points are no longer ia the same plane, and the two ends will not coincide with the zero iiae. The com- pass must then be so placed that the two ends of the needle appear at the same distance from the zero line. The north emi of the compass case is protected from dust by a glass-plate, ia front of which is hinged a plate of ground glass, by meanof which the artificial illuntiaatioa is assisted.

As the magnetic meridian is continually changing, it ii advisable that the observations at the surface and undergroimd should bo made as nearly as practicable at the same time The best results are obtained when the bearings at the sur&oe ua observed before and after those of the underground-Unee.

If a considerable interval elapses between the observationSi the magnitude of the changes in the magnetic meridian muil be observed, and the error thus arising eliminated by calculatioa A knowledge of the absolute declination of the needle k not indispensable. The most important jjoint is to determine the diurnal variation. This can only be done with sufficient accuracy by means of a magnet suspended by a long thin fibre, provided with a contrivance lur observing the vibrations by means of a telescope. Magnetic-needles supported on pivots, as in the miner's dial, do not admit of sutficient accuracy.

Two contrivances are used for observing the vibi'ations of ths magnetic- needle — (I.) Attttched to a cylindrical magnet, sus- pended by a silk fibre, at the north end is a glass plate with a soiali photographic scale, and at the south end is a small achromatic leua. The centre of the glass -pi ate is in the principal f( the lens, so that the line joining the middle division of the is nearly parallel to the axis of the magnet. The scale is viewed through the lens by means of a fixed telescope. The motion o( the magnet can thus be followed by observing the apparent motion of the scale across the cross-wires of the telescope.

(2.) Another arrangement is to rigidly attach a mirror to the magnet, so that the perpendicular to its surface is nearly

Underground- An'D S0Bface-Subvsy9,

Sss

parallel to the magaetic axis. In this mirror, the image of a fixed bomontal scale is observed by means of a fixed telescope, and the angular motion of the magnet deduced &om the motion of the scale divisions over the cross-wires of the telescope. This is called the mirror-method, and was first employed by 0. F, Gauss in the magnetometer constructed by him in 1830. The magnetic observatory belonging to the Olausthal mines in the Harz is arranged in accordance with this method. A Gauss magnetometer is undoubtedly the beat means of observing the variation of the declination. The cost, however, puts it out of the reach of most mine-surveyors.

A small magnetometer may easily be constructed of ordinary surveying instruments. With a second theodolite or a levelling instrument, the readings can be effected, and a scale can be easily prepared. There is then only necessary a magnet with a mirror. It is not absolutely necessary that the mirror shall be perpendicalar to the axis of the magnet It may be attached at any point of the magnet, suited to the station at which the telescope is placed.

A portable magnetometer, on the coUimation principle, in- vented by Professor Borchers, has been used with great success in the German mines. It consists of a magnet suspended by a silk fibre, provided with a lens and licale, and enclosed in a glass case. It ifi attached by a brass ami to the tripod head of the theodolite.

The use of a somewhat similar instrument has been advocated by Mr. R. S. Newall.* In this, however, the needle is mounted on a pivot instead of being suspended by a silk fibre. Attached to the centre of the needle at right angles to its axis is a small mirror, whUst a minutely graduated seals, consisting of a short length, about 4 inches, of a cirile 3 feet in diameter, is fixed at the eye- end of a theodolite telescope, and so adjusted that the degrees are reflected back to the eye by the mirror fixed on the needle. In this way, the scale is magnified twice, and may be easily read to a small fraction of a degree. The arm carrying the telescope is attached to a circle graduated into 360*, and provided with sights, so that bearings may be taken in the same way as with the ordinary niiner'a-dial.

In the declinometer invented by Mr. A. Fennel a long quartz fibre is suspended in a vertical tube, at tho lower end of which a horizontal magnet, consisting of a hollow steel cylinder, is hung. In this tube, which acts as the comgiass needle, a small mirror ia placed transversely. The instrument ia attached to the theodo- lite BO M to stand directly before the object end of the telescope. To the latter a short tube ia attached, containing a half-lena, an rcoiw. ivr. Engl. Imil. M,B., vol XX., 1871, p. 108.

Ss8

UINK-SVBVBVISa.

iuolmed mirror, aad a glasB scale. Through ui opeumg in tbi upper part of the tube a ray of light itnpingeB upon the mirror, and is reflected forward through the scale into the bodj of t!i declinometer, where it is further reflected by the mirror in tbe magnet. It then passes back through the balf-lena and througti the object glass.

In order to Irsaen the influence of torsion of the quartt fibre on the position of the magnet, it ia noceHsary to make the magnet light, to magnetise it to sataration, und to hang it hj as thin a fibre as possible. Ae it is found tliat mirrors of 4 millimetrei diameter give good images of the objective scale, it is possible to give the tubular magnets an internal diameter of only 5 milli- metres, BO that with a length of 36 millimetres the total weight of the magnet, inclusive of the tubular holder wit)) lioofc and mirror, doea act exceed 46 gnins. The magnets are made of tungsten steel, and are magnetised bj a high-tension mrreiit The diameter of the on art* fibre capable of safely supporting magnet of this kind is less than Q'0004 inch, and a turning of the fibre through causes a deviation of the magnet of leu than 1 seoond.

MBASORtRG DISTANCES BT TBLESCOPB.

Fig. 78.

CHAPTER XV. Mbabdrino Dibtanoks Br Telescopb.

Theot; of Telescopic MeaBurements. — The indirect measure- jueutt of diataaces by means of the telescope is baaed on the solution of a triangle (Fig. 76). Bappose the instrtunent to be at A. and a graduated staff at B ; chen the length A D will be known, if the angle DAO and the height D are known. Two classes of instruments are em- ployed. In one, the angle D A is constant, and the height of the staff D varies with the distance. In the other, the height Df the stafl' is constant, and the angle DAO variable.

The tic&l instrttment of the latter class is that of Stampfer. IhJs consists of a telescope that may be moved in a vertical direction. Two divisiona on a staff, held at a diatanoe, are lighted sncceasively. These embrace a constant height By Eneans of a micrometer screw it is easy to determine the angle, tLrough which the telescope has moved in passing from one (division to the other. Let a represent this angle, which is equal the number of turns n of the screw multiplied by a constant c Ihe angle being small, it may be assumed that tan a on. The

distance req aired will then be equal to r — - or — , The

constant c is determined by observations along a known distance,

&nd tables are constructed giving the distance for any number of

turns given to the screw.

The same principle is applied in Eckhold's omnimeter,* an instmnient used in revenue snrveys in India and in railway surveys in America.

In American transit-theodolites, a so-catled gradienler screw is frequently attached to the horizontal axis of the telescope. It consists of a tangent screw with a micrometer head, graduated into 50 equal parts. As the screw is turned, the head passes over a small silvered scale, ao graduated that one revolution of the screw corresponds to one space on the scale. Thus, the

number of whole revolutions made by the screw in turning the

VKloftble information regarding tlie ne of this instnjinetst Is E. W, Yottog, Mm, Prot, /tut, O.M., vol. civii,, lS9i, p. 2aft,

h

228 M1Ne-S0Rvevisg.

telescope through a -Pertieal arc lau be ascertained from lh' scale. When undamped, the teleEcope may be revolvil ; l>ui when clamped, it can only be moved b; the gradienter acre*, which thus takes the place of the ordinary vertical tangtnt screw. The micrometer head is ao gradaated that one revolution causes the horizontal cross-line of the telescope to move over space of half a foot at a distance of 100 feet. The mi head being divided into 50 parte, each diviaion is e, to one-hnndredth of a foot in 100 feet. It is evident that, wiiii this screw, slopes can be established with great rapidity.

It is also usejiil for obtaining approximate distaaeea, itaoe ff any horizontal distance, the space on an ordinary levelling-flteff u- pressed in hundredths of feet, included in two revdattmiaortb* Bcrew, will be the number of feet the staff is distant from instrument. , if the difference between two readiojt of ti staff is 2 '854 feet when the telescope is moved vertically thmjli two revolutions of the screw, the staff is distant 285 '4 feet.

On sloping ground, the staff is still held vertical, and lh distance read is too great. If a is the angle of elevation, th* true horizontal distance may be foond by multiplying the qnoi on the vertical staff included in two revolutions of the gmdiRotcr

Borew by —r cos ' a — sin 3 a, in which A is the height abotv

a horizontal line subtended by one revolution of the grsdiwi'M screw at a distance d, and n is the number of revolation> in any given case. The gradienter screw is usually so cut ftnJ placed that when d 100, n 2, and A — f , the &ctor Uico becomes

100 cos tt - I sin 3

With the object of reducing the computation to a plication, Mnasrs. C, L. Berger & Sons, of Boston, with their transits a table of factors calculated for vertical aogia ofO* to IB'.

Inatrumenis in which the an<;]e is constant, and the beijhtl of the staff variuble, are mnri importitnt and man noueroos-l The originl instrument of this class is the ttsdia, invent'd Jaims Watt in 1771, and independently by W- i"— '-'- in 1778. An early furm of the instrument uned ti with the stadia or staff consisted of a tuhe prnvidru wild inr Mralll wirt-s. In Fig. 76. let H, £, and F repreitent these wirc* O being the axial wire, and E and F the and wires ; then Itfoostant angle a will be determined by the height G F, or i, acl Ithe distance A Q, or r, from the eye-piaea to tha wlraa. If A U,

MEAaUUlKG OI8TAK0GA BT TELKSOOPE,

distance to he tneasured, is represented hy d, And if B repre- :8 the height of the stRft' D 0, intercepted by the wires G and

equation obtained is d -rg.

I Btsdia IB no longer employed in this primitiTe form. In however, ft siniilar instrument is occasionally used in prelling for railway sections. In this the tuUe is replaced by & MT of Btghtvanes, one of which has two parallel wires 003 lfetre apart, stretched across the aperture. The distance from

Fthat, in order to measure distances in metres with this inatru-

Boent, it is merely neceasatj to use a staff divided into dpci metres.

As a rule, the distances to be measured are so great that a

(eiescope has to be employed ,' in which case the formula is

sight to the othor being 0'3 metre, the ratio -: is equal to 10,

with the stadia tube ; r, however, is not constant, but

varies according to the proportion - + 3 /being the focal

T €i J

length of the objective lens.

Ill the telescopes used in sarveying, / is equal to 12 to 15 iacfaee, and r varies as much as 0'24 inch for distances of 20 to 700 yards. Thus, for distances of 100 yards, the variation of r in proportion to the focal length is very slight. It must, how- ever, Ihi taken into account, because r is used as a multiplier. Various methods are employed for remedying the variability of The telescope may be employed like the old stadia tube ; the GT being gradaated for a single distance, and no corrections plied wlien the distance is greater or less than this. This Ihod can he used only when great accuracy is not required. ~irly in this century, Eeichenhach, a Bavarian engineer, pro- a method that is still in frequent use. He eliminated r in

.111 r , . /

the equations - + j -j- and obtaining d t a + /. The

▼aloe it is seea, is composed of two terms, one being propor- tioiuU to and the other being the focal length/. The distance neasarpd from a point as far in front of the object-glass as the focal length of that lens, is thus proportional to Then, if the distance is to be reckoned from the centre of the instrument, a constant, c, the distance from the centre of the instrument to the obJMit-gUss, must lie added. Iliis may be made by the instnunent- Buiker equal to O'd/. The formula is then

230 MINE-SDRTKTIim.

All distances will thus be reckoneil from the centre of the instro- meut, if the sum of the focal length and the dfstajice from tlio object-gla,a8 to the centre of the axis of the telescope is added to the reading at every sight. For example, if the object-gljigs hu a focal length of 6 inches, and the micrometer wires are 6 inches fVom the object-glass, 1 foot is the constant to be added to each reading.

A stalf maj be graduated to read the distance direct. It is, hov- evur, useful only for measuring distances, and not for levelling at the same time. It is preferable to use an ordinary leTelUng-gtaff

and a telescope, in which the instrument-mier has selected for-, some multiple of 100. Suppose, for example, that —. — 100. The

distance from the centre of the instrument would then belOOi -f tbe constant. The calculation of distances is thus grestlj facilitated.

When the line of sight is mcUned towards the staff, the space intercepted is increased in the ratio of 1 to the cosine of the angle with the horizon. Thus, the space for the staff perpendicokr to the horizon becomes for the staff when vertical, and, by approxi- mation, s' s cos u. The inclined distance is then equal to 100 1 cos (L + + e), and the horizontal distance is equal to 100 oi>s' a + (/+ c) COB a. But since ( / + c) is, at most, equal to 2 feet, and the angle a is so very small, c may be taken as equal to iti horizontal projection. The horizontal distance will then be eqotl to 100 cos* a + + c).

In Germany it is usual to bold the staff* perpendicular to the line of sight. The inclined distance is then e<}ual to 100 + (/ -t- c), and its horizontal projection is equsd to 100 1 + (/ + e)] ooi or, approximately, 100 cos a + (/ + c).

The most effectual method of remedying the variability of r ia that pi'oposed by Porro, a Piedmontose officer, afterwards proftisaor at Alilan, who in 1833 modiGed the construction of the scope in such a way as to remove all neoessitr for addiog constants. He introduced between the object-glass and eye- piece a third lens. The function of this "auallatic" or un- changeable lens is to mtike the size of an object, that forms an image of fixed dimensions, proportional to the tiistance of the object from the axis of the theodolite, instead of to its distance from the anterior focus of the object-glasa as in the case in an ordinary telescope. By this means the intercept of a pair of fixed wires in the diaphragm on a graduated staff ia d>--"- uroportionaV to the diBtance. ot tb* taff from the af eodoUte. In otAet TNoxi-*, va. ooustieaGib

MKASDRIMG OISTAirOES BT TELESCOPE,

the interpoaition of tlie anallatic lens,* the rays coming from the

end- wires to the staff, form aa angle a with ita vertex at O, the

centre of the telescope. The angle

is termod the dioatiniometric

angle, and O the anallatic point.

The angle varies with the distance

of the anailatic lens from the object-

8. If this distance increaaea, u

decreases, and conversely, whilst

the distance remains constant, is

invariable. It can easily be seen

that the distance iroio O, the centre

of the telescope, can be deduced

from the length A B interctpted by the wires. In fact the sidei

of the diastimometric angle form with the staflf virtual triangles,

P A B, O A' B'. These triangles being similar give —

Fig. 77.

Op

OP' yB'

It is thus merely necessary to determine a simple constant, the diastimometric ratio, and then to move the anallatic lens until M coreaponds to it. Aa a rule, k is taken as y, in which case is equal to 0-32 centesimal degree. It follows that at 200 yards, for example, the length of staff intercepted should be 1 yard. The diastimometric ratio is represented by the expression 2 tau

The distance is then s

2 tan t.

The original instruments, tacheometers, made by Forro wera very favourably reported on by a French Government Oom- mission. Their extremely delicate nature, however, prevented them from coming into general use.

In 186, M. Moinot gave the tacheometer a form resembling that of the larger modem theodolites. His instrument is based on the same principle as that of Forro, but is much less delicate and less expensive, while giving results of great accuracy. Like Porro's original instrument, Moinot's tacheometer permits dis- tances to be measured at the same time as angles and differences in level. Ita use has led to a new method of surveying for railway purposes, termed tacheometry, which is quite as accurate as the older method of longitudinal- and cross-sections. By the advantages it presents of greater rapidity, and the small number of assistants required, this method hus undoubtedly contributed

The theory of th analUtio lena is ex pounded by A. E, Young, Mi. Proe. iMt. O.S., vol. oxiii'i., 1900, p. 338.

I Pm

to the derelopinent of railways, notably in moantiiinous districte. The aim of tacbeometry is to survey and level simultaneottBly a tract of ground with the greatest possible accuracy in the least 'jiogsible time. In mountainous districts, it is a method of the greatest value, since it dispenses with the chain and spirit level, and thus the laborious, slow, and expensive processes of chaining over bad ground and of levelling up and down bill, are avoided. By means of a single observation, the distanoe, azimuth and height arc determined of every point visible and aocesaible from a given station point. In this way, surveys are made in one- third to one-fifth of the time that is required for the older methods. Biace its Erst application by Moinot in 1856, on the line from Nice to Genoa, it has been employed in most of the continental countries, excepting perhaps North Oermaay. There Beicheabach's method is still used ; instruments being constrncted under the name of tocheometers, more or less similar to Moinot'i tacheometer, but without the anallatic telescope.

The tacheometer is so constructed that 2 tan is equal to

The distance being equal to 200 t may be read direct from the staff, if the latter is graduated in half-centimetres. Thus, if tbe lower wire coincides with the division marked 100, and the upper one with the division 110, the height* will be equal to 110 - 100 10 half centimetres, and the distance will be 10 metres.

In order to reduce the measured distance to the horizontal, the work is always carried on with the staS' held vertical, and the angle of inclination of the optic axis is determined.

Calculations. — For calculating the results of a tacheometer- urvey, the slide-rule may advantageously be used. The rule contains scales of numbers, sines, and taints. To these Moinot has added a scale giving the values of sin-, the origin of which is so placed that a single setting of the slide gives simul' taaeously the horizontal distance (s sin <p), and the difierence of leveL By means of these scales, the co-ordinates of points observed from a single station with the tacheometer are rapidly computed, without any direct measurements being made.

The Protractor designed by Moinot for plotting tacbeometer- urveys differs from the ordinary protractor, in that it gives at the same time the direction and the distance of the point to lie determined on the plan, It is a semicircular protractor, of transparent horn, or of thick paper, provided with a needle- pointed pivot at its centre. Its straight-edge is gradu&ted so that distances can be measured off each way from tho centra.

M

Ueasdriko Distances Bt Telescope, 233

Dgles re obtained from the graduated semicircle, reading front marked on the plan.

The Tacheometer is nothing moro than a theodolite with a concentric distanco-inesauting telescope. It differs from the theodolite in being furnished with an anallatic lens, and usually in being graduated according to the centesimal method, the circle being divided into 400 parts or degrees, Though not indispensable for a tacheometer, this division ia very convenient. The angles are read more rapidly, on account of the simplicity of the division into tens and hundreds, and since they are read from two verniers, one at each end of a diameter of the circle, errors are at once evident, the readings difTaring by 200°, Lastly, with the centesimal division, the slide-rule computations are greatly Eocilitated. Tables of logarithms for the centesimal method have been prepared by Callet, fionla, Plausolles, Lalaad, and others, and have been in use for many years. The best forma of tacheometer are those made by Messrs. Trough ton & Simms, Mr. W, F, Stauley, and Mr. L. Casella.

The Staves used in tacheometry are always graduated with suiScient distinctness to be read by the observers. Forro's stalf is triangular in section, and has three graduations with different subdivisions according to requirementa For short distances, the divisions are extremely fine ; for greater distances only whole metres are marked in bold figures. Moinot's staff ia graduated in such a way that it can be used for short or for long distances.

The staff should not exceed 12 to 16 feet in length, and should be made of light wood. During the observation it must be held perfectly verticaL It should therefore be provided with a plumb-line, or, better, with a round spirit-level, aud a pair of light sliding legs attached to the back of the staff.

The Field -Work. — Tacheometric-surveys ate usually conducted by a party of three, (1) the engineer to direct the work ; (2) the observer at the instrument ; and (3) the recorder to bonk the

suits. On level ground two staff-holders are employed, and

irregular ground one or two more are necessary, in order to prevent loss of time to the observer. For Jess important surveys one observer and one staff-ljulder suffice.

When the instrument has been set up at a suitable point, staff-holders are sent to all the points to be surveyed. To each point a number is assigned, and noted in the field-book, and on a sketch made at the same time. The tele' cope is directed towards the staff, and the micrometer wires are read and noted Kl the proper column of the field-book. The horizontal and

attSE-SUBTSTIHa.

vertical angles are then read and noted. This opRratioo b repeated for all the points that can be seen from thia sttioa

In this way, for every point three figures are obtAtned — tlB distance, and the horkontal and vertical angles. Tlie point thas fixed by means of polar co-ordinatea

If the survey has to be connected with one previously Dud< Bome data from the former work are necessary in order to inak the connection. Two points, if accurately determined, sufficient.

The instrument having been set np and levelled, the engiiiB* makea a reconnaissance of the ground to be surveyed, axxd inatructtons to the staff'holder, who goes successirely to points selected by the engineer, and at eacit one holds the BteodUy vertical until he receives a signal to pass on. observer at the instrument now makes the neceas&ry ohaerralioi which are noted in the field-book by the recorder.

When the ground to be surveyed is so extensive that stations are necessary, the engineer sck-ct-i two points via'm' from both stations. When the observation at the firat statSoo is finished, the instrument is moved to the second, and Um fcnro points are observed. The connection could, of coarse, be m by means of one point only. It is, however, lulvi.sable to etnp>Ji two as a check on the accuracy of the work. When a nuBxfj of stations are required the method is similar. Th described is that used by Porro.

Moinot employs the tocbeonieter in preliminary surveys fori railway lines in the following manner: — Before the belt o' ground is surveyed, nn extensive reconnaissance is undertakcis- and the main direction of the railway determined, so that th survey may be limited to a comparatively narrow strip account of the rapidity of the method there is no occasion to too anxious about limiting the width. A strip should always selected of sutficient width to allow if necessary a lateral placement of the lino. A width of 400 yards is quite sn Marks are fixed 200 to 300 yardn apart, and nambera assigned to them. For filling in detAils, pointji nrn wherever th ground presents any derirteii ch.i: L Thu

instrument is set up at a point so se!f.i-ecl thui tion can

be made with any existing survey or niiiway. i'hii aHiatant then gives a signal with a whistle or horn to announce that Iw is ready. In the meantime the recorder has lucoHured and noted the height of the instrument, and the .i,..;r> r J„,m ,..,1. Kkrboh roughly to the scaie of the plan t all tlie roads, rivrs, boundarifs, linldM, m,, nv,..j,, inatrumtiut. As soon as hr> hnars the signal, the enginwir

araiHH

!

KASURIIia DIBTAIiCES BT TELESCOPE.

lictes to each staff-holder his place, care bmg taken tliat only one staff ia ready at a time. The other staff-holder is still ou the road, or, if already at his post, he tuma the narrow side of the staff towards the Instrument, and remains in this position until it is signalled to him that the preceding reading is finished. He then turns the graduation of the staff towards the instru- ment, and hy mesna of a signal directs attention to his position. He then awaits the signal that he can pass on.

The assistant at the instrument has to read the upper and the lower wires with each staff, and then the vertical and horizontal angles, and to call them out in this order to the recorder, who notes them in the field-book. The recorder enters the points ia Older, as 1, 2, 3, ia At every fifth or tenth point the assistant gives a double signal, whereby the engineer, although at a distance from the instrument, has a check on the occuiscy of the booking, seeing that he has entered the points in bis sketch in the same order.

In order to economise time, the engineer selects the points in uch a way that he comes finally in proximity to the point hs regarded as being most suitable for the next station. Here he places a mark and sets up a staff, at the same time giving a special signal to the assistant.

When the readings for this next station are finished, the observations at the 6rst station are complete, and the instrument is carried on. In the meantime, the man who was holding the Btaff at the new station returns to the preceding one just left by tilie instrument. The recorder begins a new station in the field- book, and at once enters the height of the instrument in its proper column. A back-observation is now taken, and the distance, height, and azimuth should coincide with tho results previously obtained.

fiy the aid of this method, Moinot has surveyed about 1,000 miles for railway purposes. The distances, when measured on the ground with extreme care, have never differed from those shown on the plan by more than one per thousand, and the longitudinal section obtained by accurate spirit-levelling has never presented any appreciable difference when compared with the results afforded by the heights given on the plan.

The Topographical Stadia differs from the tacheometer in that the micrometer is not appHud to the telescope of a theodolite, but to the alidade of a plane-table. The points are observed from one station, the distances from this being reduced to the horizontal, and the heights calculated on the spot by means of a special glide-mle. The data thus obtained are at once plotted to the scale required on s sheet of paper stretcUed ou iW

h

Uine-Surtbyimo.

the height of each point being accurately noted. When tht height of a sufficient number of points is determined, contour lines are traced with the ground in view. In &ct, ihe grooiul ii practically sketched from natura

On the United States Ooaat and Geodetic Survey, the plane- table has been exclusively used for making toftographical sumya; the stadia, or ttlemeter as it is called on that service, being used in connection with it. The stadia is graduated experimentally for the particular instrument, and for the eye of the observer who has it in use. It is simply a scale of equal parts painted upoat wooden staflf, about 10 feet long, 5 inches wide, and 1 inch thiok, so graduated that the number of divisions, as seen between the horizontal wires of the telescope, is equal to the number of meba in the distance between the observer's eye and the staff held perpendicular to the line of sight

American experience tends to show that the plane-table ii adapted to open country and long distances, where no contour lines are to be determined, and where the stations are compan- tively few, as well as where a multiplicity of detail is required. Against the advantage of plotting the work in the field may placed the disadvantages of having no record but the fieldheet, which is liable to be spoiled in a storm.

The Theodolite and Stadia. — The method of surveying with the plane-table and stadia is being superseded in America by the asa of the transit-theDdolite and stadia, a method introduced in 1364, when it was officially adopted on the United States Lake Survey. All that can be done with the plane-table may also be done witli the transit-theodolite. The plane-table can be used only for topo- graphical work, and requires special practice, whilst the theodo- lite for the stadia survey can be adopted in all cases where a theodolite is required, and but little special training is required in order to use it with the stadia.

The best instrument to employ is a theodolite reading to 30*. The micrometer wires should be tixed ; when adjustablei, they are not sufficiently stable to be trustworthy. The stadia is usually a staff, 1 inch thick, 5 inches wide, and 14 feet long. In order to graduate the staff, it is necessary to know what space on it cor* responds to 100 feet (or yards, or metres) in distance. To deter- mine this, it is best to measure off e + f in front of the plurab- line, and set a point. From this point, accurately measure a base-line of (say) 200 yards, on level ground, and hold the blank staff at the end of this line. Have a fixed mark on the upper portion of the staff, and .set the upper wire on this, Theo let an assistant at the staff record the position of the lower wire, as he is directed by the observer &t the mstTiunent. Repeat tha

HKAaURtKa DISTANCES BY TELESOOPB. 237

>tion until the mean gives a satisfactory result. If tfae base was 200 yards long, diwde the apace intercepted by the two wires into two equal parts, then each of these parts Lato ten smaller parts, and finally each imall space into tive equal parts. Each of these last divisions will represent 2 yards. Diagrams are then to be constructed on this scale, in such a way that the number of symbols can be readily estimated at the greatest distance at which the staff is to be lield. If, when tested by re-niestsuring the base-line, the wire interval is found to have changed, the staff mast be re-gradaated, or a correction must he made to all the readings.

If the wires are adjustable, any unit scale may be selected, and the wires adjusted to this. By this method, distances may lie obtained from le veiling-staves, where it is desirable that eaeli foot on the staff should correspond to 100 feet in distance.

In making a survey for the purpose of preparing a contoured plan, a series of points should be determined with reference to each other, both in geographical position and in elevation. These points should not be more than 3 miles apart. The points of elevation, or bench-marks, need not be identical with the points fijced in geographica,l position. The latter are best determined tnangulation.

A system of triangulation points being established, the anglea observed and the stations plotted on the plan. For small the plottiJig is best done by means of rectangular co- ordinates. The survey may, however, be plotted directly from the polar co-ordinats (azimuth and distance). For this purpose the plan should have printed upon it a protractor circle, 12 inches in diameter, by means of which the lines can be plotted accurately to 5'.

A line of levels is next run, bench-marks being left at con- venient points. The topographical survey is then made, and referred to this systeni of triangulation points and bench-marks. The surveying party should consist of the observer, a recorder, three staff-holders, and, if necessary, two axe-men.

The record in the field-book consists of (1) a description of the point ; the reading of the vernier ; (3) the distance ; (4) the vertical angle. Two columns are left for reduction ; (5) the difference of height corresponding to the given vertical angle and distance ; (6) the true height of each point above the datum- line. The right-hand page of the field-book is reserved for nketching.

The only calculations necessary are to find the height of all the points taken, with reference to the datum-line, and sometimes to correct the distance read on the staff for inclined sights. These-

fijced

S38

UINE-SQRVEriKO,

calculations may be performed by means of tables computed Mr. A. Winslow, of the State Geological Survey of PennsylTania, or by means of a diagram prepared by Profesaor J. B. Johnson, of Washington University.

The beat available infonnation as to the accuracy ol thii method of surveying is given in the report of the United Statti Lake Survey for 1875. The entire stadia work of that year wu co-ordinated, and compared with the coiresponding distanm obtained by triangulation. In this way 141 lines, on an average IJ miles in length, were tested, the average error being 1 in G50, The length of site between the stations averaged 800 to 1,000 feet. The limit of error allowable in closing on a triangulation was 1 in 300. The reailinga were taken to the nearest metre; the staves were graduated for a single distance ; and no oorreo- tions were applied when the distance read was greater or leas than this. Had more care been exercised in the work, the readings limited to 1,000 feet, and all corrections applied, it would have been easy to bring the error within 1 in 1,200.

This method was used by Mr. W. B. Dawson in 1882 for the preparation of a map of the gold-field on the Atlantic Coast of Nova Scotia, on a scale of 2 inches to the mile. The traverse lines ran along the roads and principal streams, forming a net- work of quadrilaterals, and were plotted by co-ordinates. The instruments used in the survey were a Sopwith levelling-staff, and a 6-inch transit- theodolite with a 4-inch compass-ueeJle. The telescope was fitted with three horizontal spider lines, unequally spaced, the larger interval corresponding to 100 feet of distance for each foot intercepted by the staff. The suiallerono was only used for longer sight, and when the view was obstructed. In five months of field work an area of 180 square miles wai surveyed, including nearly one hundred lakes from 7 miles long, downwards, all the work being done by Mr. Dawson with one assistant, and one or two men according to circumstances. Wet days were devoted to the reduction of the observations. The total cost of the survey was 1675 dollars per square mita

Atmospheric refraction presents difficulties. Mr. Cooke shows that the atmospheric refraction of the lower line of tight, which traverses air strata close to the ground, is much greater than that of the upper sight, and the eflVct is variable. With the staff placed horizontally the refraction is equal (or the two readings. The best results can be obtained in the early mornings and the evenings when the atmosphere is compara- tively still.

Telescope Measnrements In Mine-Surveys. — In mine-surveys very accurate readings may be obtained on account of tiiS

MR.iSURITFG DISTANCES DV TELESCOPB.

of tLe air. in this way

Fron Goch tuine, North WaloB, was rvfiyed in this way by an Itnlian engineer. A transit- eodolite magnifying ten times, with adjustable micrometer rea, was uged in 1S65 with great succeaa by Mr. B, S. Lyman

surveying in an American colliery. It saved much dig* reeable groping in the mud to count tlio links of a chain, and 'els were taken at the same time. The wires were placed so

apart that I foot of space intercepted on the staff indicated distance of 100 feet. The figuree on the staff were painted tb red ink upon thin paper that had been fastened to strips common window glass by transparent varniah. Then over b paper another coat of varuiah was poured, and upon this placed another strip of glass. The glasses, with the paper tween them, were then put into a narrow wooden, frame, licb formed one side of a long box. This had neither top nor ttom, and its aides were so hinged together that they folded er upon each other when not in use. The back of the box d holes tti rough it to supply air to the lighia, and either Tetj-lomps or candles were lixed to the wood of the back, le box was made 5 feet in length ; but for low mines one ght be made much shorter. This staff lighted inside makes esoopic measuring and levelling easy underground, where aining is particularly disagreeable.

To remedy the difficulty of getting suiEcient light to read the lioary Htoif, Professor Johnson proposes to use two strips, one- arter of an inch wide, one of which is fastened with its top en with the zero of the stadia scale, whilst the other is moved suit the position of the other wire. The reading of the top go of the upper atrip then gives the distance, which is read ofT tbe ataff-holder.

Tacheometry is specially adapted for geological -surveys, which ve frequently to be made in mountainous districts where aining is laborious and inaccurate, and where levelling np and wn the sides of the mountains is not practicable.* The Gradient- Telemeter Mining DiaiThe principles of tacheo- >try have been successfully applied to underground-surveys in

' For farther infcmialion on this method of surveying, the student ia eiTd to B. JohnEsOns Topogro/phicdl iurveyijuj by mtan of th& antit and Stadia, New York, 1885 ; and to B. H. Brough's paper, JUin. oc, Itut. C.E., vol. loi., 1888, p. 2S2, in which b bibliography o( tho jject is given. See also pspcra by N. Kennedy, Min. Proc. Ijul. C. &'., L xcii., 1890. p. 308 ; by W. Airy, ibid., vol. ef.. 1890. 222; by B. K ddleton, ifeirf., vol. oxvi., 18W, p. 311 ; by W. Poole. 6ifi.,vol. oxxxi%., p. 269; by H. G. Dempster, ibid., p, 273 i by H. P. Seale, Tram. Mralasian InM. M.E., vol. vi,, 1900, p. 62; and by A. H. Webb, with cussion by L. H. Cooke, Trans. Inat, Afin. Met., Jan. 18, 1906.

f40

Minb-Surveyiso.

the mining dial invented bj Mr. S. Short and uianufactureil Mr. L. Caselln of London (Fig, 77a). Like the gradient-telemeter level, of which it is a modiiication, the dial ia furnished with horizontal limb on which ar marked the gradients of 1 in to 1 in 24. The gradient marks are such u distance apart they can be easily read at the index without tlie aid of a readiog microBcope, no vernier being necessary. This, together with the fact that the observation that gives the gradient also giv - the distance of the observer's station from the object, eaabit accurate levelling to be done with remarkable rapidity. A hori-

uontal circle is also provided for fixed-needle dialling. This read by a vernier to five minutes. Distances are meagnred or set out by simply reading a levelling staff or a suspended tape placed at the distant positiou. The instrament has a telescope 11 inches in length with an extra large object-glass 1-7 inch in diameter. It is adapted for surface work as well as for mine- anrveye, and can be used as a higb-class dumpy-level. M

For ascertaining the gradient between two stations, the inatra*f ment is set up at the first and levelled with the gradient limb Wsmned At lero. The Vieigbt ot tiTaB cmAtsi c1 Vfiww3Mss.

A

J

Mbasdrikq Distances By Teleboopg.

Sil

the ground is then read from a, ta])e hanging from the base-plate of the instrament. A levelliag staff is then held upright at the second etatiau. the teleacope directed to it, and the reading taken. If the reading on the staST is the aame as that on the tape below tho instrument, the two stations are at the aame level. If, however, the reading differs, the clamp screw fixing the two axei of the instrument is loosened, and, with the tele- Mpe held lightly in one hand, the graduated horizontal limb is moved with the other hand (by means of radial bars or ribs on its under surface) until the cross wire of the telescope exactly cuts OQ the staff the same height as that given by the suspended tape. Dnring this operation, the index attached to the telescope will have moved on the graduated limb of the instrument, and, on the reading of the index being noted, the gradient between the two stations will be given without any calculation whatever. A screw attached to the clamp, gives a fine adjustment and permits a very accurate reading of the staff.

For meanring the distance between two stations, the iuatru- ment is set up and levelled with the index clamped at zero. An ordinary 14-foot staff divided in hundredths of a foot is then sighted at the second station. Suppose the reading to be 10'66. Then unloosen the clamp, and move the telescope until the index reads exactly 100 on the graduated limb, and fix it there by the clamp. Then move the telescope round on the outer axis of the instrument, and again read the staff. Suppose the second reading to be 6-42, The difference between the two readings is 4'20, and the distance between the two stations is 426 feet. In other words, eliminate the decimal point from the diff*'rence of the two readings, and the figures as they stand give the distance in feet without any calculation whatever.

An extension of the method ie to use other gradients, thus—

Gradient 50 and divide the difference by 2,

m

S.

h

Provided the staff is divided decimally, the metre or any other scale may he used.

For fixed-needle dialling, the instrument is used in the usual manner. It is provided with a 4f-inch aluminium compass-ring read by a prism. It has a locking plate and three levelling screws, and the telescope cap is graduated for elopes of side sections. The tripod stand is jointed at ahotl WlXv wi lOMjr be used in a 2- foot aeam. Yb

Mine-Sdrvktiho.

The Dnnbar-Scott Mine Tacbeometer, — Mr. Dunbar D. Scott bas Buccetafullj applied hie idea of an introhangeable uid

Fig. 77b, — D unbar- Hoott Mine Taoheometer.

adjuBtble auxiliary telescope to the mine tacheometer. The iastrutnent is arranged to prtoT:m Vt twat i\&ca.Ui coblem*

M£as[;kinq distancbb bt telescope. 343

to be enoouatered in ahaft-surveyiiig without the oorrection for eccentricity neoesaary with the earlier typea of top or aide ftuxilikry teleacope. This ia effected bj extending the horizontal itxia sufficiently far beyond the beariogs &a to terminate in a. threfkded hub. Open vertical pillars are caat in one piece with the hub of the main telescxjpe of exactly the same length as the horizontal axis thua extended. The auxiliary telescope has a peculiarly coniitructed hub which may be apj>lied to the threaded extension of either the horizontal axis or of the vertical [lillare, and rapidly ranged into the same visual plane with the main telescope, Tacheometers on this system are made by W. F. Stanley & Co., London, and by the American firms of Buff &. Bufl' and F. E. Brandis & Sons, The instrument made by Wittstockj of Berlin, is of a more sturdy type. The (iimensions of the instrument shown in Fig. 77d are as follows : — Iforizontal circle, 5 inches j vertical circle, 4J inches; main teleacope, 20 to 35 diameters power and 8 inches long ; weight of instrument complete, lbs., and extension tripod 6 lbs. additional. The counterpoise, which is always to be attached oyiposite the auxiliary telescope, weighs but a few ounces. It Iwaye remains in the case, with the auxiliary telescope, except "when the special occasion demands their use. In ordinary "work the threaded extensions to the pillars and the extended horizontal axis are protected by small caps. The edge gradu- ation of both circles is noteworthy, and the vernier of the "vertical circle is very conveniently placed.

The Mayer and WieBmann Tacheometer, — For surreying oper- ations in the Simplon tunnel, Messrs. Mayer and Wieamann designed a tacheometer, resembling an ordinary transit-theodolite, but with three additional pieces. On the side of the standards, liding in a slit and to be connected with the telescope by the tightening of a screw, is a vernier which travels backwards and forwards, following the movewients of the telescope, It thus dfscribes the tangent of the vertical angle. The distance between the telescope axis and the vernier pivot being 1, the scale on the alit is made equal to it and subdivided into 100 parts. Readings of the tangent are, therefore, made to three places of decimals. A similar apparatus is attached to the horizontal plate and gives the secants of the horizontal angles. To the horizontal plate is also attached an arc, giving horizontal tangents, for setting out curves. In this way the use of tables is obviated. Drawings of the instniment are given in the Engineer of December 15, 1905, The Hammer-Fennel tacheometer is another improved instru- ment of great accuracy by the aid of which slide rules or tables can be dispensed with.

Trang. Itut, Jlin, £ng., voh xxvii., IW5,

S44

OHAPTEH XVI. Settuic-out.

Bong Lines. — Setting-ont, or the location of prs- determined points, is defined as that branch of geodetie openk tiona which ia the converse of surveying and levelling, the litwr consisting in discovering the position of a series of actually- existing points.

In ranging and setting-out a hase-line for a Burfaoe-snrrej, ranging rods, 5 to 7 feet in length, are used. They are osually circular in section, and painted in lengths of 1 foot or 1 link, black, white, and red alternately. When one colour cannot be clearly seen, one of the other coloured portions can generally be distinguished.

The rods are planted vertically in the ground, the verticalitf being judged by the eye. When great accuracy is required, plumb-bob must be used. Its string is turned over the first and second fingers of the hand, so that when it bangs vertically, the rod may be placed parallel to it. The distance apart of the rods varies from 66 feet to 300 feet.

For ranging straight lines of moderate length, the most con- venient instrument is the transit-theodolite, because the telescope may be turned completely over about its horizontal axis, so uto range one straight line in two opposite directions from onestatioD. The error with this instrument should not exceed 10 seconds in angular direction — that is, about 3 inches in a distonoe of a mile.

For straight lines of very great length, the theodolite is no* sufficiently exswt It Is then advisable to use a transit-instru- ment. In order that a vertical circle may be correctly described by that instrument, it is necessary that the line of coUimatioa hall be precisely at right angles to the horizontal axis about wbicb it revolvea, and that the pivots of that axifl shall be pre*

8Ettimg-0Ut.

iiely level with each other when they rest io the Va on the 'On st&iid.

Plotting the Undergroimd Traverae on the Surface, — If it is ?quired to plot the traverse on the surface of the earth, a process 'hich in former times was in general use for determining the oeition of the boundary of the mine, the first course, from which diDiitbs were measured, must first be laid down in horizontal mxiih and direction, and its ends marked with stakes. The osition of the first station being thus determined, the second t&tioQ may be found by layiag off from the first station, at the roper angle, a horizontal distance equal to the length of the aurse. In the same way, all the successive underground stations lay be marked out on the surface.

This process is tedious, and liable to error, and should conse- uently only be employed when absolutely necessary. Instead f repeating the traverse on the surface, the required distance nd its bearing should be calculated trigonometrically, and marked Ut on the surface.

Betting- Oat Hallway b to Mines. — Railways to mines may easily

tBct-out when the ground presents no great irregularities, the t line for the railway being determined by levelling from the tarting-point to the mine. The line, of which a trial section hows the fewest difficulties of construction, having been selected, t is roughly marked out on the ground by strong pegs. The sntire line is then carefully levelled and an accurate section Irawn. From this the amount of catting and embankment keccssary may be determined. The entire Ime is then set out on he ground.

Two stakes are driven into the ground -with their heads at the ntended formation level, at distances of about SO feet apart, near commencement of a proposed cutting. The excavators are 'hen able to carry on the cutting at the proper rate of inclina- Aon by & process called boninff. This consists in ranging a line, )f uniform inclination, from two points in it with T-shaped jistruments, called boning rods. Boning rods of the same height ire held vertically upon the two stakes driven into the ground, md a third rod is held at some point along the intended slope ; then, if the inclination is correct, the tops of the three rods irill be in line, If the third rod is too low or too high, it must be raised or lowered until it is in line with the tops of the other rods.

Banging Curves. — Eailway curves are of frequent occurrence, md even branch railways to mines, which are usually not of great

, can rarely be made without them. A common method of setting-out a railway curve o(& N&ixtikxxA

tKE-80BV8TnfO.

on the ground is by means of ofisets. 1 n Pig. 78, A and G are the ends of the straight portions of the line to be connected by a curve, being the two pointe at which the corTS filli into the straight lines. Let A 0, £, £ O be the distances which it is desind that the points found in the carve litall be apart. Then measure, upon tht straight line A produced to D, the distance D equal to E, and join D E. This distance D E is called the offset, and gives a point E in the cnrvo. Range a straight line through the points E, uid upon it lay off the distance E F equal to E Q, and join F Q. The point O will be the next point in the curve. Proceed in tiM same way until the whole extent of the curve has been set oat Let r be the radius of the curve, and d the distance A 0, E, or E G, which it is desired that the points found in the curve &hili be apart, then the value of the oS'set is

Fig 78.

De

Oead

2r

If E and E G are two equal chords, the offset ia

A B being a tangent to the curve at A, the value of ths ofit from the tangent is

A

The values of D and E F will be found from the following equatious : —

;,/OEs - DE OD, and

r

For mampU. — Let r 15 chains or 990 feet, aad the distance rf 1 chain or 6G feet, the length of the first oS'set is g

Bktting-Oct.

a 3'2 (et. Tbe dutanoe to be laid off upon the line A O produced to give the place for this offset ia V66* - 2'2*

66 X 65-963

65-963 feet Again the length of tht second offset is

K 4-397 feett and the distance to be laid off upon the chord

produced to give the place for thit offset la " ' aqq — —

66 85 feet A rough method of setting out curves ia to extend a line &om tAngentifil portion of tbe railway and measure an offiet at e end of each chain along the tangent. The successive offsets fractiuns of a chain should be —

at-" 2r' 2r' 2? ' " 2r' here r is the radiua in chains. The length of the farst offset in

chea would be -— or — , in which 792 represents the number

' incbea in a chain.

For txampie. — If the curve has the radiua of 40 chains, the length, in inches, of th offset at the end of the lirst chain is 9-9. The second offset ia 39*6 inches, the third 89-1 inches, and the fourth 1&S'4 inohes.

A more rapid and more accurate method of settingut circular eurvea is by meana of angles at the circumference, a method first doecribed by Rankine in 1843, It is baaed on the theorem

iittclid. III., 20) that the angle subtended by any are of a circle

the centre of the circle is double

Hbe angle subtended by the same arc

aoy point in the circumference of

rcJe. In Fig. 79, A B is an arc of ft circle is a point in its circum- ference lying beyond the arc. The ASle A B is half the angle sub-

by A B at the centre of the

Hltxile. When the point at which the

Kagle is measured lies upon the arc,

Pa at E, it is the angle B E F A E O

' that is equal to half the angle at the centre of the circle. When the point at which the angle is measured is one of the ends of the arc, aa at A, it is the angle A B that is equal to half the angle at the centre of the circle, expressed by a formula, the angle at the circumference in minutes AOB A B half tiif fttiv'tc at the centre

Kg. 79.

UDtS-SUBVEYlNQ.

17I8'-873 y f." radius of circle

in which formulft, the coefficient ia the value in minute* of one half of the arc that is equal to the radius.

The English practice of designatiag curves by their radii b chains has but few advantages, as there are no acreage el- culationa involved. It is preferable to express the radii in hundreds of feet, or chains of 100 feet. This method is no* coming into general uae. The American practice is to desigiuita curves by the number of degrees in the angle subtended at the centre by an arc whose chord is lOU leet in length. Tlma, corrM are named one-degree curves, two-degree curves, <fec., whoa the central angle subtended by 100 feet is one degree, two degrees, it. In this method, which is one of great convenience, coufusioa u created by terming the centre angle " the angle of deflection." The value of this angle in degrees ia 6729 '6 divided by tlx radius in feet.

In setting out curvei by means of angles at the circumference, a 6-inch transit-theodolite is set and adjusted at a tangent point, u A, and directed along the tangent to D. An angle equal to the degree of curvature is deflected from A D towards the sideoa which the curve is to run. Of the two chainmen, the follower boldi his end of the chain at A, and the leader, keeping the chuu stretched, is directed by the observer at the instrument into line with the axis of the telescope. In this way, the positioa of the point E on the curve is fixed. From the line A £, the s&me angle is set off, the instrument remaining at the tangent point The chainmen move forward ; the follower stopping at E, and the leader moving the stretched chain around that point u centre until the other end comes into line with the axis of the telescope. A second point B on the curve ia thus obtained. By continuing the process of setting off angles equal to half the degree of curvature, and causing them to subtend distances of 100 feet each, the entire curve is sot-out. It is necessary that the angle formed by producing the straight portions of the line, should be known, in order to find the place on the ground from which the curve is to . As a rule, this may be taken at once with the theodolite. If an obstacle as intervenes, a point y it J Beleoted on one tangent, from which the distance y z to the other

ngent may he measured. The lengths x y and x x are then found by solving the triangle x ;/ s.

When obstacles prevent all the points from being aet-out from one tangent point, the theodolite roust be moved to the last point sct'out, having the last angle clamped on its upper plata.

8ifrnso-0DT,

original tangent point being sighted with the vernier Dlamped at that angle, by setting it olT a new tangential direction it obtained- By revolving the telescope, the tangent is produced in the other direction, from which tangential angles m&j be Bet- off to fix more points on the curve.

For €xttmple.-~Jt the radius of the circle is 19 chains or 1254 feet, kac! tbe distance required between the points in the curve lOO feet, the tangent angle to be Betoff will Iw

137 07 njinuta - 17' 4'

Tlie method of setting-out carves assumes that the chord of an ii equal to the arc itselt The difference does not, however,

re rise to sensible error.*

Cross- BeCtiOD8, — When each curve has been ranged, stakes,

mded with the distance from the beginning of the line, should

I driven in.

ascertain the amount of excavation or embankment re- to form the railway, cross-sections must be taken at each

un length at right angles to the longitudinal-section. The loj>e at which it is desirable to form a cutting or embank- ment depends on the nature of the ground. The usual slope is 1 foot fall in IJ foot horizontal, or exprested by the ratio of tfop to 1. Mtperience shows that dry sand will stand at an angle of 3&*, dry loose shingie at 39*, and damp earth at 54°.

Oriving Levels Undergroaiid. — In driving levels, it is usually oocessary that a certain inclination shall be maintained. The miner must consequently be provided with suitable applianoea in Older to enable him to fultil the required conditions. The best grAtltenl is I in 120, as with that rise from the shaft the work performed in drawing the full load out is equal to that expended in taking the empty load in.

In tnetal mines, if the level has to be driven horizontal, the eaaieat method is to conduct water into it. A dam is erected joat before the working end, and the level is so driven that the water always maintains the same height This method can,

twever, only be applied when no water is given off from the :k in the level, as with the slightest inUuz of water, the surface disturbed and ceases to be horiEontal. The inclination of the level may be checked by means of a

For acuODnU of the method* of settbg-ont onrves tn cases when aooiu-Bov ii required, the student mtty cocsalt L. D, Jackson's rqt Praetif, Loixlon, 1880, pp. 208-2S8 ; J. C. Trftutwine'l raefiif* o/ /.gying <iut C>r:'ular Onrj for lluilroatU, New York, oditlon, ISSti; W. J. M. RAnkirie'i Civil Enginttring, London, stvfinil edition. lOOii.

MIXB-SOaVEVISG.

plumb-bob. The inatrument usiusUy employed (Fig, 80) is mad

of deal boards, inch thick. The foot-piece is $ feet ia length and ii inches broad. The vertical piece is 3feetiiilength,i!l 6 iaches broad at the lower ead, tapering upwuxls until, at the top, it is i inches broad. In addition to the plummet, there ai small spirit-level fixed to the foot-piece to serrew R check. The inBtrutnent is placed on the floor of the IstsI, snd if the latter is being driven truly horizontal, the plummet will hang in the hole made in the vertical piece for its reception, and at the same time the bubble will be in the middle of its tnbe. The main horse-roada in collieries should be driven with slight inclination towards the shaft, so that -water may flow from the workings to the sump. Experience has shown that an inclination of 1 in 130, or a little more than inch in the jtii, gives the most advantageous eflect in drawing by horse-power the loaded waggons towards the shaft, and the empty ones bick.

Fig. SO,

Ftg. 81.

Oare must be taken that this inclination is not exceeded, as, in driving levels, there is always a tendency to rise too fast. For j maintaining the required incUnation, a piece of board, incb ,

Skttino-Odt. 261

tliick, should be screwed to the foot at the end of the instrument, which is nearer the 6haft.

In order to test the inclinatioQ of an undergroand roadway with an inclination of 1 in 5, Mr, W. Wardle usea the inBtru- ment shown la Fig, 81. It is provided with two sole-pieces, the bottom of the lower one being at a distance of 1 foot from that of the upper one at one end, wbUst at the other end it is brought to a feather edge.

An ingenious clinometer, invented by Oolonel G. P. Evelyn (p&tent 1885, No. 1964), may be advantageously used for setting out levels at any inclination. It consists of a curved tube filled -with water or dilute spirit, on which floats a small bubble of compressed air. Adjacent to the tube, and concentric with its outer periphery, is the graduated arc of a circle. When the air- bubble is at the zero point of that arc, the base of the stand, in which the tube is mounted, is horizontal, and any inclination from the horizontal is shown in degrees by the position of the bubble on the graduated arc. The tube is easily filled and emptied, and the size of the bubble is regulated by a screw-cap fitting over the cork.

To drive a level straight at a given bearing, plumb-lines are suspended from points in the roof previously fixed by the dial or theodolite, "niese lines indicate the direction in which the level has to be driven, and should be placed 30 to 60 feet apart.

Mr, J. B, Jameson has devised an adjustable portable instrument for ranging lines underground. It consists of a small bronzed metal plate with a sight vane in the centre. Above this is a swivel open triangle, that enables the plate to be turned in any direction required ; and attached to it is a long metal cLaiu, with a book at the end for hanging to the roof. The chain works through a small adjusting plate so that the sighting plate can be raised or lowered at wiD. The instrument, which is made by Mr. A. G. Thornton, of Manchester, weighs G ounces, and ia used in conjunction with one suspended cord.

Curves for Engina Planes. — Ourves may be set out under- ground by means of a theodolite on a abort tripod, and candles or Samps instead of ranging ]>oleB.

The direction in which curves for engine planes should be set out is sometimes roughly ascertained by making a careful survey and plan of the pillars and headings, through which it is required to drive the curve. The survey is plotted on a large soalee.y,, 16 feet to an inch. The curve drawn on the plan is divided into equal distances marked by points. The latter are then con- nected by dotted lines. By means of a tottactor, the beating

k

S5S

mSE-SUBTETIKO.

ot e*cfa of thrae liaes is determined. For gre&tr accuracy, off- eta are measured every 6 feet on each side of the lines to the of the ccrve. In tliia way data are obtained from which the corre may set out,

Setting-Qnt Tonaels. — The centre-line of the tunnel having been ranged on the surface of the grouAd, a. series of shafts are suol from 100 to 200 yards apart along that line. In order to er&nifer the ranging of the line from above to below the surface of the ground, it is necessary to have two marks, consisting of nula driven in the cross-timbera in the centre-line at the bottom o( each shaft as far apart as possible, to enable the line to be fto- longed from the bottom of the shaft in both directions. To determine the positions of the marks underground, a rangioj- fiume is erected over the shaft It consists of three half-timben framed as a triangle and supported at the angular point by itont props. From the frame are suspended two plumb-lines, whiob are ranged by a transit-instrument.

As this process cannot be satisfactorily used except in calm weather, Mr. F. W, Simms introduced the following modifies- tion : — By means of the transit-instrument, tlie engineer rangM two stakes in the centre-line at the surface, each being about 16 feet from the centre of the shaft, so as to be safe from disturbance while the work is in progress. To mark the exact position of the centre-line a spike (Fig, 82) is driveo into the top of each stake. The hole of each spike ii carefully ranged in the centre-line, a piece of white paper being held at a short distance behind it, so as to render it visible to the observer at the telescope. A string ii stretched centrally across the monib of the abaft, and iU Fig. 63. ends are passed through the holes in the spikes. It ii then drawn tight and made &st. At each side of ths shaft a plank is fixed at right angles to the string, and so placed that one aide hangs over the shaft about 3 inches, so that i plumb-line may hang from it without coming in contact with the iide of the shaft. A plumb-line being hung from e>ach plank directly under the cord marking the centre-line, the lower ends of these plumb-lines represent two points in the centre-line at the bottom of the shaft.

The approximate ranging of the heading connecting the lower ends of the shafts is effected by means of candles, each hung from the timbering in a sort of stirrup. The upper portion of the candle-holder (Fig- 83) employed by Mr. Simms is made of thin sheet-iron with a number of holes in it. The lower portion is of iron wire, carrying a socket for the candle. By means of the rack, the latter can be raised or lowered to the proper

aElTXNa-ODT.

Fig. S3.

level, being bung by a flat plate, it is prevented from rotAting. ,Tbe accurate ranging of the centre-line, when the heading haa been made, is effected by stretching a string between the marks aJreadj ranged at the bottom of the shaft, and fixing, at intervals of about 40 feet, either small perforated blocka of wood carried by cross-bars, or stakes with eyed-apikes driven into their beads, so that the holes may be ranged by the string exactly in the straight line. This method was employed by Mr. Simms for setting-out the Bletcbingley and Stilt wood tunnels on the South -Eastern Railway. Both these tunnels were straight from end to end, as is generally the case. Their centre lines were ranged with a transit-instrument of 30 inches focal length with an object-glass of inches aper- turei. In order to command a view of every shaft, the instru- iiK-ut, mounted on a cast-iron stand, was set up on the highest point of ground as near the middle of the tunnel as possible, and raised above the surface by the erection of a temporary observar tory. This consisted of a building of larch poles, in the centro of which was a brick pier 30 feet in height for the support of tha instrument.

When the length of the tunnel is not very great, tho transit- uutrament and temporary observatory may be dispensed with, and the 6-inch or 6-inch transit-theodolite used with advantage. Thia wta done in settingjnt the Olifton tunnel in 1871 to 1874. tumel is straight, on an incline of I in G4. It is 17371 yards in length. At a distance of 276 yards from the lower end of tho tunnel, where it approaches to within 140 feet of the BIa<krock Cliff, a side drift was opened &om the face of that cliff to the line of the tunnel. The tunnel was driven from this drift, and from two shafts sunk 998 yards and 4-63 yards farther on.

When the tunnels are of great length, and can only be driven from the ends, the setting out is much more difficult than when shafts can be sunk along the line. The direction of the axis of the tunnel is determined by a traverse or a trianguiation con- necting the two ends. In very long tunnels, such as those of the Alps, traversing is not sufficiently accurate, and recourse must be had to trianguiation, as was the case at St. Gothard. The St. Gothard tunnel, one of the longest railway tunnelr made, IB 9 miles in length. Its construction lasted from Siptetnber, 1878, to February, 1860. The holing was effected February

l>tN£-SUEVEyiNO.

o

D rr

O

n

a

Bbiting-Out. 256

1880, the length being 25 feet less than was expected. Tbo in level was 1*97 inch, and the error in alignment wai 2-99 inches. (Fig. 83a.)

The Mont Cenis taunel was set out in the jears 1357 to |858, without triangulation, with the aid of a high observatory. le length of the tunnel was determined by triangulatioD, and le line of levels wais carried over the mountain. The tunnel is upwards of 6 miles in length, and the junction was effected -without anj error horizontally, and with only a foot of divergence Tertically.

The Simplon tunnel was completed in 1905. The total diatance between the two portala is SlgSG-l yards or 1226 miles, and the junction was effected with a lateral divergence of 0'663 foot, and a difference in level of 0'286 foot. The altitude of the highest poini ia 2,314 feet, being 1,474 feet lower than that of the St, (jothard, and 1,934 feet lower than that of the Uont Oenis. The gradient on the northern portion of the tunnel is 1 in 500, hut on the southern portion the gradient is 1 in 142. For setting-out the tunnel recourse was had to tri angulation. The network of triangles comprised 11 points, including the two terminal points of the tunneL The highest point was on Monte Leone, 11,666 feet above sea level, and the lowest at the southern portal, 2,076 feet. The signals used had to be very solidly built. They consisted of brick pillars with cement mortar with an iron tube inserted in the axis in such a way that its top was level wit)) the surface of the pillar. In the tube a wooden staff was placed, and over its top a conical caj) of sheet sine was firmly screwed on to the stone pillar with four iron bolts. The top edge of the tube the point of the staff, and tbv apex of the cap were accurately centred. When an observation was made, the zinc cap was removed, the staff taken out, and the levelling screws of the theodolite were placed on a circle drawn in pencil on the surface of the pillar concentrically to the tube. As a check each signal was also determined by three crosses chiseled in the rock at measured distances from the signal axis. A special base line was not measured, bat the triangles were connected with a side of the existing Swiss triangulation. The coincidence of the headings on holing is affected not only by the measurement of the triangles, but also by the setting-out of the direotion under- ground. Special precautions were, therefore, taken to ensure accuracy. In the direction of the axis of the tunnel on each side an observatory was erected from which the direction was tested once or twice a year whilst work in the tunnel was suspended. At first it was easy to sight intiO &ft WkwJv. Ixam.

IIIlfX-SURVETI!ta,

rbich if Dbtiinfl

the obgervatoiy, but as the dist&Dce driven beo&ine gnktef auxiliary instrument had to be emplojed. Heavy tri[ made entirely of iron with centering head, were used for instrument and for the lamp sighted. The latter consiiti an acetylene bunier protected by a semi-cylindrical corn* polished inside for reflecting the rays of light, and prOTidcd in front with an adjustable slit for sighting at. The burner is connected by a rubber tube with the generator which if Buspended from a hook below the tripod head.

Kemarkably accurate results in tunnel aligmuent were ol in 1888 in the Croton aqueduct at New York. The point* oommencement of two hidings were 6,100 feet apart, the being 270 feet and the other 353 feet below the sur&ce. Tbt diameter of the heading was 16'S feet The direotioa VM obtained by means of two plumb-lines, 16'& feet aiart, let down each shafts When the two headings approached each other, tiie final connection was made by two drUls meeting in the hole from opposite sides of the rock, and after the blast had \ma fired, it was found that the error in grade was 0014 foot, acd in alignment 0*09 foot.

In the construction of Division No. 6 of this aqueduct, Mr. F. W. Watkins, the engineer in charge, found that the oeati> line wires were very difficult to distinguish, as the cross-hur of the telescope and the two plummet lines appear so nearly ilika He was, therefore, induced to devise an Uluminated slit appsr at US to replace the wires at the bottom of the tunnel. Xhi* instrument consists of two vertical strips of brass (3 inches ia height) attached to separate liorszoutal bars moving in guidei, and provided with a tangeat-aorew motiouj by which one or both could be moved right or lett and the vertical aperture between them made as small as desired. One of these iDstruments wu screwed to a platik-bracket, close behind each plummet wire, and so placed that the farther one could be seen through the scope in line just above the other. When these slits v adjusted so as to be directly behind the plummet wires, latter were removed, and lights placed behind the slits, this way two fixed and illuminated points were subatitu' for the wires. The results of tests of the alignment effeoted in this way show that the accuracy of the surveys

Ten

remarkable.

Taking cross-sections for measuring the areas and quantitinT of excavation in tunnel work is best done by measuring the irregularities of the contour of the section by angles and tanoes from some point in the vertical plane through the axis i the tunnel. For the Croton. aueduct tunnel, where sectlo

Sbttiho-Ogt.

to niftde every 10 feefc for over 30 miles of tunnel, a con- it ioslrument wa designed by Mr. A. Craven, Thia neat, known from ita yellow disc of varniBhed wood aa Am aunfloweT instrument, consiBtB of a light wooden tripod with xteanble lga, a ahifting top, ball and Bockct joint, and levelling crews. A vertical braaa tube slides through the socket, and tfarries at ita top a wooden graduated disc, 18 inches in diameter. Aa WiB revolving on a central socket traverses the face of the disc, and a wooden measuring rod, H feet in length, in placed on Uiis arm, and slid out to toucli the surface of the tunnel, the utd of the arm at the aame time indicating the angle from the TOTtie*}. The measuring rod tapers from '2 inches to 4 iaoh in width, and is graduated in feet and tenths from the smaller end. In order to ensure the croas-section being taken at right angles th axia of the tunnel, the disc is provided with a small noting tube perpendicular to its face. The meaHurements are rBOorded in the held-bouk, and the areas of the cross-sections are detennined bj calculation, or by the [ilanimeter.

When the ilitBculties of the task are duly considered, it is probable that the accuracy of the work at the Hoosac tunnel hag never been equalled. This tunnel passes through the Hoosac HoantAto range in MaBsachusetts, and is 25,031 feet in length. The taoael was driven from the two ends, and also from a shaft 1,0S8 fSMt deep, sunk in the vaUey between two mountains in tho line of the tunnel. On the east side, the headings met at a distance of 1,563 feet from the shaft, and ll,27i feet from the end, the lateral error being Q-025 foot and the vertical error boing 0*33 foot at the point of junction. Proceeding west- , the tunnel extended 2,056 feet from the shaft before naetiiig tbe excavation on the western side, which was 10,138 fisot £rom Ibe west entrance. The holing showed that the error oS Alignment was 0*045 foot. The alignment in the central shaft was oDtained by two plumb-bobs 25 feet apart.

Ouriously enough, the oldest piece of tunnelling of which there is aoj written record was bun at the two ends, ita constrnc- Uon recorded in the oldest example of Hebrew writing known. The inscription, now known as the Siloam inscription, waa discovered by some boys bathing in the Pool of Siloam, in Jerusalem, in 1680. It is cut on a tablet 27 inches square at the nottth of the tunnel, and, according to the translation of Fnfessor Sayce, reads as follows : —

" [Heboid] the excavation I Now this is the story of the tmuisl : While the miners were still lifting up the pick towards esioh other, and while there were yet 3 cubits [to be broken], kiie Toioe of one e*Ued to his neighbour, for there was an excess

j7

2o8

lU3rB-ftUltK I uu.

ill tlie ro on tlw rii. Tl]r rose up— tlie stnidc on tin vect of tlw tnniMl ; the minen e*ch to meet the other pick to pack. And than flowed the wten from their ontlet U Pool for 1,200 cnbita, and [three-qnutera] of cobit wu tiie heit of the rock* oxer the heads of the miners."

rram tbu inscriptioa, it is evident tb&t the tunnel wu begun &otB the two ends. And this view is ooit£rmed bj the reaulU of recent ezplontioas. The Fool of Siloojn is supplied witli WBter from uie so-called Spring of the Virgin, the otOy nttinil pring ae*r Jerasalem, by this tunnel driven in the rocL Aooording to Colonel Conder's sorrey, the tnnnel is 1,708 feet long or about 1,200 cubits of 18 inches. It does not, however, mn in a straight line, and towards the centre there are tiro e%Uf-d-ae, of which the inscription offers an explanation. We thus gee that the engineering skill of the day was by no mewu despicable. like the Mont Cenis tunnel, this aqnedaot begun simtiltaneously at the two ends, and in spite of its wind- ings the workmen almost suoceeded in meeting at the middle. They approached, indeed, so nearly to one another that the doim made by the picks of one party of miners was heat by tbe other, and the parting of rock was accordingly holed. Tbii accounts for the two &lse cuttings now found at the centre of the tunnel, these lepreaenting the extreme points reached bj the two parties before they had diacoTered that instead of meet- ing they were ptasing one another.

Though the inBcription contains no indication of date. Pro- fessor Sayce is of opinion that the tunnel was made in the reign of Hezekiah, or possibly even in the time of Solomon.

With regard to the interpretation of the last line of tlie inscription that " three-quarters of a cubit was the height of the rock over the heads of the miners," it is remarkable that tb difference of height of the two channels at the point of jnnction is just 13 inches, or close upon three-quarters of a cabit. Unfor- tunately, however, the text is deticient juat in the place where the number occurs, and it may possibly indicate that the minen knew the thicknesB of the rock abore them. In this case, the correct interpretation is probably 100 cubits, the average thickness of rock above the aqueduct. Several marks, evi- dently artificial, were discovered by Colonel Oonder in the tunnel — square or triangular notches, measuring inches in width. These appear to have been used, like the peg and nail of the Cornish miner, to mark the end of a periodical survey, or else to serve as a guide in setting the contracta to the miner.

It is certainly remarkable that should have been so

igbt s difference in level between the two portions of the tunnel. It would h&ve been eaay, by means of a plumb-line or a rude water-level, to preserve the level of the channel floor j but it is extraordinary that the two ends should diSer by only a foot in level, considering that they were star ted independently.

Id New South Walea, a. very fiuccesisl'ul alignment was etiectd by Mr. T, W. Eeele in the construction of the Nepeau tunnel, a conduit for supplying Sydney with water. The tunnel ia 23,507 feet long, the bases at the east and west ends being 254 feet and 212 feet respectively, situated at the bottoms of precipitous limestone gorges. There were six shafts, admitting of only 12-foot basea, the depths varying from 210'6 feet to 324 feet. The length between shafts Nos. 2 and 3 was 4,341 feet, the headings meeting at a point 3,018 feet from shaft No. % The etror in alignment was inch, and in grade i inch. The tunnel ia feet high and feet wide, and is inolined at the r&te of feet per mile.

The line was transferred from the surface to the bottom of the ahafts by plumbing. At the shafts brick pedestals were erected, one on each aide, on the centre line, and about 60 feet apart, the tops being a foot above the shaft platform. Points were then accurately established on each, and a steel wire, 0-02 inch in diameter strained, at its utmost tension, from point to point across the shaft. The process of plumbing down the shaft was then proceeded with. An 8-inch transit theodolite on its centering logs was then set up in one of the headings, and the intersection of its cross-wires brought into coincidence with the line as given by the plummets. After the instrument had been adjusted to prolong the line into the heading, a hole was drilled in the roof and a wooden plug inserted ; and on this the point was obtained by sighting on to a plummet lamp, of the type Qsed in Pennsylvania, suspended from it. In order to give the levels in the tunnel, the value of a bench-mark at the bottom of a shaft was ascertained by measuring the calculated distance from the surface with a steel tape ; and the levels were run into the headings. At intervals of 100 feet, hooka in pegs in the sides of the tunnel, and opposite to each other at right angles to the line, were so adjusted that stringa stretched through them were exactly 24 feet above the grade. The plummet lamps, hangiBg from the centre-pegs in the roof, being then lowered ontil their lights were even with the horizontal strings, the axii of the tunnel was determined, and the miners were provided with both fine and grade. AH that they required to do was to place a candle at the face in line with the tights from the Jfra. Proe. Jiut, CM, vol. iciL, 18S8, W.

S60

UlNE-aCBTEtlHO.

pluraniet lampfl, &nd measure down 2 feet 9 inches to find tb grade of the invert. liench-marks were estAblislied at inten&ii of 500 feet, and were frequent] j checked.

The lengths of the beaiiings and the results of the iiijgiiiueiit, when the junctiona were etlected, were as follows : —

Sum or Hwllsi.

bwiUiliiFMt.

XmtimJattm.

la LiliL

IsOndi.

Inlet.

No. S, West.

No. fi, BMt.

No. 4, West.

No. 4, £rti. A, Wwt A, EMt.

No. 3, Wti,

No. 3, EMt

No. 2, Weit.

No. 2, EMt.

No. 1, Wet

No. 1, EMt OaUot

9350 /

1970-0 )

246S-0

ass-o

22S6-0

2148 -€

Nu.

After the tunnel bad been pierced through, daylight at on end was distinctly seen, without the aid of a telescope, from thf Other, miles away.*

On tunuBlliag, oocsult F. W. Simtni' Practical TmmeUina. Sid ei, rtvwed by D. K. . London, 1877; H. S. Drinker, TumeUimg, Nt York, 187S, F. Raha, der gMamvUen TiinndbauJbimM, 3 toU.. Berlin, 1867-72, with the uthoritioa thero cited, and F. W. Wstkini "Tunnel Suryeying od the New Croton Aqueduct," Traiu. Atner Soe- C.E., vol. Ilia, 1890, p. 17. ValQttble information on the tettinji-out rf

J'tvr

, Tol, oivl., 1894, D,

mss-soBVBTixa pkoblbju. 26t

Chapter Xv Il

MiNK-SURTBTlKtJ FbOBLEU&

BetemdnatiOD cf the Direction and Inclination of a Mineral DepOsit.Problems relating to the vorking of minea may h& tolved graphically or numerically. Graphic solutions are the most simple, but they require the plans on which they are hosed to he of undoubted accurticy. Most probleros are therefore more conveniently solved by the ordinary methods of descriptive geometry.

To determine the strike and dip of a vein that has been opened by a level driven along it, a simple method is to select two pointa in the axis of the level, either on the floor or on the roof. At these two points two vertical props are set up, when the bearing of a horizontal string connecting the two props will be the strike of the vein. Instead of the stretched string, a rod may be held horizontally.

The strike being determined, the direction of the dip may be determined by setting off a line at right angles to the strike. The dip may be measured with a clinometer.

A convenient instrument for determining the dip of mineral deposits is the so-called gradomiter, Invented by Mr. W. Fairley, It consists essentially of a 9-inch or 4-inch scale made to move up and down a vertical bar. When the lower edge of the scale is placed on the plane of which the dip is to be determined, and ii shown to be level by the spirit-lfivel on the upper edge, the plane is horizontal. When the plane is inclined, a slide, like that of the slide-rule, marked on one side in degrees and on the other la inches per yard, is taken out and passed through a slit at right angles to the longitudinal axis of the scale. For measuring dips above i5*, a second slide is provided. The gradometer is of less weight than a clinometer of the same length, and can be read with greater facility. If the strike of a deposit is known, its dip may be calculated.

J

se2

UINE-BUBTSrtKO.

Kg. 84

Thus if a line A £, Fig. 84, is drawn on the plane of the defiosit A B D, and if through the point A. a horizontal plane A F passes, A B, the line of intersection of the two planes, IB the line of strike of the deposit. From kny point O on the inclined line A E, let fall a perpendicular Q H to the horizon- tal plane A F, and in the latter draw a horizontal line A J, which is the line of Btrike of the inclined line AE. The horizontal angle B A J is the difference in bearing between iba line of strike of the deposit and that of the inclined line ; whilst the angle G A H in the vertical plane E A J represents the dip of the inclined line A E. Let fall in the horizontal plane A P (torn the point H a perpendicular line H K to the line of strike A R and join G K . Then G X is the line of dip of the deposit ABOD, and the angle GKH in the vertical plane OHE represents the angle of the dip of the deposit.

If the strike A B of the deposit is expressed hj e, and the &&gl* B A J - e, and the strike of the inclined line a, then s In the right-angled plane triangles A G H and A H K,

GH AG sin 6, and HE -AG oofi&Bint.

Then from the triangle G H K, the value of the required aimta of dip may be found from the formula —

Gh

AG sin b

He "

A CO! 6. ala

tan b

sin e

UnGKH

Conversely if the angle of dip d is known, the strike may be found from the formula sin e - tan 6 . cotan ti.

For example. — 1. What is the dip of a seam coursing 137' 30', If a diagonal heading driven in the seam has a dip of 4', and courses 90° or due east and west ! The angle it 127° 30' - 90° 00' 37° 30'. The dip d is then found from the equation

tan d

sin 37' 30"

MIDE-SUBVBYIMQ PROBI.eiia,

Smplojiug logarithms, this gives

Ltac 4° 8-5446437 LsiD37'30'= 9-7844471

LUn tf 90601966

riiua (f 6' 33' 10*.

2. Example. — Determine the itrike of a seam dipping H'', m rhich a diagonal he&ding is driven, dipping and coursing 60*. In thifi cae

ttaii un . Tr - tan b hi

Employing logarithms, this gives

Ltati5° 8W19al8 hUaS" 9'14780-35

Lsine 9-7941493

ierefore e 38' 30'.

The strike c required is fouad from ths equation e e + a,

e 38° 30' + 60* 00' 98* 30'.

The strike and dip of a seam may be determined if three

aiats in it are given. Thus if three bore-holes, not in a straight le, have been sunk to the floor of a seam, as shown in the plan. Fig. 85, H M T, the problem ia solved as follows : — Measure the depths of the three bore-holes from the same assumed horizontal plane at the surface. In thb case, T represeats the deepest, and H the highest point of the deposit. Imagine per- pendiculars to be erected to H M at the points H and M, and on them laid off the heights H H' and M M', representing the heights that the floor of the seam at the bore-holes H and M is above the floor at the bore-hole T. In this way, H' M' repre- sents the line of inclination of the seam between H and M. That line is produced until it cuts the line H M produced at N, Thus a point in the seam is determined, which is situated at the same level as the bottom of the bore-hole T, and T N is the Una

ef strike of the seam.

uei t

d

iu

KlNE-aUK7BTIK6.

The line H N is found, from the eimilar right-angled tri&DgUi " H' N and M M' N, to be equal to

Hn

21. M. — Af Ai.

From the bore-hole*, the strike of H T and the angle K H T are kaoTTtt, and as H N is found from equation 1, in the tri&ngle H N T there are two aides and the included angle known, coa- nequentl;

H N -I- H T : H N - H T tan i (T + N) : tan J (T - N) (1)

From this, the angles T and N are found, as half their sum ii known. From the given strike H T and the angle T, the atrilce of the line T N may be deduced.

la order to determine the dip of the deposit, imagine a line H O drawn from H perpendicular to the line of strike T If, then

H O

in the right-angled triangle HOT, wm ain T, whencse it

follows that H O H T sin T.

At the point H erect a line perpendioular to H O, and along it lay off the height H P, being the height which the floor of the seam in the bore-hole H is above that in the bore-bole T. Tteo the line obtained O P is the true line of dip, and the angle HOP represents the angle of dip of the deposit. Thus ten

Hp Hp

E P fY-p:, or, by substitution, tan H P . — HO a. J. sin T

Expressed by general formuls,

tan S

a'

a sin V

., and

Bin W

tan V

a :;,- cos W

a

in which S is the angle of dip of the bed, Y the angle between the strike of the bed and M H, a the distance from M to H, a the distance from M to T, W the angle in a horizontal plane between

Iiike-S0Rvetiko Fboblehs.

M H and M T, rf the difference of the depths of the bore-holes M mnd H, and d" the difference of the depths of M and T.

Fijj- exampU.—lxi. Fig. 85, H T 150 yards, H M 112 yards,

M T 100 yards, measured horizontally. The angle M H T 41* 48' 37". T is the deepest bore-hole, and the floor of the seam in the bore-hole M is 32 yards, and in the bore-hole H 73 yards higher than in the bore-hole T, It is required to determine the strike and dip of the seam, when T H coursea 172* 30'. From the first equation giren,

Hf

199*41 yards.

Sow, T -1- N 180* - 41* 48' 37"= 138° IV 33', and half T N 69* 5' 41-5*. From the second equation

tftu

T-y 199-41 - 150 , 3 199-41 + 150 '

tftnC9*5'41-&'

aT6l 'tan 69" 5' 41-5'

349 '4 1

From this, half T-N is found by logarithms to be 20* 18' 65". Half T + K being 69' 5' 41'5*', T is equal to 89* 24' 36-5', and N b equal to 48* 46' 46' 5".

As the strike of T H is 1T2* 30', and as T N lies to the right of T H, the strike of the latter is

The angle of dip H O F is found from the equation

Ip

tan H P

160 ain 89" 24' 36-5*

By the aid of logarithms, the angle H O P ia found to be 25" 67' 7'.

The strike of the seatn, as found above, can be set out at the urface in the usual way.

Betermination of a Point at the Surface directly above one UadergTonnd. — If it m required to deterjnine the position of the

UtKE-eUHTKTING.

end of a level, it will be found advisable to calculate it trigoao- metrically instead of by plotting the travei-se at the sur&oe.

The rectangular co-ordinates of the underground-aurvef an calculated, and the distance and bearing of the end from ths shaft found from the forraulie :

,, , departure .

tan of bearing - -r.-, and

latitude distanoe latitude x sec of bearing.

For exmtiple. — In order to calculate the bearing and distance of the end of the level from the centre of the shaft in the torre; of the Work and Rest mine, the record of which is given on p. the latitudes and departures must first be calculated, vitJi th( following results : —

Work And Rest Mine. Reduced Survey Notes.

Lat

T17Dk.

nxTAATriA

BeulJic.

N,

S.

K.

w.

A

Fwt. 74 -SO

N. Oms'W.

O'sa

B

N, 00- W.

63 '00

N. 27' W W.

D

N. 84* 67' W.

%M

B

S. 74° 06' W.

6 -Co

22-U

P

N. 67° 45' W,

N. 8S* 00" W.

H

8. 84" 06' W.

33 8!

S. 52° 00* W.

2S9'37

MlNE-SDRyETIHO PROSLEMB.

S67

be total latitude is 289 37 - 24-61 264-76 feet, aad the total ture is 429-13 feet The distance from the shaft to the ion point J at the end of the level ia found from the formula s

tan of bearinfif „,. , and at)4'7tj

distance 264-76 sea. of bearing.

be calculations are performed moat quickly by means of loga> ithms;, thus —

tog 42913 tog 26476

2'63S68S 2'422Ss2

10 + 0-2O9736 L. tfto 53° 20'

h, tea 58° 20' 10-27118601

tog -264 TS 2-422a52

12-7027121 - 10 log 501 32

'o determine the position of the point at the surface correspond- ing to the end underground, it is merely necessary to set-out from the shaft a horizontal distance of 504-32 fset at a bearing of N. 58° 20' W.

This problem is of great importance for the determination of the position of the underground workings in reference to the boundaries of the concession or royalty.

Holing from one Excavation to another. — The usual problem relative to holing consists in determining the length and direction of the axis of a gallery joining two given points. The problem may be solved graphically or numerically. In the former case the plana employed must be rigorously exact. In the numeri- cal method, the length and bearing are deduced from the co- ordinates of the end points.

For aaximpla. — In the survey between the Speedwell and Netherthorpe shafts at Staveley, of which the record is given on p. TJ, the latitudes and departures of the 15 drafts underground from the Speedwell downcast shaft to the face of the main ven< titatiug drift, intended to hole into Netherthorpe shaft, were calculated with the following results ; —

'

1 9S8

HIXS-SOKVETIKa.

Reduced Survey Notf.S,

Ho.

Bewlot.

Dilluifln.

LATIttDI.

VtntntM,

M.

t.

K.

w.

A

N. 34° 24' W.

7-a

B

N. 58" 35' E.

333 D8

™.

N. 46' 41' E.

191 '42

D

N. 37' 20' E.

Iso

E

N. 8° 40' W.

F

N. 15" cur E.

N. ir 67' E.

Ibs -97

H

N. U'Sfi'B.

16S

J

N. 35° 37' W.

4S-&1

K

N. is-acE.

24G'S0

N. 18° 14' B.

M

N. 69° 42' E.

3S4

„.

N

S. sr 45' E.

N. W 32- B.

P

N. 71* 67' E.

f

The total latitude amoimt to 2441 -69 - 65-75 - 2385-94 I in to, ind the total departure 1781'58 - 69-37 - 1712'31 IitiIth

The direot bearing and diata&ce measured at the sur&ce from 'he Speedwell downcast nhafi to centre of Netberthorpe shaft, ntended upcast, were N. 37* 02' K, 3U3 links, representing MS6-06 links north latitude, and 1874-89 links east departure.

The positions from Speedwell shaft, in terms of latitude and eparture, were consequently as follows: —

—

HIME-SURTETIira PROBLEMS.

Netherthorpe shaft, FM of becuiing,

N. Lltudc.

18T4'90

B9'12

Now, ton of bearing departure latitude, and distance lati- tude X sec of bearing, therefore the difitance to be holed is found aa follows : —

log daparture

Iog

B,

log l&titQde

log

1 -906191

L tan of bearing

10 +

0>214g33

bearing is therefore N

58' 38' E.

log latitude

tog

L 6S° 38'

10'283563

log dintmice 12-279729 - 10

The distance is therefore 190-43 links.

Having thus calculated the bearing and horizontal distance- from the face of the heading to the intended upcast shaft, Mr. Howard determined to drive direct into the shaft, and the drift was accordingly set-out at the calculated bearing and distance. His sarvej and caloulations were proved hj the holing to ba absolutely correct.

If it is required to determine the inclination and distance of the axis of the heading uniting the two given points, and the co-ordinatea of those two pointa referred to three axes of rectangular co-ordinates are x y it and x' y' % respectively, the distance d, the bearing ;3, and the inolination a, may be found &om the formulK —

x')4

X —

y -

m -

/

-r

+ (v

-yr

Attention must be paid to the signs of the co-ordinates, which always indicate the position in space of the axis considered.

A remarkable example of successful holing is aflbrded by the Emst-August adit level in the Harz. This great adit, one of the longest in the world, was commenced in L860 and cocnileted

liiKE-auitVBYtNa.

22nd July, 1864 ; it has a total length of 2S,956 metres. It wu drivea from the bearinge and distanoes calculated from tli resulte of a survey made with extreme accuraoy by means of the theodolite and spirit-level from a number of pointa. The reEultt of the holingB were as follows : —

Ernstauqust Adit Level.

diom 05

Houio.

Snrfejitd.

Id DIkcUdh.

tiLenl.

Fttlioiui.

Ischa.

IlClM.

2. Boling btwen the ttiouth of the &dic at GitteMe, itnd the FaUea- berg ahsft,

Sso

0'40

3. Holing between the Meding shaft and the George shaft,

2,700

4. Eolinv between the Uiilfe Oottea shiut and the mouth.

2,760

la

5. Holing between the George shaft anrt the Kneaebeck shaft,

1,680

l-

O-60

6. Holuiz between ths KnceebKck ahalt and the HiiLfeGottes abaft,

Oh

7. Holing between the Sqhreibfeld sluuft and the Haas Sachsen

1,890

8. Hohug between the Meding shaft and the Knist-August shaft,

3,900

9. Holmg between the Ernat-Augast hut and the Haus Sachiea

I.Im

0-oa

To drive a tunnet through a hill, the line of the tunnel is set out over the hill, and carefully levelled from the commencement at the foot of the hill. When it ia thought that the level of the starting-point haa been reached, or, in other words, when the rises are equal to the falls, an assumed mark is placed, and the levels accurately calculated. The assumed nnarh is then raovetl up or down the height by which the rises and falls differ, to give the

MINB-anRVETinO PROBLEXS. 371

exact position of the floor of the tmmel oa the farther aide of the hifl.

If the levelling is efTected hj the theodolite inatead of bj the spirit-level, the total of the calculated bases of the varione drafts gives the length of the tunnel.

Sinking Shafts from Several Levels. — Similar problems to those relating to gallories are preeented by shafts which have to be sunk from several levels. If the shaft to be sunk is near an existing shaft, the problem is comparatively simple, as it is then merely necessary to drive headings from that shaft at different levels until their ends reach the axis of the sbafl to be sunk.

The conditions are not always so favoui-able ; the shaft to be sunk may be at a considerable distance from any existing shaft. In such a case, points are selected at each level of the mine- workings, as near as possible to the shaft to be sunk. From these pointe headings are driven to the axis of the shaft. The length and direction of these headings may be calculated from surveys made at the various leveis of the mine. It is, of course, necessary that the surveys shall bo made with extreme accuracy with the theodolite.

This method was employed in the Harz for sinking the Konigin Marie shaft, the perpendicular shaft sunk in that difitriet. In 1851 it was decided by the Government authorities to drive a deep water-level at a depth of 120 fathoms under the Emat- Auguat deep adit, by which the mines of the Upper Harz were then drained. The new deep water-level was intended to serve as a great common water-reservoir for the mines of the distriot.. From this level, which is 324 fathoms below the surface, and IIS feet below aea-level, the water is raised to the Ernst-August adit For the reception of the engine for raising the water, it was decided to sink a new perpendicular shaft, the Konigin Marie shaft, which should also be utilized for raising the ore from several mines.

In order to expedite as far as possible this important work, the shaft had to be sunk from several levels. It was sunk from the surface to the deep Oeorge adit, a depth of 146 fathoms, and at the same time commenced at a level 202 fitthoms below the surface, and at another 270 fathoms below the surface

Oareful surveys having been made at each level, the shaft was set-out from the points obtained from the calculated co-ordinates. The different holiugs were successfully effected in 1866.

The accuracy of the work was then tested by suspending a plumb-line in the shaft, and determining the position of the shaft at the three levels. The plumb-line at the surface was exactly

yin the centre of the hoisting compartment of tka %W i&

KIKE-eUKTKTIira.

distance of 40 inches from each of the long sides, and 70 inchei from each of the short sides.

Designating the shaft as A B D, the distance of the plumb- line from the sides at the different levels was as follows: —

At the BQrfoce, . At th 146- fathom lerel, At the 202-f8thom level. At the 2;0-raihom level,

Ab

42 G

Cd

Incom

38 '5 39'2

Ac

Inrtw.

At the 146-hthoin level,

At the 202.fathom level, At the 270-fathom level.

aidra.

Frouj these results it follows that the deviation of the shift frou) the vertical was as follows : —

Thus, the Konigin-Marie shaft presents a brilliant illustratioD

of accurate mine-surveying.

The Cabical Content of a Mine-Eeaervoir may easily be mined by the aid of a levelling-instrument The cubical content must be calculated so as to ascertain the quantity of water which the proposed reservoir will hold. In shape, a mLae-reservoir resembles most closely a trnncated pyramid. It is therefore supposed to be cut, at given vertical distances, parallel to the suriace of the water. The cubical content of the reservoir then determined from the area of these horizontal sections aii their vertical distance apart.

When a suitable site for the reservoir has been selected, anj the height of the dam fixed, the highest level (1, Fig. 86) oif the water is marked by a stake fixed into the dam. The water-line of the reservoir ia then determined by find- ing with the spirit-level a number of points lying in the level of 1. All these points are then marked by numbered stakes. 3ome to 3 yards vertically l>elow the first stake, a second stake is fixed into the dam. The contour of the reservoir At this level is then deterrnvned KV[\, and marked !

ISK-8UHVBTIIfS PROBLEMS.

numbered stakes. In a aiwilar way, contoure of the reservoir ftt lower water-levels are determined and marked OBt. The contours marked out by the numbered atakea are then surveyed by means of the dial, the prismatic compass, or the plane<table, and laid ilown on a plan to a large scale. From this plan, the areas, the cubical content of the reservoir is calculated by means of the formula V i, A (B + + 6), where h is the vertical height and B, b the area of the ends.

J''or example. — In the mine-reservoir, shown in Fig. 86, five horizontal sections were determined at vertical distances of I'OOO, 1-050, 1-000, and 0-875 fathoms apart. The vertical distance from the fifth and last section to the bottom of the reservoir was 0-375 fathom. Ech of the five water-levels were distinguished by numbered stakes, so marked that all belonging to one section had the same number. The five horiisonta.1 sections were then surveyed with the compass, and plotted on a suitable Male (1 r 1,000). The cubical content was then found to be il814-13 cubic fathoms as shown in the following table : —

CtJBICAL CONTENT OF A MINE-RESEBVOIR.

An..

VsttldnlDMuiMof

Lev ell Apsrt.

Cublal Cuumt.

Bottom.

Sacun Fitbunu.

(Inlili.- ittioma. 1S931U

68'5-46

The cubical content of a dump-heap is found in a similar manner.

Detemunation of the Strike and Dip of the Line of Interaectioa of Two Veins.— It is important to determine the position of this line, as it is frequently found to be a line near or along which a

lXE-aDBVB¥lMQ.

in solving problems relating to the dislocations of veins. Rulet for determiniog hj means of spherical trigonometry the strike of the line of interseotioQ are given in the treatie'S on min&arrey- ing by Von Oppel (1749). Kaestner (1776), and Lempe (1782). The simplest trigonometrical solation to the problem is th&t given by A. RhodiuB,*

The problem may be solved by construction. Let a b' and b' c (Fig. 87) be the lines of strike, at a given level, of the two lodes dipping at angles of ciand a. In order to determine the line of intersection, the perpendiculars t k and I m are let fall in the direc- tion of the dip of the lodes, and made the bases of right-angled triangles, the hypothenuses of which are inclined at angles of and a' respectively, the perpen- dicular being the same (A) in both Fig, 97. cases. The lines k n and m o are

then drawn parallel to a 6' and b' e, and continued until they inte sect in the point e. Then 8 is a point of intersection of the two lodes at a level which is deeper than the point of intersection 6, by a distance A, and consequently 6 is the line of interseetion of the two lodes. The strike of this line can be measttred with the protractor.

By constructing a right-angled triangle with its base equnl to the line of intersection, b e, and its perpendicular equal to K then the angle at represents the angle of inclination or dip of the line of intersection. This angle may be measured with the protractor.

The preceding construction is generally to be recommendei The problem may, however, be solved by means of plane trigono- metry. The following is the solution given by Bhodius : — If i e, as in the first solution, represents the line of intersection ot the two veins a J' and b' c, then eq and r, lines parallel toi and / m, are lines at right angles to the strike of the veins. The angles which e q and r form with the line of strike be of the line of intersection being indicated by a; and y respectively, the following equations are obtained ": —

eq h cotan ; r A cotan a', . . (1.)

FrtUM. ZUefir. , vol. v., V1466, t. VVQ,

lII>'KOElV£YlNa PBOBLEUB.

cotan a cotau

cos y'

ootaa K + cot&n a,' cos a; + cob y

kad

But

ootan a

eotan a - cotan a' cotan a.'

cotaa + cotan tt ootAii - cotan a'

cotan a 4- cotan a ootttn a - cotan a'

cos y

COB IB - cos y cos y '

cos ae + coa y

cos a: - cos //

coa a ' sin a' -4- sin a coa cos a sin a - ain a coa a'

27S (3 and 4.)

sin {a' + a) sin (a' — a)

SabstltDting u + v for ai and v, - v lor so ttiat tt half x y aoid half x — y, the equation 7 beoomes

aio + a) ain (a' — a,)

COB u cos

sin u am V — - cotan J + y) cotan (x - y).

cotau 4

!/)

am (a + a ) . , , .

) -r( tan J (as + y)

-; — 7 if cotan i i, .

Ib this, J reprent the value of the angle a bo, included bj the Uoes of strike of the two lodea, so that 4 3 90' - i + y)t ad i (a: + .v) 90' - 1 4. The angle 3 la known, and and y are rotind from these two equations.

The angle of dip of the line of intersection ia calculated In th following way : — h b e tan thereibre.

, A A 'Cos X

tan -i) J—

cos X

h cos y

Si"

cos y

cotan cotan m .la ordr to employ this formula, the value of the angle a; or y

IttTtS-SUBTBTJKa

first have been determined. The angle of dip ii found more conveniently from the formula

, n sin a sin a' . , . , , ,

tan s/ 2 —. — ; i sin o cos A (x — v).

for example. — strike of a lode is 101* 15', and its dip 80° towards south; the strike of a second lode lb 170* i'\, and its dip 75° towards west; required the strike and th dip of the line of intersection of the two lodes,

By applying the formulee given, the former will be found to bo 62' 271', and the latter 74° 15' 26'.

The Search for Dislocated Lodes. — In following s lode, it frequently happens that a cross-course is met, and, after driving through it, the lode is not to be found on the other ude. Id such cases it ia said to be dislocated or heaeed. The two inter- secting veins seldom form an intersection at right angles ; more commonly one ia inclined to the other. In ComwaU, of 372 es of intersection, recorded by Mr. W. S. Henwood,* 227 }ier cant, were intersected but not heaved, 26-2 per cent, were found by driving to the left hand, and 61*1 per cent, to the right hand ; 63 '5 per cent, were found by driving on the side of the grwitM angle and 12 '9 on the side of the smaller angle. The averigs distance of dislocation was 16*4 feet.

The first clear views on the subject were put forward io 1810 by Schmidt, who stated that dislocations were to be ei- plained by a siiiking of the hanging- wall of the dislocator, Schmidt's rule, as modified by v, Garnall, is as follows : —

If the dislocator is struck on its hanging-wall, it moel bt passed through, and the diiving continued in the hanging-wtU of the dislocated lode. If the foot-wall of the dislocator is struck, it must he passed through, and the driving cnittianed in the foot-wall of the dislocated lode. For obtuse angles dislocation, the rule is reversed. The angle of dislocation ia tlie angle formed by the line of intersection of the two veins, and that portion of the line of strike of the dislocator which enten into the foot- wall of the lode.

On Schmidt's theory, Zimmermann in 182S based hi rule, which is more convenient to use, as it makes no exception of the obtuse angle. His construction is as follows: —

At the point D (or E), Fig. 88, in which the dislocator A ii cut, erect, on the line of strike and towards the inside of the dis- locator, a perpendicular line D L (E L') lying in a horizontal plan& Determine the position of the line M N <M' N) in wbioh. the

Trant, R. GtoL Soc., CormoaU, noV v. 1843,

UISE-eURVtTlKO PBOBLEUS.

plauea of the dialocator and of tise lode interaeot. Prolong the use to N (M') towards the oppoaite selvage making it D K (E M*). Observe to -whiob aide the perpendicular D L (E L') deviatea fipom the liae of interBection whett it ia directed towards the opposite selvage, and after passing through the dialocator, eek the dislocated portion of the lode on the side towards which tlie perpendicular D L (EL') falls.

Fig. 88.

Tlie construction is very simple. The line of intersection of the lode and the dislocator is determined by the method de- ribed. It is then merely necesssxy to erect a perpendicular at be point D (or E). If tlie line of intersection is to be determined plane trigonometry, formula 8 is employed. For joami)le. — On driving along a lode, dc, from d towards Ig. 8&, it is found that the lode ends at c, having been dis- kted by a fissure a 6. The fissure lias a strike of 118°7AV and a dip a.' of 65' towards

the south-west, and the lode has a strike )3 of 150", and a dip a. of 82° 30' towards the north-(?iist.

The first problem is to determine the line of intei section of the two veins. Tbe i>oint of intersection t being found by the process previously described, e i re- presents the strike of the line of intersection. By treetiBg a perpendicular c £ at the point e, it u evident that

Fig. &J).

MIITE-SDRVSTtNa.

the lost vein I m will be found, ufter (lie dislocator has been passed through, by driving from e in the direction c 6,

If the line of intersection is to be determined hy raeaiu of plane trigonometry, by employing formula the required tine of intersection will be found to have a strike of 145* 6' 23'.

If recourse is had to spherical trigonometry, the calculationi are more simple. With e as the centre of a sphere, the spherital triangle A B C is described, in which the aide (=j9- jS') is in the horizontal plane A c B, A C is in the plane of tlie fiMure a b, and B C in the plane of the lode c d. Again, e D i) the horizontal projection of the line of intersection S c 0, and D an arc perpendicular to A B, and &om the two right-ftn|led triangles A C I) and BCD,

: sin X ' tan ot', and ) tan y ain - x) " tan a.

From these two equations, it is found that

tail a'

cotau t.

(1.) tany

cotanic

tan a ' sm 9

Kumerical valoea being substituted, tan 55*

cotan X

tan 62 30 sin 31 52) '

a! 26° 58' 53"

strike of the fissure a 6 is 118' 7'; therefor, tlu

118*

7i' + W

68' 53"

Now, the

strike of the line of intersection S c C

145' 6' 23".

If, ill the examjile given, it was found necessai-y to driv 11 yards from c towards 6, in order to reach the lost lodesti, the sinking H of the hanging-wall of tlie dialocator, must, according to Zimmermann, have amounted to

11 -sin 3 1° 52i"

H

coa 65* COB 31° 9 '76381 yards. Irregularities of Seams

cotan 83* 30' - sin 55'

Irregularities of Seams and Beds Beddeil deposite are

frequently found to be interrupted by faults, causing a outtinj-

off of the bed, and ii displacement of it up or down. A &a]t of

this kind ia teruied a hitch or trouble; if on a very large scale,

a dyke. In order to represent the direction of the displaoement,

iLe fault is known as an up-throw or down-throw.

The alterations in position of stratified deposits undergOQe

Minr-Subtetiko Problems.

%

3en

thir deposition, niay be divided into three claasea — (1) Faults canaed by folding of the strata ; (3) throws or faults cns0d bj fiMores ; (3) displaced faults. Faults of the first and third class are only met with in folded strata ; faults of the secoti') class alao occur in homontal strata. All these faults give rise to dislocation of beds and Beame, and rules have been fonniilated, like those for lodes, for ascertaining the direction which to search for the displaced bed or seam.

ulta of the first cl&sa are, as A. Heim first showed, merely the Gual result of folding. In many cases, tlie progressive stej may be observed in the strike of the same fault. The mode formation of such faults must therefore be considered, not as an. bypothetB, but as an absolute well-establtBhed fact. Thus, at the Mansfeld Mine near Langendreer, a folded fault is rery apparent in a certain cross-cut, whilst 162 feet further north it beoomea a ciaple folding. Folded faults can only occur in beds and seams, bnt not in veinfi, for these, being GUed-up fissures, are of more recent age than the country roek, and its foldings. With faults of this kind, the same seam is frequently met several timea at one level If a fault is recognised as belonging to the folded oiass, the direction Ln which to search for the displaced seam may easily be decided by means of a fiectiunal sketch.

Throws, or normal faults, are those which have arisen entirely through the slipping down of the strata on the banging- wall ot the dislooator. The rule for ascertaining the direction in to search for the displaced seam is as follows: — If the dislocating' fisaure is met on its hanging- wall, the displaced seam must be ought in the direction of the hanging- wall of the strata after the fiuure is passed through. Oonversely, if the fault is dipping from you, you must proceed downwards. Zimmermann's con- struction is applicable to dislocated seams as well as veins.

Faults of the third class were first observed by Professor Koehler Ln the Westphalian coal-fields, and subsequently in tlie lodes of the Harz. Under the term displaced fauUs (Verschie- buuzen) are to be understood those dislocations, in which a part of the previously folded or vertical strata, with the seamil eootsined therein, was torn away, by the force that caused (biding, from another part of the strata, and slid or pushed away. Id aoch cases, the seams and the strata appeared curved in the direction of the movement, and gradually thinned out, though XM) folding is to be observed, as is the case with folded faults. In addition, the plane of disruption exhibits traces of the tnorement in the form of slickensidea and striations.

Tlifse displaced faults may thus be easily distinguished from Other faults. A fault hitving been recognised as oe longing to

Ik

M

Xi K C-Surtetino.

r

this category, the displaced |)oi'tioa of the seam do&t be found b; crossing the plttne of disruption, and seeking (be shifted portion of the deposit oa the aide towards which that plane is inclined.*

Sabaidence and Draw. — Interesting problems are presented bj the surface subsidence caused by the removal of ooftl in th mine. By means of very accurate levelling, Mr. J. 8. Dixon made a valuable series of observations at Bent Col 1 iery''n' tte" anbject of the subsidence and draw from working the wal ; tlie &oto disclosed upsetting many old rule-of-thumb ideas on th subject. III order to arrive at correct conclusions in an intuiry of tliin kind, the best way is to select a line for a section on the surface, and peg it ofl', or have some other means of fixing kreb that can be tested from time to time.

The line selected at Bent was at right angles to tlie advantung workiugs, and as nearly as possible on the level course of the ooiL Pegs were put in at first every 1 00 feet, and aftei-warda every 50 feet. The Ell coal at this colliery was worked by the pillarimd- stall method until the middle of 1881, when the removal of the pillars was conimenced. It was, however, sometime before tiiis operation reached the line along wliich the section was taken. The excavation was 5 feet 6 inches in height, and the superin- cumbent strata were allowed to fall and fill it up. The strata are of a firm nature, and the surface is mostly boulder clay.

The original level of the surface before the pillars were removed is shown by the figures in the table on the next page. Tfas pillars were removed for a distance of 240 feet bock from the solid coal on January 21, 1882, and no subsidence of the sur&os had ensued. Ou May 27, 1882, tho levels showed the marimttm subsidence to have beeu 1*80 feet at peg 1650, 145 feet back frova the face, and the draw, that is, the disturbance at the surface beyond the point of excavation, 60 feet outwards from a point perpendicularly above the working face. On November 14, lti82, the face was 610 feet fi'om the solid, and the subsidence fi:om the origiual level was as stiown in the table. On April 15, 1883, die face was 750 feet from the solid ; on November 37, 1863, it was lOGO feet distant; and ou October 23, 1884, the removal of the jiillars had been completed for some months, and the face was 1230 feet from the solid. The levels were again

On the dislocatioDi of veios, beda, imd seams, conaalt 3. C. L. Sohmidti Theorie der Vtrechiebungea iUterer (jdiii/f, Frankfurt, ISIO ; C Zimnvermftao, Die WUderaumeHttag verwor/mer HAn', Lri'jer find FiOUf., D&mutAdt, 1828; R. von Camall, KaTflen Ardiiv., vol. 1%,, 1842, p. 3 ; H. Hoefer, OmtT. ZUthr.. 1881., p. IBS, traiwlated Uv R. W. Raymond, Troti". Amtr. ImiI. At. E„ 1882; K. Uannenberg, Urber Tifrirfr/uaffen, Saarbruckuo, 1S8>] O. Koehler, SlOrungeii tiff GUitj/-, Fidlze, uiul tagrr, Leipdf, 1886.

t Tra7iJS. Mining InsC. Scottaiul, vol. vii., 18S6., p. 224.

m

Ej

S'

p

" MINE-SURVeVIKG PnOBLEMS. 281

*tken on Jime 17, 18li5 ; the workinga being in the same position &s they had been for fthoiit a yenr. On December i, 1B85, it waa tbunii that the subsidence had pi-actically ceased, and the draw Imd not altered .

P

Subsidence At Bent Coluery.

fa

OUOIXjU.

Htb Not.,

Slh April,

th Not.. 1S83.

MnlOot.,

nib Jna,

less.

Ism.

... , 0-25

0:15

0-4.)

6fiO

Ms -9

0(50

|]ti4-6

ri8

80*t

ecTo

0'S3

sso

K

075 e

U7f)0

3-H

r

tooo

a -60

lOSO

Oso

2-80 3-52

llfiO

2-93 j 3 -57

6S0-0

3-5e

I2&0

eso-9

1-eo

3M

13S0

1'60

1*50

6tJ0-l

Isso

3-ao

672*8

2-S(j

2-So

2-So

2 So

04S-0

0-m

Sooo

0-04 i 004

Uinb-Bdhvetiitg.

The conclusion arrived at La that aubsideiice from the remoTal of coal in this case attains its masimum towards the centre of the excavated apace, and gradually decreases in each direction. The tnaximnm aubaideuce was 4*00 feet, and the average from peg 1,000 to peg 1,600 was 3*7 6 feet, or 73 and 68 per cent, reapeotively of the height of the excavation. The wave of man- mum subsidence regularly followed the working face at &n average distance back of 186 feet, or 1 foot horizontal for ea<ib feet perpendicular. The permanent lengths of the draw tnty be taken as 100 feet (Nov. li, 1882) on the one side, and 83 feet on the other (Oct 23, lSj84). At these points, the depth to tlis coal was 650 and 646 feet, representing a draw of 1 horiKintal for each 6'5 feet perpendicular, and of 1 horizontal for each T'I8 feet perpendicular respectively.

The coal at Bent, it should be noted, dips at right aogles to the line of section st an inclination of about 1 in 20.

The question is one of great importance to miae-aurveyors in relation to the effect, on the surface, of mineral workings, tnd to the area of ooal that should be left to prevent damage to buildings. It is consequently highly desirable that similar investigations should be made in other coal-fielda,

From a careful study of the subsidence ooourring in the Saxon coal-field, R. H ausae,* of the Zaukeroda Colliery, has arrived some interesting results. The direction of the plane of fracture occurring on the breaking of undermined strata is determined by >the an gle of fractur e — that is, the angle made by the plane of fracture with the bomoutal plane. Then if p ia the angle of fracture, and (3 the dip of the strata, the following equation obtained : —

tan f

1 + cos* iS sin ;3 cos j3

Then, if is equal to 0°, this equation becomes tan — os, and I f 90'; in other words, in horizontal strata the plane of fracture coincides with the line of gravity. When $ 90°, the equation gun becomes tan p O), and p 90° ; that is to say, in vertical strata, the plane of fracture coincides with the line of gravity. By means of the formula, the angle of fracture may be calculated in any case from the dip of the strata. In tiiia way the following reaulta are obtained : —

UpJUUy,* Saecfia. Jaitrbuelt, ISS6, p. 111.

HtB40RTRYI!fO PROBLEMS.

0° then ip

dif w

85' lO*

30'

80" Sc

80*

76° 10"

73-00'

iS"

71' W

6lf

70'Bo'

60*

n'ov

70"

74" 00'

So*

80" 50*

90°

90°00'

I of

w

To bIidw how these theoretical reaulta compare with results ftctu&ll; obtained in practice, the following example may be cited : — For supporting the Siemens' glass works at Uoehlen in Saxony, a safety pillar of IC yards horizontal brt*adth was left, and, in addition to this, the last atall up to that pillar was packed witli gob to a horizontal breadth of 16 yards. Assuming titat a dense gob-packing is compressed to 0'6 of its original volonie by the pressure of the superincumbent strata, the gob-pillar, for purposes of safety, represented a ooat-piUar of 16'0 X 0'(j 9*6 yards in breadth. Oonaequeutly the coal-pillar ad the gob-pillar together had the same eli'ect in supporting the bnildings as a coal- pillar of 16'0 -t- 9 '6 25 6 yorda in breadth. 17 ot with standing the pillars, the suriace was found to have sunk considerably.

The thickness of the coal seam was 4 yards. It dipped 12° towards the west, and had a perpendicular depth from tlie tirface of 180 yards. Oalonlated from this depth and the width of the 25*(i-yard pillar, the angle of fracture p is found to be aa " illows : —

25'6

cotau p

The dip of the strata being 12°, the theoretical formula gives 1 + (cosl2°)

tan p

sin li" ' cos 12°

p 84° 20'

or 3° 20' greater than the result obtained practicaiDy.

The theory of subsidence is ably discussed by Gallon,*

"Lectures on mining delivered at the School of Mines, Paris," by J. Gallon, translated by W, Gnlloway and C, Neve Fter, vol, ii., London, Igdl p. 30*.

S84 UIKK-SUBTKrUTQ.

taya down the following proposition; — If the ooal hu been removed over a certain area, and the space filled up in a kui worked by the methods adopted in Belgium and Nortlieni Prance, the subsidence of the roof on the filUog-up caii* fractures along the perimeter of the area at right angles to tbe plane of stratification. The subsidence of the ground within die cylindrical space indicated by those fractures continue gradiudl; without sensible diminution in amount quite up to the nrftoe, wbatevei may be the depth of the mine.

Tlie effect of subsidence due to co&l workings has been ex' baustively investigated by Mr. 8. R. £ay,* who has dedtictd from many examjiles of modern practice the following empiricit formula for the necessary pillar to be left under normal eoo- ditions. The formula is :- —

in which d denotes the depth in yards, ( the thickness excavated in feet, and r the radius of the support in yards. For exMnple, on applying this formula, it will be found th&t if the depth of the seam is 400 yards and the thickness of the material excavated 4 feet, a pillar of 68 yards radius will, under nonsal conditions, give the necessarjf support.

The Volume Excavated in Open Workings, — At the "My Forster iron ore mine, Putnam County, New York, an in- genious system of measurement has been adopted by Mr. K K. Landis. t The mine is now worked as an open cut to a depth of 430 feet from the surface. The mine was divided into 10-foot squares, and lines were marked by stakes set well back from the edge of the pit. A wire rope was then stretched oyer a lon- tudinal line, and a trolley carrying a steel tape and a plumb-bob was traversed along it. A levelling instrument was set up at the north end, the plumb-line was dro}>ped to the bottom, and the reading of the tape noted, The tape was then wound up until the plumb-bob coincided with the cross-hairs of the level, and the tape was again read. The results of these measurements were plotted on cross-section paper, and the volume excavated in the interval between the monthly measurements was calca- lated, the areas on the section being measured by a platiimetcr.

' Min. Proc. Imt. O.B., vol. ., 1809, p. Hi. The subject hu slao been dealt with by_J. Diokinagn, J'raiu. MaHehenttr (Jioi. Soe., voL rxv., 1S98, p. 583; by W. Gallowdj, Traiig, S. IVala InU. Bng,, ToL xs., 189, p. 304; and by C. Menzel, Saecha. Jahrhueh, 18S8, p. 147.

iJoum. Frariklia ImL, vol, cl„ IflOO, p. 223.

Vine Plans.

CHAPTER XVIIl.

MlWK PlASJS.

Plsin and SectiOD, — For the representation of mine woi'kiiig plan and a vertical section are required. The plan is a rejection of the mine working! on a horizontal plane ; the Btion is a projection of the worfcingB on a plane running Icl to the main longitudinal direction of the mine. With Dmplicated and irregular mines, one section is not sufficient. In ich a case, several sections have to be made in given directions, (a.) Metalliferous Mines. — Four drawings are necessary in ler to represent a metalliferous mine — (1) the ground plan ; S) the working plan ; (3) a longitudinal section ; (4) a tranaverse "ection.

The ground plan gives a geueral representation of the whole concession. It may be on a scale of about 3 chains to the inch, and on it the boundary of the property of every land owner ibould be distinctly marked, and aU the lodes indicated, The working plan gives a geneil view of the underground workings, as they would be seen from above if the ground was transparent. This plan should be drawn on a large scale, 4, 5, 8, and 10- fathoras to the inch being scales used for the purpose. The longitudinal section is drawn on the supposition that a section of the ground is cut away, and that a side view of the mine is exposed. All the vertical shafts, the stopes, the dip of the ore- coorses, and the surface-line with elevations of the mine buildings, will be correctly shown. The levels, diagonal shafts, and winea will have a false appearance. The levels will appear perfectly straight however crooked their course may be, the diagonal -s and winzes will appear perpentLicular, and the cross-euta will be represented as open doorways. The transverse section is of great value, as it shows the dip of tlie ore-couraes. In the tranaverse section, the view ia taken at one end of the workings, at right angles to the longitudinal section. Thus, the inclination of the shafts and winzett sunk on the lode is shown. The levels driven on the lode will be represented as open doorways ; the cross-cuts are correctly shown ; and all variations in the dip of the lode may be aeen from the surface to th bottom of the minei

Fig 90. — PUii adA LoDitndinal Sctioti of a MeUl>Mina.

MINE PLAHa.

\VTien the lode Is very , aa at tlie Corniali mines of Wheal Ikne and Wheal Kitty, the section is made along the lode. Tn

this way a true idea is glyen

' ' an erroneous one with re-

gard to depth. This method of projecting the section is neoeaaary to en- able the ground stoped away to be shown, as when the lode ia so very flat, the back of one level in a vertical section would touch the floor of the next As a rule, lodes are so vertical that a perpendi- cular plane may be taken for the section.

The workings of a metal- liferous mine are repre- sented in Figs. 90, 91, on a scale of about 30 fathoms to the inch. The mine htta an adit-level and below that, 10-, 20-, 30-, 40-, and 60-futhom levels. The adit is north of the shaft. The engine shaft contains the pumps which lift the water from the sump or lowest point of the shaft to the adit-level, which comes out to the surface on the adjacent hill side. This shaft was sunk vertically to intersect the lode at the lO-fathom level, a croas-cut being driven to the adit. Then, instead of con- tinuine vertically, necessitating tb driving of croaa-cuts to the lode, the shaft follows the latter. The shaded portions shown ia the longitudinal section represent the prDJection of the ore masses, removed by stoping. In practice, such portions are not generally shaded butcoloured — f urple for tin, green for co[)per, blue for lead, 4tc. Between the 10- and 20-fathom levels a mistake arose, the winze and rise did not meet owing to an error of the dialler.

It will be found advisable to colour all the levels on one lodeths same tint Formerly it was the general practice to colour each level a different colour, the aditlevel being blue, and the leveU below it red, green, yellow, violet, and Vu uccawswsa.

91. — Transverse Section.

MtNE-BURTIYINO.

No acale la prescribed hy l&w for the plans of the Britiih metalliferoua mines. The variety of scales used presents grtat difficttlties with regard to the comparison of the plans of different neighbouring mines. In many districts, the plans are prepared in a slovenly and nnsatlB&ctory manner. This is notably tii case in the Derbyshire lead mines. There, according to Sir. A. H. Stokes, H.M. Inspector of Mines for that district, ths majority of the mines have no plans whatever. Even at the larger mines which have plana, they are very roughly drawn and rarely indicate the extent to which the ore has been worked. The variable width of the levels is not shown, the latter being represented by a coloured line. The position of the best and most profitable parts of the mine, that is, the width to irldcii the ore has been extracted, ia shown as an ordinary narrow heading. In fact, the plans are not true representations of the mine, but merely represent the length of underground tramways. Sections of the mine are seldom made.

(6.) Collier; Plans.— By the Coal Mines Begiilation Acta, 1887 and 1896, the owner, agent, or manager of every colliery is eoifl- pelled to keep, in the oSice at the mine, an accurate plan of ths workings of the mine up to a date not mure than three months previously, and the general direction and rate of dip of the strata, together with a section of the strata sunk through, or if that be not reasonably practicable, & statement ot the depth of the shaft, with a section of the seam. Every such plan must be on a sals not less than that of the Ordnance Survey of 25 inches to the mile. The plan must also show the position of tlie workings with regard to the surface, and the position, extension, and direction of every known fault or dislocation of the seam with ita vertical throw.

Representing collieries on a plan is a much more simple operation than representing metaUiferous mines. The wot)cingi are projected on a horizontal plane. The coal withdrawn is coloured dark, and the direction of the air-current indicated by arrows. The intake air-current is coloured blue, and the return air-current red. The water-courses may be coloured green, drowned waste also green, and faults bright red shaded off on the dip. Main doors may be indicated by a D in blue, main stoppings by blue lines, and caution-boards by a in red. The heights of the different points above the level of the shaft-bottom should be shown in red figiires, and those below the level of the shaft-bottom in blue. The signs shown in Fig. 92 are employed on colliery plans.

When two or more seams are worked one above the other, and are shown on the same plan, they are distingoished by means of colour.

(

d

JiL

S89

rr Piffi-fM m O

//ejtpiftff „ . 11_

fifffiinUrt -

Fig. 93.

Admirable illuatrationfl of the manoer ia which colliery plana honld be executed are afl'orded by the plans which accompany the annual reports of H.M. Inspectors of Mines.

Surface Plans. — The surface plan of a colliery or metalliferous mine requires great diatinctiieBS of detail. If the scale or abont 23 inobes to the mile in adopted, the conTentional signs used on the maps of the Ordnance Survey should be employed. If the scale is larger, care must be taken to give the convontional signs such dimensions as will accord with the scale of the plan. Buildings are coloured crimson lake for houses, and dark gi'ey (a light wash of Indian ink) for outbuildings. The roine buildings may be distinguished from other buildings shown on the plan by having a darker tint of red. lu representing objects on the plan, their natural colours are sometimes adhered toj in other cases a conventional colour is used. Thus, tot gt.'a \a.tA, 'a. Wv

MINE-SURYSYISa

tint of green (Hooker's No, I) is emploved ; it is made of gm. boge ajid indign. Cultivated l&nd is represented liy flat lint vi burnt Bienna, Adjoining fields are sUglitly varied in tint, furrows sometimes btjing Indicated by coloured strips. Lakes and rivers are coloured tight blue (oob&lt), with a darker tint on each nde. MariitieB are represented by tbe blue of water, with bori- sontal B]>otB of grass green. Roads are coloured with a light wash of bamt sienna, or yellow ochre. Hedges are represented by green dots for bushes, brick walla by a red lino, and woodea fences by lines of a neutral tint. In large scale plans, the Cornish hedge, some 6 feet in width, is shown by two linus the true distance apart, with a wash of neutral tint along each sida In all cases the shadow is put in. The boundaries of the mine concession are indicated by strips of colour.

When the undergroond workings are drawn on the surface- plan, in the latter there should be no more colouring than neoiJ sary. It will be found sufficient to colour the roads, buUqlH

(c.) American Collier; Plaai, — In Pennsylvania the law require ail anthracite colliery owners to prepare maps of alt workiiigs on a scale of ICK) feet to an inch for the use of the mine-inspector. This scale is rather too large for convenient use, and consequently most of the working maps used for reference are constructed on a scale of 200 or 300 feet to the inch. These mapa generally show all the important surface features, buildings, streams, roads, bind railwHys, as well as the underground workings. The latter are commonly drawn in blue, red, or green ink. When several beds are worked, the workings are shown by different colours a device especially necessary when the workings on one seam are above or below those opened on another bed. In addition to the general map showing all the workings, separate maps showing the workings on each seam are usually luade. The siirvey-liiies are plotted with a vernier-protractor, or a protractor of very large sisce, and the results checked by latitude and departure cal- cutations. Tracings or blue-prints of the workings are supplied from time to time to the viewer. When notin nse the plana are stored in large tire-proof vaults. The survey-notes arc copied into office record books for future reference. With the exception of the work done by the U.S. Coast Survey, no other surveys in America can compare in accuracy with those of the anthracite mines.

The sharp foldings of the carboniferous strata of the an- thracite region of Pennsylvania, have made the study of tlie structural geology of that region one encompassed with great diificul ties. The necessity of Vv%vvn\ bot&q dA&iibe informatioo

Lt,

regfkrdmg the structure of the cqilI beds, before aucceimfui luiamg o|>eralionB can be proaecuted, induced Mr. C. A. Asliburner* to introduce in 1880 new method of repreaenting on aur&ce maps the underground Btructure of the coal beds, from whicli could be ascertaiiied the aitoation of the outcrops of the beds, the position of the ajnclinal and anticlinal axes, tlieir depths io special coal beds below the surface of the ground, and the dip of the bed from the crest of the uotLclinal to the bottom of the SjrnoUnftl. This was accomplished by contourcurve lines drawn aiuiig the door of the coal beds. The contours were obtained [>m eleyBttons determined in the areas where the coal beds were mined, and from exploring the shafts, bore-holes, and surface ex[>oswres in the areas where no extensive mining hud been done. In areas where no utidorgiound e>X|doFation had been made, the positions of the contours along the J]uors of the coal beds were deduced from surface exposures and an extension of the structure from explored areas.

Importance of Coirect Bectiona. — The im- portance of keeping an accurate section of a mine is shown b; a serious accident that occurred at Pantgwyn mine. On February 17, 1886, while three men were at work sinking a new shaft, water broke in suddenly and unexpectedly, and drowned them. The exact nature of the casualty will be beat understood by means of Fig. 93, representing a cross-section of the mine. ABC is the old pumping and winding shaft, sunk perpendicularly for the first 20 fathoms, and then following the dip of the vein. In la84, owing to the stoppage of some neighbouring mines, the pumping engine at Pantgwyn was unable to cope with the water, which gradually tilled the workings. The ownurs then resolved to sink a new perpendicular shaft D E, and provide it with more powerful pumping machinery. It was intended that the new shaft should striku the Pantgwyn lode in virgin ground below any of the existing workings, which were to be drained gradually by percolation of the water through the porous vein- stone. In February, 1886, the new shaft had reached a perfjcn- liicular liepth of 62 fathoms from the suri'ace. The old shaft was then supposed to be in the position indicated by th dotted

J'rans, .inter. Itut, M.H., vol. is,. 1881, 50,

292 M1Se-8U8Veting.

lines, and the distance between the two ahafia at E was reckonad to be 40 feet. Ou exaiuiniiig the shaft as aooa as it had been cleai'ed out, the Oovernroent Inspector of Mines, Sir C. Le Neye Foster, found that the thickness of the barrier was only 9 feet ; the section of the mine being incorrect, It naturally appeared to him very strange that such an error sLouid have been made in a small survey of recent date, with two shafia leas than 50 yards apart at the surface, until he ascertained the inclina- tion of the shaft had never been measured below the iO&thoDi level. The drivages at the S5-fathoni level and the 70-£tlioni level had been deliberately laid down on the plan just as if the shaft had been correctly dialled. The primary cause of tli accident was, without doubt, the want of a con-ect survey. In reporting on this accident. Sir Le Neve Foster points out specially that it was not a case of approaching old workings, wliow exact position was unknown, or imperfectly known, owing to the abandonment having taken place before there wu any statutory obligation aa regards the keeping of plana ; but here was a new shaft, started by the same company and the same agent, within 50 yards of their own workings, which had discontinued only a few months before.

nniformity of Scale aod Conventional Signs. — In Belgium and in France the liiw demands that all mine plans Bhall be lMi<l down on a scale of 1 : 1000. The surface plan is prepared on tlie same scale as that of the iindergi-ound workings. In Prussia, the scale imposed varies in the different mining districts htiia 1 ; 500 for metalliferous mines up to 1 ; 1600 for collieries. In Atistrui, the scale for mine plans is usually 1 : 720. For oom* parifion, it may be added that the scale for colliery plans in Great Britain must not be less than 1 : 2S00, PreTions to 1888 the smallest scale allowed was 1 : 1594. In America, the scale imposed in Peaasylvania for the anthracite mines is 1 : 1300.

I The usual scale prescribed in the various States for the prelimi- nary plan of a metalliferous mine-claim is I : 2400. It is desirable to have not only a uniform scale, but also uni- formity in the conventional signs used in the plans. With this aim, typical mine plana have been published in Belgium by Mr. J. ran Scherpenzeel-Thim ; in Germany by Professor Schmith, of the Freiberg School of Mines ; in Hungary by Mr. P6oh, the director of the Sohemnitz mines, and in Sweden by Mr. G. Nor- denstrdm. In Prussia the taw demands uniformity in tlie drawing of mine plans, and special rules are issued by the Oovem- ment for the purpose. Unfortunately, there is a great want of nniformity in British mine plans in the various mining districts. If plans were always drawn B,ftic tVie Ba.m model it is evident

(

Mine Plans. 293

that the working would be Dioru uniforui, and that each new mine- manager would be enabled to decipher more readily his predeceasor'a work. The owners, and other persons interested in niineral property, would thus be able to gain a clear understand- ing of the plans, and successive generations would profit by the stores of information thus recorded. Uniformity of system in the ptaos, too, greatly facilitates the construction of general mapa of mining districts.

Preservation of Plans.— Bo long ago as 1797 the importance of a systematic mapping of mines was urged at Newcastle by Mr. Thomas, and since that date the value of such a system Itai frequently been dwelt upon for the purpose of dirainishing the probability of the reourrence of fatal accidents in collieries, and of prolonging the duration of the coal resources of the TTnited Kingdom. It is always a matter of regret that faithful records of all underground work iu important mining disti'icts have not been carefully preserved. The importance of the preservation of such records was strongly urged by Mr. T. Sopwith in 1844. In tlie United Kingdom plans of all abandoned mines are now carefully preserved. The Coal Mines Regulation Acts (1867 and 1896) require that where any mine or seam is abandoned, the owner of the mine or seam at the time of its abandonment Bhall, within three months after the abandonment, send to a Secretary of State—

1. An accurate plan of the mine or seam, being either the original working plan or an accurate copy thereof, made by a competent draftsman, and showing —

I (a) The boundaries of the workings of the mine or seam, including not only the working faces but also all headings in advance thereof, up to the time of the abiindonment ; (b) The pillars of coal or other mineral remaining on worked; (c) The position, direction, and extent of every known fettlt or dislocation of the aeauj with its vertical throw; (d) The position of the workings with regard to the surface boundary ; (e) The general direction and rate of dtp of the strata ; and A statement of the depth of the shaft from the surface to the seam abandoned ; and 2. A section of the strata sunk through, or, If that is not leasonably practicable, a statement of the depth of the ahaffc ith a section of the seam.

k

Every such ptau must be on a scaAe ot not \es& VaaJii ctV

MINE-BOaVBTIMa

the Ordnance Survej of 25 inches to the mile, or on the &tle as tlie plan used at the mine at the time of ita ah&ndan- ment, and it accuracy must be certified, so far as is reasonably pmctitable, by a surveyor or other person approved ia that behalf by an inspector of mines.

At the Home Office the mine plana are preserved, rolled ia cylindrical lacquered tin cases, closed with a lid, on which & number is jjaiuted. The cases are placed side by side on ahelvea, so that their numbers can be at once seen. At Freiberg a similar plan is adopted. This method is very onmbrons. A better method is to keep the plans without being rolled or folded in portfolios. At Przibrara, in Bohf>mia, the plans are kept ia k neat of drawers, each drawer forming the frame of a plan placed between two sheets of glass.

Sopwith entirely dispensed with the large and unwieldy rolls of piiper on which the workings of collieries and metallfierous mines are usually pi'ojecbed, by drawing the plans on impeiial drawing paper. Each sheet was divided into squares of inchea, forming an area of 400 square inches. An inch margin was left at the top and bottom of the sheet, and 3 inches at one aide for binding a series of plans into a volume. At the other side a margin of 1 inch was left, with a column 5 inches wide for the insertion of written descriptions, scales, titles, references, and other explanntions of value as permanent records, with which the plan itself ought to be encumbered as little as possible. In this wny, plans are kept perfectly fiat, and their accuracy is not affected by the tensiou of the [>aper caused by frequent rolling. Rolled plans, on the other hand, soon become so cvaoked and defaced, as greatly to impair the cleamesa and accuracy of the plotting, whUst their bulk is a hindrance to frefjuent inswetion and to the plotting of new workings.

Practical Hints for ConBtmctmg l£iie FlanB. — The paper on

which the plan is drawn should be the beat hard drawing-paper.

If plans are requii'ed on invass, the paper should be mounted

carefully dried before the plan is begun, in order that the

contraction in drying may not alter the lines. To mount tlie

paper, a piece of linen or calico, rather larger than the plan ia

required to be, is placed on a tilted table with a Dat surface. A

strip, It inch wide, at the edges is glued, and pressed on the

table, the linen being at the same time pulled tight. With large

Ltbeets, two person a pulling at opposite aides are required. The

paper is then placed with its rignt side on the linen. Its back

IB then pasted until the paper becomes quite limp with the

moisture soaked in, Tlie vaper is lifted Up cai>efully. and

[ilaBeii with the pasted side on Xmatv, wx&.'giBawi.Sm'ov vk*

atlNE PLAHS.

Butre to the edges. The rubbing-down may be done witli the liand or with a cloth; in either caae u ebeet of cleau paper is inter- posed. Paper thus mounted may be drawn upon nearly as well when stretched on a board. To give an edge for the T-square, if required, a atraight edge may bo temporarily nailed on.

If Bev-eral sheets of drawing-paper have to he joined end to end, the edges to be joined should be reduoed to half their thickness. This may Im done with a knife or with sand-paper.

In mounting and joining drawings, a. great deal depends on the paate employed. It muat be sufficiently liquid and contain no lumps. To prepare it, a eimall portion of good starch is com* pletely dissolved in as small a quantity aa possible of cold water, and to this solution boiling water is poured with continual stirring of the starch'paste thus formed.

Plans may be varnished by applying several coats of isinglass aize, allowing each to dry before applying the next, and finishing with a ooat of Canada balsaiu diluted with oil of turpentine.

The tead-pencil used for plan-drawing should not be very hard nor very soft. The degree of liardness marked H H is the most Buitable. The quality may be tested by holding the point in a candle-flame. Good pencils suffer no change in this experiment, whilst bad teadti burn away to ash with a sulphurous odour. It is best to use two pencils ; one with a flat or chisel point for line drawing, and one with a point in the shape of a perfectly acute cone for sketching.

Short lines should be drawn with the roUing parallel ruler. The plotting scale should never be used for this purpose. Straight edges, used for drawing long lines, may be tested by drawing a line along the edge of the ruler, then laying the ruler on the other side of the line, with the ends exactly it, and drawing a line ia the same manner. If the straight-edge is true, these lines will exactly coincide ; if not, the error ia rendered apparent by being doubled.

For inkiug-in plans, Indian ink is always employed, as it does not corrode the steel points of the instrument and preserves its colour unchrtnged. The best ink, as imported from China, has a tinely granular texture and a conchoidal iridescent fnictura. When mbhed with water on a slab, it is not gritty, and smells like musk. Inferior ink smells like camphor, and the worst ink smells like soot and glue. The latter is useless for plan-drawing, as it runs when other colours are passed over it. Indian ink is prepared for use by rubbing it with water on a perfectly smooth slab or saucer. It should only be rubbed backwards and forwards, as, for some unexplained reason, rubbing it round and round hardens it. The preparation must be \iftAft<iV\ Vwje*.*,

h.

296 MlNB-aURVKTINO.

but after it has become black, further mixing rendect it

Tiscoiis.

For removing pencil lines and for cleaning the paper, iiatin india-rubber, vulcanised india-rubber, or stale brrad maj he employed.

The drawing instruments abould be of the best workmanship as accurate resulta cannot be obtained with imperfect instm- menta. Very few instruments are required, a pair of com with a Bteel drawing-pen and a pencil-leg to fit, and a dra- pen being all that is required for plan-drawing. Bow-oom[ are unnecessary. A pair of turn-in compasses constitutes of instruments sufficient for most mining purposes.

The best compasses are those which are sector-jointed. Tba greatest caro should be taken to clean steel drawing-pens erery time they are put away, and common ink should never be osed in them. It will be found desirable to have two of these instni- nients, one for fine lines and another for thick lines. When th proper opening for fine lines has been found, it is thus unneces- sary to change it, as the jeu can always be cleaned by passing a piece of paper between the nibs.

The most useful colours for mine plans are — for surface boun- daries and underground workings, crimson lake, indigo, cobalt, Prussian blue, burnt sienna, gamboge. Purple, green, and other tints may be obtained by mixing. Opaque colours, such as ver- milion, red lead, and ultramarine, should be avoided. The end of the cake of colour is moistened, and rubbed with a drop of water. This is afterwards diluted to the proper tint. The art of taying-on a flat tint consists in allowing the coloured water to flow uniformly over the paper. This is done by applying, with a large camel's-hair brush, kept always moderately full, a tint across the upper part of the portion of the plau to be coloured, and by continuing it downwards from right to left and left to right alternately, never letting the edge dry. The drawing- board should be inclined towards the draughtsman, and the paper is moistened with water before the colour is applied if the portion to be coloured is irregular. A little prepared ojt-gall used with the colours obviates tlie difliculty which often arises from the smoothness or greasineas of the paper. It b, however, almost impossible to use it too sparingly. In drawing the outlines, car should be taken that there is always a piece of clean paper between the hand and the drawing, in order to prevent any gteasiness of the paper.

Neat and distinct lettering is very essential in all plana It frequently happens that a perfectly accurate plan is absolutely spoiled by a badly printed title. The formation of letters

Uine Flans.

requires long practice. lines drawn in pencil to be afterwards erased, will be found usefui as guides. No style of lettering more effective than the Egyptian or block letters, in which every line is of the same width. By the aid of copper stencil plates a great saving of time is effected. The lettering should be in line* parallel to the bottom oS" the plan ; except the names of lodes, rivers, and roads, of which the i2;eneral course should be followed.

Tlie plan may be enclosed in a rectangle by a border, which ntnally consists of two parallel lines, one lieavy and the other finer. The simplest border is the beat, and time should not be wasted over ornamental comere to embellish the plan.

The plan is usually drawn ao that the top of the paper repre- eenta the north. Whether this is the case or not, a ineridian- liue should always be drawn. Tlie north ]ioint is sometimes itrstwn in the form of an ornamental star. When it represents the magnetic meridian, the abbreviation niag. nier., with the date and declination, should be written by the aide of it. A scale should invariably be drawn on the plan, with a description of it written above.

CopyiDg Plans. — Plana may be copied by means of geometrical methods employed to determine the points of the plan bj intersections or by co-ordinates. The operations are, however, very tedious. In preference to geometrical methods, there are several mechanical methods which should be employed.

1. Copying by Tracing. — A targe sheet of glass is fixed in a wooden frame, and inclined at an angle of 25° before a window or a lamp. The plan to be copied is covered with drawing-paper, and placed on the pane of glass. The lines of the original can thus be traced with facility.

2. Copying on Trocing-Paper. — A sheet of tracing-paper or traeing-clotli is fastened with drawing-pins over the plan to be opied. The lines are then copied in indian ink, a set square being used for ruling the straight lines. The tracing is mounted on white paper, and colour is tlien applied. If tracing-cloth ia used, it will be found advisable to apply the colour to the back of the tracing. In copying plans on tracing-cloth, considerable tlifficulty is experienced, owing to the greasy nature of the surface in getting tlie ink to run freely. This can t-asily be obviated by sprinkling the surface of the cloth with finely- powdered chalk or pipeclay.

3. Copying by Transfer,— The transfer-paper used for this purpose, is made of very thin , one side of which ia rubbed with black-lead powder, smoothly spread with a cotton rajj. The transfer-paper is placed with its prepai-ed face down-

298 MlNB-JSDBTBItNO.

wards on the cle&n paper. Over It is placed the plaa to bv L-Ltpied, and all the luics are gone over with ao agate point, or otiier bluDt-{>oiuted instriiment. If the original caanot be treated in thu way, a tracing of it must be employed. In this way, a copy of the original plan is obtained in black lines, which may be afterwards inked in.

4. Prickiug-Throngli.— lo this method, the clean paper is fixed on a drawing hoard, and the plan over it. All the angular points in the latter are then pricked through with a very fine needle. The points obtained on the clean paper in this way are joined up, and the plan inked in.

5. Copying by Photography. — Photographic prooeBses present the advantages of rapidity and fidelity of reproduction. The apparatus necessary includes thin bluish tracing-paper, printing frames of thick plate-glass hinged at the back, with a piece of thick soft felt for equalising the pressure exerted by the springs or clamps, a developing bath, non-actinic arrangements (yellow window blinds by day, and a ruby lantern by night), and cases for Btorin;r paper. Drawings on ordinary paper may be copied if exposed to light sufficiently long. Instead of ipriDst or clamps on the printing frame, use may be made of Streeti pneumatic frame, with an air cushion, inflated by blowing, press- ing uniformly over the whole surface of the frame.

The process most commonly used is the cyanotype sensitising process, invented by Sir John Heraohel. White lines are produced on a blue ground with a solution of 140 grains of ferric ammonic citrate, 120 grains of potassic ferri-cyanide and 2 0£. of distilled water. The solution should be kept in a stone- ware vessel. This process depends upon the actinic action of light reducing the ferric salts to the ferrous state under certain conditions, one of which is the presence of organic matter, such as the size contained in the paper. The ferrous salt then ooin- bines with the potassic salt to form insoluble Prussian blue.

In these processes a sheet of paper, a little larger than the tracing to be copied, is fixed on a board, and with a sponge a thin unifornn coating of the liquid is applied as rapidly as possible, and allowed to stand in non-actinic light until perfectly dry. The tracing is placed against the glass of the printing frame, and at the back of the tracing the prepared sheet is placed. The frame Is then exposed to light untU the prepared sheet becomes of a dark olive-green colour. The sheet ia then removed from the frame, and thoroughly washed in pure water for a few minutes until it assumes the lequired shade of blue.

On the Ordnance Survey, Willis' platinotype process is em- phyed. It gives white 's ou a-VWV omtA, mvI baaed

Mine Plak8.

be reducing action of a ferrous salt, when exposed to actinic light, on platinum cbloritie. The seusitisitig solution is com- posed of 60 gr-iiLQS of potiBsic-platiDouH chloride, 60 grains of ferric oxal&te, and 1 oz. of water. The exposure lasts until the paper ikcquires a dull orange tint. It is then developed in non- actinic light by floating it for 4 seconds in a solution of 130 grains of potaasic oxalate and 1 os. of water at a temperature of 150* to 200° F, When properly developed, the print is washed for 10 minutes in 1 part of hydrochloric acid with 60 parts of watr, and finally washed iti relays of fresh water, for 15 minutes,*

Reducing and £nlargiiig Plans. — A plan may be reduced or enlarged, by tahing from the original a fraction of the dimensions required. For this purpose proportional compasses, or scales, may be employed. A very rapid method of reducing or en- larging plana consists iu coveiiug the original with a network of quares, and the copy with a network of equares having their sides smaller than those of the original squares in the proportion in which the plan is to be reduced. The details may then be sketched in by the eye. This method may also be used for oop'ing plana on the same scute.

Flans may be rednoed by mechanism by means of instrnments called the fiantograph and eidograph The pantograph ia made in various forms. It always consists esaentially of four brass rulers, E D, D B, FG, and G 0, Fig. 94, jointed together at P, D, O, and G, ao as to form a parallelogram. The two atdcs D and O F are extended to double their length. The side F G and the branch F E are marked from D with successive divisions, P P being to D F always in the ratio of F A to D T. Small sockete for holding a pencil 'r tracing point are placed at P and T. The pidnt A is made the centre of motion and rests on a fulcrum weight. From the property of similar triangles, the three points A, P, and T must range in the same straight line, shown by the dotted line PAT, which is divided at A in the ratio required Thus, whUe the point T is moved over the lines of the plan, the point P will trace out a similar figure reduced in the }troportion of T A to A P or of D F to F P, the proportion required.

The eidograph is more complicated in construction. Although not BO frequently used as the pantograph, it ia superior to that

Eight other processes (ur the ctint<: copyiug of eDgineering drawings are deaoribed by B. H. Tbwaito, ;Vtn, Frac. IM. CS., vol. Ixxxvi,, 1886, p. 312, At the Tmuuiuck mine the plans are iihottujraYiKed byotij wvissSii, A coalinuout rccotd is tliiis utitJtincd with p\i!>iv8 (A cow6\VLtT\V %vi.

Uine'Sorvetino.

instroment, within the range of its working power*, irhiel) I he conaidei'ed to be limited to reducing between tbe full i " the original nud one-third of the size. Its great merit ts tint within its range it reduces aouurDtel}* in all proportionB ; far inatance, it will reduce in the proportion of d to 2-5 rdilr u 1 to 2.'

Plans may be enlarged by imy of the methoiLx given for reducing tliem. It ie, however, always better to mako a fheab pjun froni the original notes.

Isometric FIbus of Mines. — The kind of drawing adoptnl ibr representing the interior of mines, and the vertioal flarfaeoi of sections of strata, is that which suppoRes the eye of th* obaemn' to be placed in a direction exactly peqtendicu lar to erery pTt cl the plane represented. In this way, two drawings are neoeaaary— the ground plan and section. By means of isometric proJeiotiMi,B these drawings may be embodied in one, in which all t4i ILnMef the projection muy be nieaswred by a uniform scale.

A solid body, the chief planes of which are at right aagJei, Uir cube for instance, is to be so placed that the three planes whid) meet together at one corner are eqvially inclined to tLo hoci- zontal plane, that is the plane of projection. Tlio thre linsi which meet at that comer will then be projected so as to tarm i three equal angles of 120* each, and will be the plans nf tbel three edges of the cube. The piftns of the oppo? ill

bo parallel to these, and hence it follows that in iaoi: i

tioQ all angles which are iu reality right angles are projeotd iawl angles of 120' or GO",

In making an isometric plan of a mine, three iinoa mual lint be drawn, making angles of 1 20° with one another, for the plans of three edges of the solid, in which it is imagined that Uie mine ia enclosed. An isometric scale must then bo oonstmoUd, 01.1 that the isometric lengths of the required edges mmj be fovuid. When found, these are measured on the lines drawn from their ]>lAn6, and the drawing is completed by parallnla.

It is known that the relation of a line to its isutu- ic-

tion is as to 2. To construct an isometric sec . nea

must therefore bo drawn in this ratio. For this purpute', m bae 1 unit in length is taken, and at one end of it a perpendicular is erected of the same length, and the ends joioed. The hyno- thenuso of this right-angled triangle will repnwM-it J2 (Euclid I., 47). If from one end of this line reprmen' -n-

dioular 1 unit in length is erunted, and this Ir: , ' 't

(he liyjiothenuae will repreaeut 3. Two lintts arc thus oli-

A (uU drauHptlon of lhi iastnimeot civen in W. V, j ilalhtmaticai brtixeimj InMlrumnU; LonduB, IWX), p. ISilL

Hinc Plan'S.

30]

ined representiiig and in the required relatioa for the

le, and if the real lengths of the edges be nieRsnred along /3

perpendiculars dropped from their ends to J2, the parts

hereby intercepted will be the iaonietric plana of the required

In making an iaometrio plan of a mine, it is desirable that a and south line may form one side of the supposed isometric ju&re that regulates the drawing, the cross-lines being of course vust and vest. The survey must be plotted by means of the calcalated latitudes and departures, the distances being set off along the edges of isometric squares. This method is of great Talue for elucidating questions of stratigraphy and for solving problems relating to the intersection of lodes. The necessity of referring every object to an isometric plane, however, renders its application to all the minute details of extensive subterranean workings not only tedious and difficult, but also less explanatory than the ground plana and sections in common use.*

Relief-Flans and Mine Models, — Instead of use being made of isometric projection for representing the three dimensions of mine-'WOTkings on a plan, it is frequently necessary to construct a relief-plan or model of wood, plaster, glass, or wire.

When a plastic material, such as clay, wax, or putty, is used, metal or wooden pins are driven into the base or level datum plane of wood, the top of the pins giving the elevations required. A contour plan, of the same horizontal scale as that selected for the model, is first spread upon the base-board. The pins are then driven firmly through the contour lines into the board, the tops left standing at a sufficient distance from the latter, to represent the height of the various contour linefl, according to the vertical scale adopted for the model. After the pins are all properly set, the plastic material is worked into position over and thoroughly covering the pins. This process was employed in the construc- tion of a model, exhibited at the Paris Exhibition of 1878, repre- senting the No. 8 seam of the Loire collieries, which is intersected by an inextricable network of faults of diiTerent ages. The model was constructed for the instruction of mine-deputies, who find it difficult to follow the dislocation caused by these faults, mora especially the dislocations of faults by faults of different age.

This method was also employed by Mr. C, A. Aahburner in the construction of an interesting model of the Panther Creek Coal Basin, Pennsylvania, showing the shape of the floor of the bed. After the construction of contours in explored areas, tho most important aid to the determination of the geological atruc-

Some excellent isometric plans o( mines are given in T. 3opwitli's Treat'iK on Itunuinctii Druviittg, Loadon, 2a& ed., 1E13S.

UlNE-SCBTBTINO.

ture of the coal beds in areas where surface expoeures cannot be obtained, is the oonstructioa of a model with the vertic&l and hon- Eontal S(les the same. The &rat area so mapped in PeuiiBylTuuk was the Panther Creek BaaLn, one of the most complicated buim of the anthracite district of that State. Manj of the difScnltiei were not understood until a model was made of the floor of the Mammoth cool bed, the thickest and most valuable bed mined in Pennsylvania. A map was first made on a scale of SOO feet to the inch, upon which contour lines were showii along the floor of the Mammoth bed, 50 feet rertically apart, in the areas worked and eiiplored. In the areas included between the two clasMi, theoretical contour lines were drawn on the map, in aooordanos with the dip of the exposed strata. Thus, the En&l model, mtA in wood and wax, not only formed a grajhic representation of the structure of the strata in a highly plicated district, but also proved of great value in the definition of its geological structure, and in the deduction of many conolusions affecting the amount of coal contained in this coal basin, and the proper methods ta pursue in its ultimate mining.

The method adopted by Mr. T, Sop with in the oonstniction of his well-known models was as foUows : — A square representing a portion of the mining district, one miie in eactent, is divided into 64 squares by parallel lines a fiirloug apart. Sections along tha eighteen lines are drawn and out out in pasteboard or in thin plates of copper. These are then joined crosswaya by half- lapping, that is, by cutting each section half-way down, where it crosses another section cut in the same way on the other edge. The model of hollow squares thus formed is placed on a ple sur&oe, and the spaces are filled in with wood or plaster, carred or moulded, so as to represent the surface. The model of )>art of the lead-mining district of Alston Moor, in Cumberland, exhibited in the Museum of Practical Geology, in Loudon, waa constructed by this method by Mr. Sop with. The model shows the thick- ness and dip of the limestone, sandstone, and day beds. The mineral veins are seen on the aides of the model dipping in nearly a vertical direction through the various strata.

Probably the best method of oonstruoting relief plans is that adopted by Mr. M. Moulton In 1876 for a map of the State of New Hampshire. The map was 16 feet long, the highest eleva- tion being inches above the datum. From copy of the map of the State on traoing-cloth, the datum sea-level line and tha contour line next above it were transferred through the cloth on to a layer of wood, 1 inch in thickness, of the same si as the map. The outside line was drawn in blue and the inside in red.

I The outer contour was then out vouixd with a fret-saw,

ItlNE PLANS,

k.

breaking off the wood outside tho sea-level line. The petiestal OD which the map was to be fijced then received the first layer of wood. The next layer was then prepared for sawing, as in the firnt case, the outside line beiag the tirst 600-foot contour and the inside or red lioe the next above. This having been cut ont with the saw, it was nailed and glued to the first layer, its position being fixed by tlie red line on the latter. Throughout the work the red lines seiTed aa guides by which each successive layer was properly placed. After three layers were fixed, the steps were carved off to produce amooth slopes at angles wirrea- pouding to those of the map. Each successive group of three layers was treated in the same way,

A complet-e view of the nature of a mineral vein and of the excavstionB upon it, is given by a model constructed by Mr. T, B Jordan, in the Museum of Practical Geology. The workings of each sucoesaive stage of 10 fathoms, are laid out on a scale of 10 fathoms to the inch on a horizontal frame of liglit wires crossing at intervals representing 10 fathoms, and tlia portions of che vein which have been worked between the levels are shown in their true position. Honce, on looking down from above, the eye may trace all the bendings of the lode, and can appreciate the comparative richness and poverty of different parts. The model represents the Holm bush mine, in Com wall, a mine of a oomplieated character from the occurrence of work- ings on cross-courses as weJl as on lodes. The excavations made Are represented in colours, while the solid ground is left blank.

The workings on each vein are distinguished by a special colour. Although affording a perfect view of the general ar- ingement of a mine, this method is too cumbrous and expenaivs to be generally employed.

An excellent method of constructing mine models is illustrated by three models of Austrian mines exhibited in the Museum of Fraottcal Geology. These models are constructed to a uniform scale of 400 feet to 1 inch. The irregulaTities of the surfs oe of the ground are represented, and central, transverse, and longi- tudinal sections are drawn on the sides of each model. On removing the tops of the models, representing the surface, the workings on the different levels are seen plotted on plates of glass, fixed at the proper height, one above the other. Tho colours of the workings shown on the glass plates, correspond with those of the named levels on the longitudinal sections. An outer line, drawn in discontinuous bars, shows the extent of the deposit of salt at each level.* A fine model of this kind,

The siethtHl of working these tninea u folly described by Mr. H. Banennati in A Daeriptivt Caialogve of (he utoiogicol, , ilttaUttrsficai ModeU in the Mattvm o/ /"rnclieal

UIIfE-BCRTBTIMa.

representing tbe Copper Queun Miae, Arizona, waa ezbibitod ia 1893 !vt the Chicago Expoaitioa.

At the Stockholm School of Mine:), the studenU are trained in tbe representation of mine workings on sheets of glass. Tb* advantage of the method is the power of simuItanronsJy repre- senting the underground workings and the* Murface.

During the laat thirty yeara mine models have ben largeijr used in Sweden. They are of two types. "When s ajuifrl to be made of a mine with a small number of levelii ('' .,o

contours of the working areas and the geological ou:. . m

each level are painted in oil-colours on glaaH plates. Then Umm glass plates are placed one above the utbor, and at a diatanee from each other exactly in proixtrtion to tbe diatanco between the dilTerent levels represented, so that each glass will have a perfectly true position in relation to the others.

tif, on the other hand, a model is to be made of a mine with a larger number of levels, these glas models caouot be usvd, oo account of the difficulty of seeing through a numbrr of Hipeck imposed sheets of glass. Another method inuat be reeoitea ta The different levels are out out of stiff white pasteboutl on which the ores, &o., are marked with the proper colours. Then these sections >tre fastened ou squares of wire stretched oo wooden frames, which are placed one over the other ao thai eadi

twill have its exact pusitiou in relation to the others. In addition to the practical value and advantage of mine models to the geologist and miner, such models will freqneatlj be found of great advantage in suits at law, in settling mioiag claims and damages in dispute, when ordinary plan* arc on-

availing.* Mine Plans in the Upper Hars. — During recent jeara the plana of the Upper Harz melal mines have Iwen theronfthly reriaod by Professor O. Brathuhn. All the nieasnremenla have bea referred to one system of co-ordinates and to a common datom lino. As origin for tbe systeuu of co-ordinates lit* centra of the stone pillar in the Olausihut Magnetic Observatory was selected.

tand, as nbsoisset axis, a line whose azimuth makes an angle of 30' with the meridian of the origin. Thf* "it

theabtciseie axis is at riglit angles to the h if

veins worked. The datum line was taken u.- ' ' aLore sea-levcl, and, oonsequontly, all the workints .u., it-low it, and only negntiro heights have to be dalt witii. In conoetiiion with the triangulation of tbe Statn Survey, a network of amall

Oa tbe ooiulnicttoi) of mixJcU, A. K. Iehmaa, TVwiu. Aimr. tmt. Af.B., vol. xiv., 1886. p. *39j O, B. HnUu. ib., roL p. vVn I M lUapt, Tht Topoirraphtr, Vow York, 1883.

HIJtE PLANS.

tmrngtM was laid over the whole region. All the triangulation points are carefully marked with BtoneB, and lortii an excellent MKU for all fotare sttneys. The number of Btations thus marked Amoaats tu '2Q0. For the underground survey a tho tlieodolite waj used exclusively ; and the method of working with fixed puinU was ado{>ted, as local conditione render this moat suitable. At aclj level a large number of angle-points remain marked in the hard rock, and these may be iised lor connecting subsequent nrveyg. Orientation was effected by meaoH of the magnetic needle. No other method could be used, inasmuch as the oooaectiub betwem the surface and underground surveys had VVUsUy to be carried out by means of one inclined . The magnetic theodolite was used, in which the magnetic needle ia Bspended by a cocoon fibre, and provided with a collimation arrangetnont, For the obst-r'atioii of the Tariation, two declino- meters, a recording and a Gauss reading declinometer, were provided. The determinations of heights were effected in the levels, which are usually horizontal, by geomi-trical levelling, in the inclined shafts hy means of steel measuring rods, the parta of which can be screwed together as required, and in the perpen- dicular shafts by means of a suspended plumb-line. There was nrely need to have recourse to trigonometric levelling. The peoial mine plans are drawn to a scale 1 to 600 on sheets BteaturiBg SO cm. by 70 cm. (16-7 in. by 275 in.). A separate ui ii prepared for each level, and the workings are shown bj means of dotted lines on the plan of the next level. The number of sheets amounts to 270. Besides these, general plans to the scale of 1 to 2,000 are contemplated. The elaborate ayatem of water supply for the Upper Plarz mines is shown on a eparate plan and section drawn to the scale of 1 to 12,500, A relief plan showing the district affected by the water supply has also been m-epared on a, scale of 1 to 12,500,

Colliery Plans in Westphalia, — In the course of an exhaustive account of the Saarbriicketi and Westph&liun collieries, Mr. V. Waltl desci'ibes in detail the method. of tnine-surveying in Togae in those districts. For the whole of the Saarbriicken coalfield oo-ordinates have been determined, the base line of which, the ordinate axis, forms an angle of €3° 46' 44* with the stroBomioal meridian. This base line is parallel to the main strike of the seama. All surface- and underground-surveys are referred to these co-ordinates. At surface, triangultitioa points re determined, and these are oonneoted by traversing. Under- ground-surveys of slight importance are mode with the oompass, Tbti ia graduat<d, iioordiog to the usual Uermaa method, in twice twelve hours. The tized points in the mines are indicated by bnus narks in the roof or floor. More important length

Mine-Surveyinq.

raeasuremente are made with a 30-metre steel band, which need in conjunction with a dynamometer in order to show tiia tension of the band. For accurate measurementa the Bonn Mining Department jiresoribea tueaaurements with rods along t stretched cord. Oompasa-surveys are plotted with the protractor, the oon>}iaas plottin'-instrunient having fallen into disuse. For important operations it repeating theodolite, reading to 30 seconds, ie used, the horizontal circle being divided into 360'. Theodolite- survey 8 are invariably worked out tngonometricaliF, and plotted by means of co-ordinates. Heights are determined with a levelling instrument, and referred to Ben-level. For the use of the mine-surveying office plans are prepared on a scale of 1 to 1,000. These are known aa fundamental plana. They ar covered with squares representing distances of 50 metres or 200 metres. From tliese fundamental plans all other plans reduced by the pantograph. These include the working plani on a scale of 1 to 4,000 for the colliery managers, and on a seals of 1 to 2,000 for the overmen, nnd ventilation and drainage plans on a scale of 1 to 2,000 to at most 1 to 4,000. These are frequently mouoted on cardboard. Coalfields maps are plotted on a scale of 1 to 1 0,000.

Mine Flans in Sweden. — According to the regulations of tlis Swedish Mimug Act, all plans and sections of ore mines must be drawn on a scale of 1 to SOD, and must be made in oonformitT with a Normal Map, drawn Up by the Mining Department AU shafts and other excavations must be shown on the plana Further, both the parts of the excavation where ore of different kinds occur and that occupied by the country, gangues, ilyke (tft, must be diabinctly marked with certain specified colotui. It is decreed that no more than one horizontal section may ba drawn on each sheet, and this rule has been followed in Sweden ever since mini- plans first came into use ia lt)2S. The miae plana made in this way give a very clear idea, not only of the configuration of the excavation, but also of the mode of occurrence of the ores contained in the mine.

According to the Mining Act, it is also decreed that all nilae plana must be drawn in duplicate. One of these copies is to be kept at the mine, and the other is to be forwarded to the Offic of Mine Maps belonging to the Board of Trade at Stockholm, where there is tlius a complete collection of all the mine plans in the country. It is also jirescribed that in all mines wViich are being worked every new piece of work must be surveyed, at the latest, in the year after it is begun, and it is the mine- owner's duty to forward these supplementary surveys to the Office of Mining- Maps, so tb&ti tW c(>Ucctvoii of plana at thii otBca in revised from year to year.

MAONKTtONSBDLE IH MININO-

Chapter Xix.

Af?LICATIONB OP TBB MAaHBriO-NSKDLB IN MlNINO,

Eloiing for Iron Ore. — In exploring fur magnetic iron orea,

': magDetic-needle aSbrris valuable aid, and has been employed For that purpose in Sweden and in the TJeited States.*

TLe theory of its use is based upoa the fact that certain minerala deposited in the earth become magnetic by induction under the influence of the earth's magnetism, and that, cunse- quently, the two poles are fixed in the direction of the magnetic meridian, or, more exactly, in the direction of the magnetic iDolinBtion at the opposite ends of the deposit It ia well known that there ure substances, such as steel and magnetite, exhibiting polar magnetism ; that is to say, they retain the magnetism once acquired even if the inducing force ceases to act. Other sub- stances, such as soft iron and magnetic pyrites, exhibit simple mugnetism ; in other words, they are magnetic only so long the induction remains.

The intensity of the magnetism exhibited by depoFiita of mag- netite varies greatly, and is frequently so slight that only delicate instruments and practised observers can detect it ; in other cases the needle is affected at oonsidemble distances. It must, of course, be remembered that a given magnetic force art'eots the needle to exactly the same degree through 100 feet of rock as through the same distance of air.

If the magnetic north pole of the earth is regarded as negative, and the south pole as positive (in the northern hemisphere), the upper end of a vertical mass of ure will be negative, and the lower end positive. Consequently, if a magnetic- needle is brought near the upper or negative pole of the deposit, the north- seeking or positive end of the needle will be attrncted. When the point of observation is very near the ore pole the needle will dip downwards. The lower or positive pole of the ore mass,

Eing ttsnaily situated at a considerable depth, will not atlect tho r See pftper on the " Use of the Maguetio-Needle in exploring for Iroo

30g IllSE-SUaTSTlKO.

obBervattOD. Otlier dejiosits, coui-siag in a more or len and westerly direction, are less nffeeted by ind action ; the being situated in the long sidea of the deposit. Freqiv the depoaite are faulted and broken. In this case tbe sepanU portions behave like fragments of a broken bar magnet, &t adjacent ends exhibiting oppoaite polarity. la exploring for ore, then, if, on advanciug from aouth to nortli, the free needle is first attracted and then repelled, a &ult in the depont ii indicated.

To explore for ore the ordinary miner's dial may be eraployed- If a straight line is followed with the instrument, the needle vill remain directed towards the same point of the dial ; or, in otlier words, will remain in the magnetic meridian as long as it ia kept nfficiently far away from iron aud magnetic ore masses. But if these are approached, the needle wUl gradually be deflectwL Tbe only case in which there will be no deflection ia wheti the attracting deposit is iipproached along the meridian passing ovrt its upper pole. It follows that in magnetic surveys tbe meridUa line must firat be found, and fixed in tbe field or on the {lUs. For this purpose at least two straight lines are set out in tbe magnetic eaat and west direction, from 30 to 50 yards a[mrl These lines wUl at some point croas the meridian line. If the dial is set up at one end of a line of this kind, at a considerable distance from the magnetic mass, there will, of course, be m attraction. On approaching the meridian the needle will be gradually attracted, and at a certain distance the maziiiisia attraction will be reached. On approaching nearer it will beeoEue smaller, nntU, at the ore meridian itaelt it wUl be ioappiedalile. The angles of defection observed at the vaiious atotiona tre noted on pegs driven into the ground, and sdso in the field-book, or on the plan. Following the same straight line to the otlier side of the zero point — or, what is the same thing, to the other aide of the ore meridian — the same attractions are exhibite<l, bat in reversed order; tbe needle turning back to the meridian. If similar observations are made along the second east and weet line it is easy to fix the ore meridian by joining tbe two point* where there is no deflection. These points are midwa,y between the two points of maximum defiection. This passes over tbe upper pole of the deposit, and if the pole is approached along tlj meridian line, the dip of the north-seeking end of tbe needle will, as a rule, be greater tlie nearer it comes to the pole. Tkii method is, however, not adapted for fixing the position of the pole exactly. This may be done by determining the isogocic lines — that is to say, by joining the points where tbe needle bu the same deflection.

MAeUETIC-NEEDLE IN HtNINO, 309

W In order to obtain one or more parallel isogenic lines on both %ide8 of the ore meridian, it la necessary to set out a number of lines jjarallel to the ore meridian, and from 10 to 30 jarda miMLFt. At the points where these lines intersect the east and 'west lines, the angles of deflection must be observed, and tsogonic lines constructed by joining the points of equal deflection. The needle being drawn so out of its horizontal position that ita free play is hindered, it be weighted and balanced by a piece of wax. If, now, from some point of intersection in the net'work of squares made on the field of observation, a line is drawn in the direction of the deflection of the magnetio-needle, it iirill cut the isogonic curve at a second point, and, eventually, the ore meridian. The two points, where the isogonic line is cut, re joined ; the joining line is bisected, and at the point of bisection a perpendicular is erected ; then, perpendicularly under the point where this cuts the meridian, is the upper ore pole, and at this point it will eventually be found best to sink the etiaft, so as to be certain of cutting the ore mass. The ore meridian, it must be noted, need not always be a straight line.

In cases where a better instrument was not available, excellent results have, in this way, been obtained with the ordinary pocket- oon)[>as8, held in the hand.

For preliminary magnetic surveys, no instrument is better than the ."Swedish compass. In this instrument, the needle, besides revolving in a horizontal plane iu the usual manner, can also turn in a vertical plane to an angle of about 60° with the horizon. The needle is horizontally suspended in a brass cast) on a long vertical brass pin by means of a long glsiss cap. The brass ter- minates above in a short steel point, on which the glass cap rotates. At the bottom of this is a brass stirrup, provided with fine holes, through which pass the horizontal pins supporting Uie needle. To enable the needle to dip, there is a long slot cut along the middle of it. The compass-boK can be suspended by Qioans of three strings passing through three small rings fastened 1 1!0° apart on the outside of the box. It can thus be easily carried in the hand. Uraduatioa is not usual, and, indeed, unnecessary. Only the cardinal points are marked, as iu using it. deviations from the horizontal position alone have to be noticed. This compass was invented in the eighteenth century by the celebrated Swedish miner, Daniel Tilas, and is still in general use. The dip of the needle is estimated merely by the eye, and is not actually measured.

The miner's or dip-compasa was invented in the United States in 1866, and was adopted by the Geological Survey of New Jersey in the systematic explorations for magnetic iron ore in

UINB-SUR%'&YlNO,

that State. In tbis instrument the magnetic-needle ia suspended BO 08 to move readily in a vertical direction ; the angle of incli- nation being meaanrcd upon tlie divided rim of a small compass- box. The needle cannot move horizontally. The oonBtmctioa of the instrument is shown in the aocompnnying figure. When in use, the ring is held in the hand, and the compass-bor, hv its

own weight, takes a vertical position. It must, of course, be held in ttm plane of the magnetic meridian, ithich can be determined by holding the in- strument horizontalty. In this way it serves as sn ordinary pocket-eon pais. Messrs. W. & L. K Ourley, of Troy, New York, make several different forma of this instrument One form has a, 3-inoh needle ; its case has tliA two sides of glass. Another form lii a brass iiack and cover, and & 2-isch needle. Fig. 9S repreaenta an im- proved compass by the same makers. It is a moditicatioD of the Swedislt oompasa, and has a needle 3 or 4 inches long, resting upon a vertical pivot, so as to move freely in a horizontal pluc, and thus place itself in the magnetic meridian ; while being atlacbed to tlie needle-cap by two delicate pivofta, one on side, it is free to dip. I( 18 usually provided with brass oofert on both aidea. With the dip-compass, whether Swedish or American, perfectly trustworthy results can only be obtained when the observer is acquainted by long experience with tlie peculiarities of hia instru- ment. Compasa explorations being in many cases the sole sonroe of income, it can easily be understood that a skilful operator will be inclined to keep his mode of procedure aecret. Consequently the uninitiated are apt to believe that the operator muBt be s]iecially gifted ; and frequently the supernatural properties formerly ascribed to the divining rod are transferred to the com- pass. Thia exceas of faith in some is accompanied by sceptidsm in others. For thia, unfortunately, there are good grounds ; the compasa being so admirably adapted for dishonest purposed , Mr, T, B. Brooks mentions nn American prospector whoM compass-needle in the vicinity of lui ore mass always showed dip of 90* when facing west, and the true dip due tj) looal attnto-:

Fig, SO.

UAGNRTIO-NEEDLB IN MtNIHO. 311

tion when &ciiig east. The former poeitiou, it is said, was very saccesafully used ia selliag iron ore groands, and the latter in huying them. Similarly in Sweden a. powerful magnet inserted in a walking-stick has been successfully employed to give a large dip to the needle when it was thought desirable to mislead the purchaser.

As a rule, surveyors assume that the moat ore must occur where the dip-compass shows the greatest inclination, or is perpendicular. This assumption, however, ia erroneous. The plaoe where the needle is attracted most by a vertical ore bed is not directly above, but to the north oi, the south pole of the deposit. For, if the magnetism of the earth is powerful enough, there must be somewhere north of the ore pole a, point at which the horizontal ootoponents of the magnetism of the earth nnd of the ore bed are equally powerful, but acting in opposite directions. At this point the horizontal forces neutralise each other, and then the vertical forces of the magnetism of the earth and of the ore bed tnd to bring the needle into a vertical position.

The evidences afforded by the needle often lead to error. A small pocket of ore near the surfacfi may act as strongly as a larger ore mass situated far below the surface.

It ia tlius seen that in exploring for iron ore with the magnetic- needle, a purely scientific method is necessary. The compass should be employed for preliminary work, in order to save time and labour ; but before a shaft is sunk, recourse should be had to a more accurate method. Improved methods, available for the purpose, have been devised by Brooks, Thaln, and Tiberg.

1. Brooks' Method.— Mr. T. B. Brooks,* of the Geological Survey of Michigan, in exploring for iron ore, determined with a pocket-compass variations east or west ; the bearinga of a standard Une being taken as in ordinary surveys. The inolina- tiona or dips were observed on the dip-compass held in the hand iu the plane of the meridian. Sometimes observations were mftde with the compass held at right angles to this position, that is, facing north and south. The instrument was always held in the hand and levelled by its own weight. The intensity of the magnetic force for the three positions of the compass was measured by the number of oscillations made by the needle in a unit of time, usually taken at a quarter of a minute. No attempt was made to eliminate the earth's attraction by neutnilising it with a magnet while the observation was being made, nor by computation ; and the great amount of friction in the compass

Otdoqkal Suraey of Michigan, vol, i,, 1873, chap, viii. See alto Magnetio Obeervations in Geologioal Mapping," by H, L. Smyth, Tram. 'mer. last. M.E., vol. x3\n",, 1398. p. 640

MINR-flURVEYiKG.

reudere the number of oscillations onlj an approxim&tion to tha number that would be obtained with a delioately mounted needle. Mr. Brooks has, however, done excellent work with this method in the Marquette region and in New York and New Jersey. Re also describes another method of workiii|, which he calls magnetic triangulation. The mode of procedure is as follows: — Remote &om any magnetic rocks, nentralifie, bj means of a bar magnet, the earth's influenoe on the needle of a solar oompasa. The needle will then stand indifferently in mil directions. If the compensated instrument is set up near the magnetic pole to be determined, the needle will point as nearly towards the local pole as its mode of mouRting wilt permii The operation being repeated at two other points near th< magnetic pole, the three lines must intersect in one point, which will be directly over the pole of which the position is sought. By using a dip-compass in a similar manner, data to determine the depth would be obtained. The fact that serentl local poles often influence the needle at each station renders thii method difficult in practice ; a place must be S'. where bat one strong pole exists.

2, Thaien's Method.— Professor R. Thaln,* of the Univeraity of Upsala, employs a uiodifi(tion of Weber's portable magneto- meter, or of Tjamont'a theodolite. In its simpleBt form, Thaln'a

instrument consists of a compass-box, A (Fig. 95a, b), inoheaio

diameter, divided into degrees or half-degrees. At right anglts to the diameter, passing through the zero point of the graduation, an arm, B, extends horizontally. This serves as a sight in setting out lines in the field, and receives the bar magnet for the deviation measurenionta A deflection of the needle is caused by means of this magnet, the longitudinal direction of which is parallel to the arm, and the distance of which from the needle always reuiatna unalteied. On the other side of the oompaat-boz there is a socket, into which a rod of sott iron can be placed perpendicularly for inclination measurements. This iron rod, Jtrnkontorttt anmltr, vol, xxxiv., 1879, p. 17,

HAONETIC'NEEDLE IN UlNIMO.

like the nifti;net, effects a deflection of the needle. Tlie instru- meat rotates about a vertical axis, and is provided with a, spirit level, D, sights, E and F, and levelling screws. It is placed on a tripod. In order to simplify the apparatus still further, the cotnpasa-box may be fastened to a rectangular board, the edges of which can be tised as sights ; whilst the board itself receives the bar magnet, which is fixed bj screws or springs in the position that in determined once for all. As support for the instrumeat, ordinary surveyor's plane-table may be employed.

" The observations with the magnetometer consist for the most part of deviatiuu measurements, for which two different methods may be employed. In one method the instrument is placed so that the needle is directed to the zero point, the bar magnet having been removed from its place. Directly the magnet is replaced, the needle will deviate from its original position, the angle of deviation being read from the graduated circle. In the second method the instrument is turned, while the magnet is in its place, until the needle points to zero. The bar magnet is then removed, and, when the needle has come to rest, the angle ia read. In this method, under similar conditions, the angle obtained will be greater than in the former method. Of the two methods, the latter, or tine riiethod, is the more delicate ; but it requires more time than the former, as the instrument has to be re- adjusted at every observation with the magnet and iron rod. This method has the disadvantage of not being applicable in the extreme north of the ore field, where the magnetism of the ore bed is powerful. In the former, or tangent method, the instrument remains unmoved during both measurements. The disadvantage, however, is that the so-called constants of the instrument vary with the angle of deviation. This does not matter if the results are to be arrived at geometrically, since it is

3U

MtNK-SDBVETIMO.

tUtiii merely necessary to join the points where the same angle is obtained, quite regaidless of the magmtude of the angle uiaof its oorreapo tiding constant. If the position of the ore is to T>e determined by calculation, the sine method must be employed

Where no ore is present, the needle ia acted npon by tvo forces, one of which ia due to the fixed magnet, and the other to the horizontal component of the earth's magnetism. These two forces acting simultaneously, the needle takes up a position in the direction of their resultant. Then if ia the angle of deviation, and H the component of the earth's magnetism, the following formulae are obtained : —

for the tangent method : H tan dt - Kj, for the sine method : H sin a Kj,

in which Kj and Kj are constants, so long as the size and position of the magnet remain unaltered. If these constants are known, the actual value of H may be found from the magnitude of the observed angle by either of the ntethods. If the constants sro unknown, only the i-elative value of H may be found When observations are made near an iron ore field, in both formal H must be replaced by R, the resultant of the horizontal component of the earth's magnetism and the magnetism of the deposit. The formuln tlien become

K tan a K, and R sin m K. Wlien the deviations are caused by the sofl iron rod instead of by the magnet, somewhat similar formulw are obtained ; but ths magnetism of the iron rod being due to induction, its intensity is proportional to the variations of the vertical componenta of the earth's magnetism. It follows that the constant K of each formitU in thb case must be replaced by a magnitude that varies with the mngnetiara of the rod. Observations with the iron rod Indicate the inclination of the earth's magnetism ; whilst observations with the bar magnet serve for determining the horizontal com- ponents of the same terrestrial force. Consequently, by combin- ing the two methods, it is possible to find out the vertical com" ponents of the magnetic force.

In order to survey an ore field, it must first be divided into squares with sides 100, GO, or 20 feet in length. Then at ever7 angle of these squares, the deviation must be observed with the magnet and iron rod. Similar observations must be made on ground free from iron, and so far distant from the ore field that the influence of the ore is not felt It is also advisable to deter- mine the magnetic declination for each point of observation. This may be done by directing tiie sights along one of the lines that have been set out, and teKdiv\g tU bearing, after the fixed

UAGKETIC-NSEDLE IIT UINIKTa

magnet and iron rod have been removed. Observations must also be made atoDg the magnetic nieridiaa north of the supposed ore ]>ole to determine where the north-seeking end of the free needie changes its direction from north to south, or whether it invariably (loints towards the north.

When these determinations of declination, horizontal intensity, and inclination have been carefully made, and the angled ob- tained noted on paper divided into squares, lines are drawn for each of the three series of observations, exhibiting equal declina- tion (isogonic lines), equal intensity (isodynamic lines), and equal inclination (isoclinic lines). This is done in each case by joining the points by which equal angles were obtained. Tha curvature of the lines is drawn as naturally as possible, care being taken to avoid sharp bends. The curves of inclinatiuu and intensity thus constructed are closed, and have an spproxi- mately circular or elliptical shape, provided that a single isolated ore mafis is being dealt with. They are grouped round two points. The one at the north is where the greatest angle of deviation was found, whilst that at the south is where the emallest angle was obtained. Between these two groups of ourrea is an open curved line representing the neutral angle. In this neutral line the intensity is the same as if no ore was present. The straight lioe joining the points where the greatest and emallest angles were obtained passes over the centre of the ore mass, and indicates the direction of the magnetic meridian of the ore field. Directly beneath a point in this line, in a vertical ore bed, the greatest mass of ore occurs. The rule that most generally holds good in searching for iron ore is, that the ore muss is to be found immediately beneath the point where the magnetic meridian cuts the neutral line.

The isogonic lines consist of concentric ovals placed, as a rule, aymmetrically on both sides of the meridian. From the shapa and position of these curves usefal indications may be obtained regarding the position of the ore pole, and the shape of the deposit.

The mode of procedure can beat be understood from the accom- panying ideal map {Fig. Sou), drawn by Prof. G. Nordenstrom.*

Before the measurements are begun, the instrument is atijuated at a place where there are no magnetic ores, and consequently no other magnetic force than the earth's magnetism. The angle of deviation found here is noted Og, and is generally so arranged that it is equal to 25* or 30*. Then begins the measurement of the ore lield, which for this purpose is divided into squares with sides 10 metres in length. By the aid of the tangent method Journal of the Iron and /aititute, itA. U- ..VSS&.-.V.

A

MlNK-StIBV£¥lXG.

the angle of deviation, a, ia afterwards obtained in each career of erery square. These ovalues are noted on a map, and the points for which equal angles have been obtAined are joined. This givea two systems of isodjuamic curves, which are grouped in a more or less regular manner around their foci or ce&trei.

NunrH

top

On

South lioc'NAmc Lines

Fig. Ojf.

One of these is situated north of the ore and where the a-value is greatest, and is therefore noted as a-maximutu ; the other is 9itutttd either directly above the greatest maM of ore or some- what to the south of it, and represents the sruaUeBt a-ya!ue, being therefore noted as a-miuim-uTO, 'B*A-weeu<afte 't.-ti ig:tiNi%

MASXBTIC-KSEDLE tX HnnK&

of curves there is an open curved line, whose aogle of dcTiation is tbe sasae a& obtained in regions where there is no ore, and ii ia noted as dp- This curved line is called a neutral line, tha angle being called a neutral angle.

The line which unites the maximum point and the m inimum point indicates the direction of the magnetic meridian of the ore field. The centre of the greatest mass of ore is situated in the point of intersection of the magnetic meridian and the neutral line when sin a. is less than 3 sin a-min.

In this case the outcrop of the ore is covered by beds of sand, gravel, or other deposits.

If, on the other hand, sin is equal to or greater than 3 sin <i>niin., the centre of the ore is situated either under the point representing o-min., or somewhere on the magnetic meridian between this point and the point of intersection. In this case the ore either crops out at the surface, or its outcrop is covered hf more reoent deposits, whose thickness is least when the centre of the ore is nearest to the minimum point.

Ftnaltj, it should be noticed that, iu order to get correct results, the levels of tbe ore field which ia being surveyed should be knowtu

3. Tiberg'B Method. — For exploring for iron ore, Mr. K Tiberg invented in 1880 a dip-corn pass, inches in diameter, and half all inch deep. The axis of the needle is at right angles to tbe plane of the box, and rests upon two agate supports. The needle can thus move freely when the compass is placed horizontally or vertically. The instrument diHers from other dipping needles in that the centre of gravity of the magnetic-needle ia a littie below its horizontal axis when the compass is in a vertical posi- tion. The needle is compensated for the vertical force of the earth's magnetism by a piece of wax or by an aluminium coon- terpoise fastened to its south-seeking end. ,

The instrument is provided with a spirit-level for boriEontal adjustment, and with a ring, by means of which it can be sus- pended vertically. The sighting instrument, used in conjunction with the dip-compass, is a brass plate about a foot in length, provided at one end with four square flanges to receive the dip- GompasB for horizontal measurements. At right angles to this square, there is a groove in the plate with a sliding receptacle for the bar magnet required for boriisontal nieaaurements. Four folding sights are attached to the plates in such a way that their lines of sight form a right angle. The instrument, consequently, can be used as a crosn-head. Two special sights are added lor levelling operations, and tbe instrument is provided with circular spirit-level.

31ti HINK-SURVKTINS.

The observations for vertical measurements are mnde at th

surface with the plane-table or by hand. The inclituition iiutm- ment is fastened to the plane-table, levelled, and tamed until the needle points to 90°. The instrument is then raised with the ring at the top, and placed at ribt angles to the magnetic meridian, and the angle indicated by the needle observe J. The same operation has to be done by hand if tfae plane-table is not iivailable. When the ore appears to be deep, or "when the horizontal intensity is poweiiul, recourse must be had to the plane-table.

The formula for calouUttng the vertical intensity G is — G K tan o, in which v is the angle given by the needle — that is, its deviation from the horizontal — and K a constant varying in different in- struments from 0'75 to I'l of the earth's horizontal magnetts force. Lines of equal vertical intensity may thus be constructed. In magnetio plans it is usiial to employ a blue colour for positive intensity, and a red colour for negative intensity. The accoracy attainable with this method is from 0'2 to O'l per cent, of the earth's magnetic force in central Sweden. With the plane-tabli) 250 to 300 observations may be made per day, and 450 to 600 by band. For each ore field surveyed the needle must be compen- sated afresh, and a preliminary magnetic survey made. The field is then divided into squares, with sides 40 feet in length. The basO'line is as nearly as possible In the middle of the field, and parallel to the direction of the strike of the deposit. In making the survey, observations are made every 10 feet, and iu some cases every 6 feet, in the immediate vicinity of the ore, an I every 20 to 40 feet or more when farther distant from the ore. The general rule is to make as many observations as may be required to indicate what the appearance of the onrvea will he. Heights are estimated by the eye, or by a preliminary levelling with the sighting instrument, and the more important topo- graphical details are noted.

The maximum of iutensity is generally presented by the point where the ore is nearest to the surface. It may also be situated between two adjacent deposits — in which case the intensity decreases, at first slowly, or not at all, and then comparatively rapidly. The distance to the centre of a vertical ore bed may he taken as at leat 0*7 of half the breadth of the north-polar attraction. This rule is, however, not very trustworthy. The vertical distance of the plane of observation from the upper ore pole is equal to the horizontal distance of the poiut where the needle deviated most from the horizontal from that where of

k

J

k

Hagketio-Needle In

the greatest intensity was found. It is also equal to of the diatanoe of the point wliere the needle dipped most from that where half the maximum waa found. The latter rule is the best.

Sometimes these calculations enable an opinion to be formed of the relative values of two similar ore beds. For two deposits of a similar character, situated at least 30 feet beneath the surface, it may be assumed that the deposit, for which the product of the greatest intensity and the polar distance is the greater, contains the larger quantity of ore for the same length of deposit. If the polar surfaces of the two beds are limited this product mast be replaced by the square of the polar distance.

A good idea of a deposit may be formed from the appearanoa the curves of intensity. Regular, long extended, elliptical curves, enclosing a long but narrow district of greatest intensity, always indicate a regular lenticular mass. An asymmetrical bend in the curves indicates pai-allel deposits. More circular curves may indicate a segregation of ore if the intensity decreases regularly. Irregular curves indicate more or leas irregular depomts.

lu exploring for courses of ore in the mine, a base-line Is marked out in the level, and observations made every 10 feet at least. At each station three observations have to be made : — (1) To determine the direction of the total horizontal intensity by means of the sighting instrument, the deviation of the magnetio- needle from the base-line being observed. (2) To determine the magnitude of its force by means of the bar magnet. (3) To deternune the vertical intensity by means of the inclination instrument. Vertical measurements must also be made at the top and floor of the level, and for this purpose the instrument may be held in the hand. On neutral ground at the surface, the borisontal force of the earth's magnetism and the direction of the earth's magnetic meridian must be determined. The results of all the observations are represented on paper, along the base-line, as arrows showing the horizontal forces of the magnetism of the ore at the points of observation. If all or part of the an-ows are directed towards the same point, there the ore may be assumed to be. The ore would be at the level at which the observations were made, if the vertical intensity is negative. When the arrows ajiproach in front or behind, the plane of observation is above or below the magnetic centre of the ore. When the vertical intensity is positive, the ore may be above or below the plane of observation, always assuming that a more or less vertical ore mass is being dealt with.

By applying this method Mr. Tiberg has discovered important depoaitfl of ore at the Swedish mines of LstuWu 6,iv&.?i'v%-

Uinb-Survetikg.

To iUostr&te the ralue of the m&gnetic-ueedle ia exploring for iron ore, it may be meotiooed that, acoordiag to the tttatistic* nTSD by Prof. Smock,* there wre 115 mines in 1868 in the State of New Jersey, whilst in 1B74 the numV>er had incraued to 200. All these ore looalities were firat made known by th QBe of the rosgnetic-needle. In fact, the annual prodaotion of the Stftte hitd been increased 60 per cent, by the addition of new producing localities foaad by tho compass. It shoaid alio be stated that in many cases there are no visible surface indica- tions of ore.

4. Combined Thalen and Tiberg Method. — For some years pact Tiberg'a instrument has generally been used in combination with Thalen 's magnetometer, partly to avoid the necesaity of taking more than one instrument on surveyiag expeditions, and partly owing to the fact that by such a combiimtion of the two instru- ments greater rapidity results, especially if the tangent method ia used.

The combined instrument is illustrated in Figa. 95d and 95a

Fig. 95(i.

Fig. 9&d shows the instrument furnished with TiheiT's ootnpa**, but in Fig. B5e this ia replaced by Thaln's compass.

In order to make it possible to use first one and then the other of these compussea, they are provided with nxle-pins fitting into the bearings in the standards, o- The ceiitre-lmes of th? axle-pina m the Tiberg compaea run through the Kero-point*. but m the Thalen compass through the 90* point. The instru- Traiu Amer. Itut. M.B., itoV.w.. Wift, 353,

HAONETIO-NEEDLE lit UISJUQ,

ment is furnished with a apirit-lcTel, 6, a transverse arm, e, and sighta, d. The arm, c, secured on one of the standards, serves to receive the bar-magnet for the deviation measurements, when measurements according to the Thalen method are to be made. The method of using the instrument in making suoh measure- ments has already been sufficiently explained.

To begin with, the instrument is adjusted on perfectly neutral ground. After the ore field to be explored has been divided into squares, with sides 10 metres long, observations are mode with the rlip-compass at each corner of every square in the following manner : —

The compass is placed horizontally and is turned in a hori- zontal plane until the central line through the axle-pins of the

h;

k.

Fig. 96-

mpasa ia at right angles to the direction of the needle, or, in ther words, until the needle is placed at 90°. Then the compua is turned on its axle-pina, so that it has a vertical position. Ia this position the needle is only affected by the vertical component of the ore, and this causes a greater or less inclination of the needle. If the magnetic fonie of the ore ia P, and the angle of the inclinatioD is V, then

P K tan V.

If the value of Y is noted on a plan, and the points for which the same Y- values were obtained are united, there ia obtained

aeries of curves (isoclinic curves), which are more or leas regu- larly grouped around a centre whose V-value is greater than that of all the others (see Fig, 95/}, Immediately under this centre, where V Y max., the greatest mass of ore always occurs.

Besides for surveys at the surface, both the magnetoiafttx and the dip-compass are also used for tui'VQ''%

Uine-Survetiio.

tlie mine itself, in searching for ore. Foe this purpose ihtf siM method it generally used. If H (Fig. 95/) la the horicontal component of the earth's niftgnetism, and F that of the ore, R the resultant of both, there is obtained for each point of observfttion B,, Rg, Ac aooording to the formula—

B H

iin a

If an arbitrary value is given to H, which is considered be constant, the lengths Rj, Bg, B|, &c., as well as their direction,

, H

Fig. 95/.

ure aacartained. The length and direction of the component of the ore, F, are then obtained by constraction.

The position of the centre of the ore sought for, 0, is indicated by thp direction of F,, Fj, Fj, ice, all of which converge more or less towards this centre.

5. Thomson-Thalfin Method To the instruments for nu

netic-Burveys of ore deposits there has recently been added the Thomson-Thal<n magnetometer, which has two magnetic-needlea with like poles in the same direction, the inclination produced by the vertical components of the magnetic forces acting upon thera being compensated by a cylindrical magnet north poU upward. The distance of the deflecting magnet may be altered by means of a graduated brass screw, and the compensated intensity of the vertical component of a magnetic ore body ii indicated on an arbitrary acale. The theory of the inatrumeut is described by Mr. A. Haanel.*

Sxaminatioti o/ Magiietic Ore DepiMnu.

J

MAONETIC-NEEDLE IN HiyilTO.

Use of the Magnetic-Needle in Surveying Bore-holes,— It has eij assumed that the diamond drill always bores a perfectly Btraight hole, even though passing through rocks of different bardnesa. Actual experience revenla an entirely different state of things, the deviations fiometimes being 80 great as to render a bore-hole misleading. An ingenious plan of correctly ascertaining these deviations has been devised by Mr. F, Macgeorge,* an Australian engineer. His plan consists in lowering into tlie bore-hole clear glass phials filled with a hot solution of gelatine, each containing, in Buspcnion, a magnetic-needle, free to assume the meridian direction. The phials are encased in a brass pro- tecting tube, and let dowa to the depth required, being allowed to remain for several hours until the gelatine has set.

The construction of the phials or ciinoilaU can be seen from Fig. 96, The clinoetat is a true cylinder of glass made to tit Accurately within the brass gtiide-tube. At the lower end it terminates in a short neck and bulb, within which a magnetic-needle is so held by a glass float as to stand upright upon its pivot in every position of the phial, and thus allow the needle to assume the meridian freely without touching the sides of the bulb. Passed through

an air-tight cork and screw-capsule at the ujiper end is a small glass tube terminating in another bu)b above and

with its open lower end inserted in a cork which entei-a ® he lower neob of the phial, thus ] ire venting the escape ' of the needle and float in the lower bulb. The upper

bulb contains a very delicate plumb-rod of glass con- of a fine rod terminating in a plumb of glass below diminutive bulbous float of hollow glass above. It is carefully adjusted to the specific gravity of the gelatine in which it is immersed, so as to Insnre the rod being truly rertioal whatever the position of the phial and bulb may be. When the gelatine is flnid the plummet hangs freely perpendicular, whilst the needle in the lower bulb assumes the magnetic meridian. When, however, the phial is at rest in any position, the contents soUdiJfy on cooling, and thus hold fast the indicating plummet and magnet in solid transparent material. On withdrawal from the borehole the phials can each be replaced at the same angle at which they cooled, and when the phial is revolved upon the part where the magnetic-needle is seen em- bedded in the gelatine, until the needle is again in the meridian, the phial is manifestly in the same direction, both aa regards inclination and azimuth, as it was when its contents were con- ;eale d, and thus the gradient and bearings of the bore-hole can Engintering, voL xx*ix., ISSfi, pp. 260, 3Si

M

Fig. 90.

sisting and a

MIlIE-SCSVKIIIId,

be detenntned. By repeating the ubsemittoas at iotervtU ni every 100 feet, the path of the bore-hole can be accurately niftppecl. The ineliDatlon nnd asimuth at the time of cooling is deter- mined exactly by the recording instrument, or clinometer, which ia a modification of the theodolite. The phial, with ita oongealeiJ oootenta, ia placed in a sheath of brass tubing (Fig. 97), attached

Fig. m.

to a movable arm carrying the index of a vertical arc. Th upper bulb of the phial is brought into the fiild of two cross- viaioned microscopes, carried with the arm round the verticil arc, which are kept tmly in the same plane at every angle of inclination by a parallel motion. Upon the object-glaas of eacli microscope vertical lines are drawn. The phial is revolved ui ita sheath, and the arm is moved along the arc by the tangent sere* until the embedded plummet is made perpendicular from each {mint of view. The phial is now at the angle of inclination it which ita contents solidified, and its lower bulb will be fouc<! nearly in the axis of the revolvin a.rm, and about an inch aboft

iboft M

UA0MKT10-NKSDI.S IV HINISCh

the centre of & Lomontal rflvolylng oiroular miri'or, haTiag a BjrsteDi of parallel lines engraved acroaa its face. Reflected in the mirror will be seen the image of the embedded needle, which, of course, pointed north before it was fixed by congelRtion In the bore-hole. If now the mirror is revolved until the number 270 of the graduated circle is opiiosite the marked end of the needle, and until the reflected image of the needle is parallc! with the engraved lines, an index at the aide of the graduated mirror nie will give the exact angle between the needle and the verti- cal plane of revolution of the phial, which is, in fact, the magnetic bearing of the inclined pbial and of the bore-hole it occupied at the time of the application of the test.

Thiti method was first applied at the Scotchman's United Mine At Stawell, in Victoria, and waa so effectual eis to enable the bore- _kole to he found 37 feet away from its supposed position at a -depth of 370 feet, a deflection that increased to the lai'ge amount of 75 feet at a depth of 5U0 feet. Au exploratory level failed to find the bore-hole at its theoretical position, assuming the drill to have gone straight down. The subsequent search works lasted for more than a jrear, and coat altogether £3,663. Had the method been available at the oommoncement, tlie level driven would have cost only X 1,352, and the saving effected would have been no less than £2,311.

Similar experiences have been met with in a number of other bor&-holes in the miuiug districts of Victoria, and the conse- quence is that mine-i)roprietors are beginning to distrust the diamond drill altogether. Yet, if accurately surveyed, the most crooked bore is quite as useful as the straightest ever imagined by drill-makers. In view of these facta, the Victorian Govern- ment has contracted with the inventor to test all approved borefl which have passed through auriferous rock.

By means of the eltTiograph, as the inventor terms bis appara- tus, a bore may be strsiglitened when so defleoted as to endanger the safety of the drill ; for, suppose a bore-hole to have deflected euddculy, the depth of the point where the most serious defleo- tloii touk place can be found. Then, if an india-rubber washer is forced down to 20 feet below this point, and liquid cement run ia antil it reaches some feet above the point of deflection, and ailo'ved to set, then the drill may be again lowered and started gently, until it has started fairly in its corrected path, when the Usual spr>(Ml of boring muy be resumed.

A less satisfactory method lor ascertining the iuclinatioQ and direction of bore-holes was suggested by O. Nolwn.* In the

Pmu*. Zriltchr., vol. xxviii., 1879. p. 176; Tmnglatios by C. Z. Bon- nlajj io<l J, K. tiuUirie in Tratit. <v. Jiny. laal, M.B., voL xxu., p. 01.

¥

Uidk-Sukvetisq.

uisirumunt eui ployed, the auiouDt of deviatioii is etelied u)ton gItMS by hydi'uSuoric acid ; whilst its direction is found by me&Di of 11 compaiiH-ueedle, clumped by the ttid of & stop-watch, after sufficient time hot! been idtowed for settling. Notwithet&nding the gi'eat imperfections of thiB instrument, its uae in GeratMij baa revealed some startling deviations of bore-lioles. For eiainple, in a bore-iioie at Dienslakea, bored with a rotating drill, ths deflection amounted to 47' at a depth of 750 feet. The bore- hole, undertaken by the Gksrman Oovernmeut, at Ueth, ia Holatein, was but little better titan the preceding ; but, by lucky accident, the defleotioa of 3° at 984 feet gi-adually changed to the opposite quarter of the compass at 1,640 and 2,624 fet, and concluded with a deflection of only at 3,:j80 feet.

The diamond drill has been largely used for prospecting in the West African guldhelds, and valuable experience in sur- veying the bore-lioles by the Macgeorge method has been recorded by Mr. J. N. Justice,* A preliminary survey wm made for dip by the hydrofluoric acid method with very satis- factory results. In a vertical hole the tendency is to deflect along the dip of the rocks. In inclined holes set at about 43' the tendency is to become steeper, In the case of one hole in- clined at 61* 30' the distance at a depth of 773 feet measured along the assumed course of the bore-holes to the same depth along the actual course was 165 feet, and at a depth of 1,090 feet the divergence had increased to 230 feet. If the deflection is considerable, the direction has to be determined, and this ii done Ity the aid of Macgeorge's clinostats.

A method of surveying bore-holes has been devised by Mr. 0. C. il'Farlane, an American engineer, in which the incHuatioD is determined from the deflection of a tangent galvanometer. Au ingenious electric recording apparatus has also been devised by Mr. H. F. Marriott, t who has detected with it aeriona deflections at the Turf mines, Johannesburg. In one case at 4,803 feet the bore-hole had deviated 2,185 feet from the vertical line piaiising through the mouth of the bore-hole.

Excellent results Lave been obtained in Germany with Gnthan's atralainetet: This instrument oomprisea a oompas- medle and a plumb-bob regulated by clock-work. The com- bined instrument is enclosed in a brass cylinder 650 mm. long and 54 miii. in diameter in such a way tliat the comjukaa at top, with clock-work on the alarum principle below, whilst the plummet, with recording piate, occupy the lower end of the cylinder. At a given time the freely swinging needle is

Tratu, Intt. 3iin. Mel., vol Jtii., 1903, p. 301.

HAaNBTIC-NEKDLB IN KIKEB.

clamped bj the clock-work, and at the same time the plummet is released aud its position marked.

Employment of a Fowerfnl Magnet in Cases of Ud certain Holing. — In 1846 Profesior Eorchers, of Olauathal, tirEt proposed to employ a powerful magnet in cases of uncertain holing from one eximvatiun to another. Since that date, he htta improved the method in many way a, and has frequently employed it in practice with great success. In order to ensure a, successful holing, the ends of the two levels mast not be more than 20 yar<ia apart. The apparatus employed consists of a powerful magnet, with a specially constructed protractor, a compass, and a small auxiliary magnet.

The powerful magnet consists of six magnetised steel bars 4 feet in length, enclosed in two wooden boxes, provided with water-tight lids. One of these boxes contains only one magnet ; whilst the other box contains the remaining five, separated from one another in the middle and at the ends by pieces of card-board. In the centre of its upper aide, the larger box is provided with a pivot, which flta into an aperture in the smaller box. On thi

Fig 98.

f

-T

Fig B9,

pivot, the small box can be rotated, and the north pole of the magnet inside can thus be made to correspond with the south poles of the magueta in the large box. Consequently, ft portion of the magnetic force of the latter is neutralised. The powerful magnet must be fixed in such a way that it can be pointed in various directions, without altering the position of its centre. For this purpose is employed a brass protrftctor, Figs. 98, 99, which can be screwed on to a thick board. At the cetitre of the protractor, a brass plate revolves, and between the turned-up edges of this, the principal magnet may be placed. At right angles to the longitudinal axis of the magnet, an index line is engraved. Provided the rock barrier is not more than 6 yurds across, an ordinary compass, with a sensitive needle, may be employed. For greater distences, the com- pass-need ie must be suspended by a silk fibre. Under these circumstancea the steel pivot ia removed from the compass, and a case screwed on to the plate, as shown in

HINE-eCSTETlKa.

Fig. 100. The sides are covered with glass to protect tbe Beedle from air currents. The u}i|)er end of the glas& tobe, ccinlaitiing the silk fibre, is prOTided with ft contrivance for centering the needle. The latter is somewhat longer than the diameter of the compass dial, and doRs not require to be centred with naatheniatical accuracy, provided that both ends are read, and the nieati of the two readings tnkeD. The auxiliary magnet ia a small magnetised bar 13 to 16 inches in length. The mode of procedure is the fuilowing : — At the end of one of the levela, the protractor is firmly fixed in such a way that its nortli and south line is in the magnetic meridian. At the end of the other level, the compass is set np, as nearly as possible at the same height as the protractor, and placed so that the needle indicates north. The needle must then be rendered astatic. To effect this, the auxiliary magnet is placed in the direction of the north and south line of the compass, on the side away fronv the principal magnet in the other excavation, and moved backwards and forwards until the force attracting the needle is iieuiraUsed. When these preparations are complete, the principiil magnet, with the small box above it, is placed on the movable plate of the protractor, and brought approximately into the direction of holing. The powerful magnet then acts on the astatic needle of the compass, and causes it to take up a direction determined by a law enunciated by Gauss, But as the needle is not perfectly astatic for all directions, what attracting force remains must be again neutralised for the position taken up under the action of the powerful magnet. This is done by revolving on its pivot the small box above the principal magnet, until the north pole of the mHf;oet it contains corresponds with the south poles of the other magnets. The action of the large magnet is thus diminished. Then it' the compass-needle is not pertectly astatic, it will alter its position, as the attracting force of the principal magnet increases or diminishes. If a change in the position of the needle is observed during the action of the weakened magnet, attempts must be made to bring the needle back to the position it occupied when the principal magnet acted with full force, by moving the auxiliary magnet very slightly. The upper bar of the large magnet is then turned back to its original position, and it is ascertained whether the oompoas- needle alters its position. If this is the case, the process must be repeated until the needle gives the same beating

J

Fig. 101,

the

Uaonetig-Nkedle Ik Hiniko.

with the fall force and with the diminished force of the

magnet.

From the bearing of the needle and the direction of the large magnet, ihe directioQ of holing may be determlDed by construction, in the folio wing way: — ABC (Fig. 101) is a right-angled triangle, with the right-angle at C ; A. being the centre of the large magnet, the longi- tudinal axis of which is in the direction of the Lypothenuse A 6, At C is the astatic* needle, which, attracted by the large magnet, takes up a poiiition in the line D. The direction of tliis line is determined by the equation — A D A B. Strictly speaking, the magnet N 8 should be very small. For practical purpoBea, however, thi law may be applied without any appreciable error.

The question now arises, in what way should this law be applied. A geometrical method in inconvenient in the mine and, consequently, it is desirable to calculate the angles a (B A 0) and (A C D), that is, the deviation of the direction of holing A C from the position of the magnet N 8, and from that of the compass-needle CD. A, B, and C are situated on the circumfet ence of a circle, the centre of which is K In the triangle DEC, the angle D E ia equal to ce + (3 ; and, since the triangle A E C is isosceles, the angle ACE ia equal to the angle A E ; there- fore, the angle D E is equal to a - The ratio of the sides D E and E 0, however, is 1 : 3, and 1 ; 3 sin ( - |8) : sin (o -t- (8) ; therefore,

sin sin (a -I-

ppo<8, for example, thut the ht-aring given by the protractor of the large magnet was 154°, and that given hy the compass 12.5* 15'; the diflcrence is then 28° 45' + 0. Now, sin 28* 46' 0-48099 ; one-third of which is O-1G033, which ia

e sine of the angle 9° 14'. Consequently,

a. + a —

28' 45'

therefore, a Ja, therefore.

19* and r 45'. The direction of holing A B

125" 15' -I-

\r,i° 0' -

45'

19* 0'

136* 0' 135° 0'

This calculated bearing haa to be subtracted 180°, since the north and south line of the compass always remains in the me position throughout the process; the needle being revolved.

330 UtNB-BURVEYINQ.

The direction in which it would be necessary to drive voold, consequently, be

180' - 135' 45°.

Instructions for carrying out the operations required kt the large magnet are given by means of prevtoasly arranged siguli by the observer at the compass,

A powerful magnet was applied with success in a somewbst similar manner in 1 8t<b by Mr. A. Haddon in seeking a bon- hole, that bad diverged from the vertical, at the Holjrood Brewery, Edinburgh. After the bore-bole had gone down 2O0 feet, it was considered necessary to connect it by a level with neighbouring well 18 feet 3 inches distant The miner entrotd with the work having failed to find the bore- hole, Mr. Uaddoa procured four B-inch bar-iuagtiets, plHCf'tl end to end, and secnfed between two laths of wood. These he lowered into the bore- hole with the south pole downwHrds, and, by noting the deflec- tion of a compass-needle at ditferent points in the mine, he founiJ that the bore-hole was 8 feet from its expected position.

A powerful magnet was also applied with success in the of the Upper Harz. There, according to Mr. O, Brathahn, on March 17, 1698, a. level connecting the Kaiaer Wilhelm II. shaft and the Hosenhof shaft was successfully holed. The requisite traverse had a total length of 2000 yards, and the junction of the two roadways was effected with mathematical accuracy. The result is of special interest, inasmuch as the mine surveyor, Mr. Plachsbart, wne obliged to employ a great variety of methods of surveying. He had, for example, to connect the eurface- and underground -surveys by oalcvilation, by means of plumb-lines and by means of the magnetic-needle. A special trisngulation- BUrvey of the surface had to be made, the two base lines foi which atiorded an opportunity ot testing the steel rods subse- quently used for measuring the lengths of the station linei underground. The Rosenhof shaft is an inclined one, and in the upper portions quite unsuitable for traversing. Consequently it was necessary to utilise the vertical Silbersegen shaft down to the south level. There plumb-lines and the magnetic colli- mator were employed, and the iravorae carried down the inclined Rosenhof shaft t<i the seventeenth level. The average inclina- tion of the shaft is 77', In the ehaft an eccentric theodolite was set up in three places, and horizontal and vertical angles measured. The seventeenth level to the starting-point of the new connecting roadway is over 400 yards in length and very torttiouB, so that the theodolite had to be set up twenty -two times, the work being rendered difficult by the number of short

Uasnbtic-Kkedlk Im Miniko.

lines of sight. The roadway driven from tlie seveoteenth level contained only eight angles in a length of over fiSO yards. The orientation of the seventeenth level was effected with the aid of the raaenetic collimator. That, of the heading driven from the Kaiser Wilhlin II. shaft was calculated with the aid cif the KSnigin Maria shaft over 900 yards distant. The azimuth obtained was tested by magnetic observations, and a difference of twenty-two secoada were observed. The calculated result was adopted. No difEcuIty was experienced in the anrvay of this heading, in a length of over 90 yards, the theodolite being set np only sixteen tiinea. The length measurements were mads with two *2-metre steei rods along a stretched cord, the fraction! being measured with a brass metre rule divided into millimetres. The clinometer wati used for determining the incHuation of the cord, and each line was measured twice at least, For levelling, the starting-point selected was the level of the water in the navigable adit level, which is horizontal and 2700 yards in length. It connects the Silbersegen and Kaiser Wilhelm shafts 760 feet above the horizon at which the connection was to be effected by this survey. Vertical depths iu the inclined Eosenhof shaft were measured with Borchers' steel rods, and these ap- pliances were also used in vertical Bhafts.

As the connecting roadway was intended subsequently to ba used for electric haulage, an accurate junction was desirable. Consequently, when the headings were within 5 yards of each other, the direction was tested by means of a powerful magnet 1 65 lbs, in weight composed of six bars, in the manner proposed by Borchers.

The level of the two headings was tested in the same way In this way an exact junction was effected. This final test is of great value to a surveyor in charga In this case he knew five days before the holing was effected that the work bad been carried out with accuracy. When the holing had been com- pleted an accurate survey was made, and the deviations fuund in the two traverses were 01 +3 metre in the ordinatea, 0-451 metre in the abscissfe, and thirty-three seconds in the azimuth. The difference in level was found to be 1*5 millimetre.

i'ii MIKE-SURVEYINa.

Chapter Xx.

Photographic Subvktikg,

Photogrammetry.— The theory of tlie methodi by which platu Aad sections uay be obtained by meiins of photographs hu been termed photogratnnietry. The principles of photogrammetry were developed by Lambei't as far back ma 1759. The fimt application was made in the years 1791 to 1793 by Beanteoips- Beaupr, who constructed topographical plans from his per* spective hand-sketches made during his voyage round the world. The first camera constructed for this purpose was used in 1851 by Colonel Laussedat, who in this way surveyed a portion of Paris in 1861. Since then the method has been largely developed in Germany, Austria, and Italy, and the liberator* of the subject is now considerable,* The principle of the method is simple. If a photograph be taken frou a point of which the position is already known, the direction of the axis of the object glass and the focal length of the lens being also known, and the line of the horizon being marked on the picture, the picture can be laid down on a, sheet of paper on which it is desired to plot the survey, and will give the direction from the point of observation of all the points the position of which is required. Two photographs of the same object taken from different known points define the position of each object, and also enable altitudes to be calculated or graphically determined. In fact, the method of surveying is exitctly that of the plane- table, with the diB'erence that a. great portion of the work which, with the plane-table, has to be doiie in the field ia, with the

'The following are the princijtal works on photogramnietry : — -Coloiliel Lanssedst's exb&uitive rtktles in the J/ntortoI I'ociar dv r/ie, 18&i, No. 16, and 1864, No. 17 ; " Uie I'hotograranietrie," by Dr. Stobe, HUe, 1887; "Die Photognunmetrie." b.v Dr. Koppe, Weiinttr. 1889; " Photo-

faphy applied to Surveying," by Lieut. H. A. Reed, New York, 188S i P. Psi{anini'a articles m the /{iaiita di Topoijrafia, 1889; "Die Photograpnie iin Dienute des Ingeoieura," by F. Steiucr, VieDna, 18S1 1 " Die Photographiache TBrrainaufnahme," by V. Pollack, Vienn*, 1S81 s "Die Photographiache MeBskunst," by F. SchiSher, Halle, 1882; "Dm Photographische Aufnehmen zu wieiisuhiiftltuhen Zwecketi," by A, Meyden- hauer, Berlin, 1802; " Sli'-inents de Photoyrammtrie," by V. Legros, Paris, 1892 ; E. Mootft's article in the Memoires di ia tocUtt dts in<ihi\atrt dvitt, 1894, p. 216, "Photographic Sur'eyiug," by E, Deville, Uttava, 1895; "Anwendung der Photographic in tier MesskunBt," by E. Doleaat, ilalle, 1896; " Les InBtrumenta topogcapb iq ues, " by A, LaUModat, Paril, 1898; "Topografin folograpbicB," by C. de Iriarteand L. Navarro, Madrid, 1809; and A. 0, Wheeler's paper, IVani. fii*(. 31, E.. vat xxi,, 1902, p. 418.

Photographic Burvkyino. 333

photographic method, done in the office. The degree of accurucy ohtainabl© is obviously not excessive. The method is, however, weU adapted for such topographical surveys &s mining engineers are sometimes called upon to execute.

Inatrtuiieiits Dsed. — There are many types of phototheodolitM In use. The principle is, however, the same in all. The inatra- ment consists of an ordinary theodolite in which the telescope is replaced by a camera, whose optic axis is accurately parallel to that of a telescope placed at the side. A graduated horizontal circle and a vertical circle enable the angles to be read with accuracy, and a spirit level tixed to the camera serves to ensure ihe horizontality of the instrument. The holder for the plates is provided with points of thin sheet metal which mark the horizontal and vertical lines on the picture. The point of intersection of the marking should coincide with point sighted at the cross- wires of the telescope. The leading maker of phototheodolites is R. Lechner of Vienna.

A compact instrument for photographic surveying has been designed by Mr. J. Bridges it consists essentially of a photographic camera fitted inside with a niiignetic-needle, which carries a vertical transparent scale divided and num- bered to 360*, and also with cross fibres which intersect at right angles. The fittings and adjustments of the instrument are of such a character that the camera can be accurately levelled and directed towards any point in a horizontal direction, and when a photograph is taken in an ordinary way the bearing of the meridiaa vertical plane which bisects the instrument through the protographic lens will be recorded automatically on the face of the photograph. The vertical fibre (and its image on the photograph) serves as an index to read the bearing ; and the ftiune fibre marks by its shadow a line riglit across the photo- graph, which marks the meridian vertical plane on the imie. The horizontal fibre is adjusted to mark on the imtige the hori- zontal plane which bisects the photographic lens. The camera rests on a divided horizontal circle, which can be adjusted to a truly horizontal position by levfUiiig screws. There is a tripod stand and head, with suitable appliances for supporting and adjusting the instrument in position. The camera is provided with a rectilinear doublet lena, and iris diaphragm and rack and pinion focussing adjustment. It is made of aluminium, and it is surmounted by a telescope adjustable in altitude, and fitted with vertical and horizontal webs and it is also surmounted by -ji revolvable tubular level.

Hoi. q/' Ungineert Trains,, liiBil, pv 171.

Uikk-Burvsyiko.

The jiresent fonn of the Bridgea-Lee photo-theodolite, made b? Mr. L. Casellii of London, lias been adopted because experimenC has proved the oecesaity of great nicety of tuechamcal aiijuev ment to obtain the best results. One very important additioa to the uaefuliiBsa ol' the instrument is the insertion of a saJe of angular distance photographicallj prepared by the same lens that fitted in the instrument when complete for surveying pur- poees. The scale is so attached to the frame that it is photo- graphed on every pictura taken, and by its aid the iingulBr distanoes of any point in the picture right or left of the median vertical plane may be read. In order to avoid |ios8ibIe oonfuaioo among the pictures obtained, it is found advisable to record notes indicating the number of the picture, station, altitude, and magnetic variation on the face of the picture rather than iti a note book ; and special proviaion has been made to enable this to be done easily.

The construction of the Bridges- Lee photo- theodolite is shown in Fig. 1 Ola, in which A is the aluminium box provided with a rectlinear pliotograjthic lens; C is the horizontal circle divided in half degrees with a vernier reading to minutee ; £, the tele- scope free to rotate only in a vertical plane ; in the most recent instruments the telescope ia held between two supports ; F, the vertical limb divided in half-degrees with vernier reading to minutes ; G, revolving tubular level ; H, falling-back to camera with hinged joints, and with a window of polished glass, in the ground glass, h, through which the vertical iadeix hair and compass scale can be read ; I, rectangular frame of naetal rigidly attached to a bottom plate that auppurts the compass-box ; it can be racked backwaiHls and forwards by the aid of a transverse pinion traverain" the bottom of the box and terminating in two milled heads, J J. Pointers that revolve with the pinion serve to show whether the internal structures are forward or back when the falling-back of the camera has been let down, and replaced by a double dark slide containing a photographicallj sensitive plate. The rectangular frame, I, can pass inside the double dark slides used, when the shutters are open, and carry back the hairs, K K', which it supports until they touch the plate L L are small tablets of thin transparent celluloid, on which any particulars required are noted. M is a magnetic compass with vertical cylindrical transparent scale graduated in half-degrees from 0° to 360*. The scale paaaes close to tlte vertical index bair, but never touches it. N is a catch to hold the double dark slide in place. U is a microscope with universal joint movement to permit of its being used either for reading horizontal angles or comijaas bearings P an adjustable micro-

MINB-SCRVETtlifO.

scope for reading vertical angles. S is the clamp and tangent screw for the telescope. 01am ps and tangent screws (not shown in the illustratioti) ore also provided for the horizontal circle and for the camera. The crosses marked XJ on the top of Ihe box indicate the focal distance. The instniment is provided with tribrach locking plates and levelling screws, and is sup- ported on a strong tripod. Attached to the frame, I, carrying the hairs, K K', is n, horizontal trans jiarent scale of aagular distances, photograjihically prepared by the aid of the identical lens and instrument used for surveying.

Application to Mining Work. — Mr. H. M. Stanley, of Arizona,* BUccessfuUy employed the photographic method in a survey of the properties of the Plata-Reina de Senora Mining and Milling Company, aitnated in the raining district of Las FUnchas, Mexico. The area surveyed comprwed about 6 square miles in broken mountainous country. In order to carry out the work as quickly and as accurately as possible, it was decided to triangulate the area, and to complete the work by photographic surveying; an 8 by 10 Eastman camera being used. The first picture was taken to the north, and to the right of the meridian. The others were taken round the circle, one after another, so as to slightly overlap, care being taken to note the height of the instrument and the index number for each picture.

The method of plotting employed by Mr. Stanley is illustrated in Fig. 102. The points marked "Corruscos," " Mejia," "N. Ooneccion," and "N. Guadalupe" are points established by triangulation, at each of which pictures were taken. This sketch was originally constructed on a scale of inch to 150 feet. The focal distance of the lens used is 20-3 half-inches.

In order to fix the point " W. Ladem," it was found on ei- B mining the pictures that this point is on VIII. Mejia and I. North Uuadaiupe. The first operation is to orient these pictures — i.e., £nd and plot the position of the optical axis and of the picture in each case. On Till, Mejia, the point "Corruscos" is known. Mark it (1) on the back of the negative. With the dividers measure carefully the horizontal distance from this point to the vertical axis. From a diagonal scale of equal parts con- structed on a half-inch, the horizontal distance is found to be + 5*53 half-inches, or units, and aa it is to the right of the vertical axis it is marked plus. This distance is the altitude of a right-angled triangle whose base is the focal distance of (he lens. The hypothenuse is the distance from the optical centre of the lens to the image of the known point on the picture, in this

'Trim*. Amer, Itul. M,£., voL xx., laSJ, y. 7iQ.

3;

MIN&SURTKYlSa

owe " CkirruitcoB." The tangent of the angle at the hue of the right-angled triangle ia equal to

The orientation angle is therefore 16" 15'.

This result is placed in the proper column ol a table nili folio wb; — Fhotographie vrvaj/ cf.

BaiLi, tauh o uo ft. FoGAi. xnataimA

N. QMdiklupe, Ua]K . . . N, QiudAlQps,

Viu.

vm.

Oo-ordlottM

+W1 01

+11" ir

ft

-rw

-in*-!

as*

Si

To plot the position of the optioal axis, draw a line through the station Mejia, making with the hjpotbenose, Mejia- OorroBoos, &n liDgle equal to 15' 15' — i.e., to the lefL Make this line equal to 20'3 half-luclies or units and it will be the optical axis. A line perpendicular to it at its extremity will be the position of the picture VIU. Mejia. In the same manner the picture I. N, Guadalupe may be oriented as shown on the sketch, using for the purjKise point (1) of that picture, which the flog at K. Ooneocion. The calculation in thu caae ia ; —

Tangent of the angle

+ 5-47 So-3

- + 26946.

Orientation angle + 16' 04'.

The two pictures haying been oriented, the positions of all points common to them both may be determined. On picture VlII, Mejia, it is seen that the point W. Ladera, point (2 in -3-80 units to the left of tbe vertical axis, and +081 unit

Puotographic 8Urveting.

ibove the horizontal axis. The Hftme point (2) on the picture I. N. Guadalupe, is + 2 -35 units to the right of the vertical axis, and - 0*51 unit below the horizon. These results are recorded on the calculation- sheet. Now,

-3'80 20 '3

tangent of ansle — - O'lSTlS.

Ition-aagle - 10* 36'

At the point Mejia draw the line Mfijia-W. Ladera, mnking with the oiitical axis an angle equal to - 10° 36'- — that is, to the left of the optical axis.

From picture I. N. Guadalupe it is found that

+ 2-35

tangent of angle +0'n576.

;>c&tion-aQgle + 6° 36'.

At the point N. Guadalupe draw the line N. Guadalupe-

Ladera, making au angle with the optica! axis of picture I.

Guadalupe, equal to + t')" 36' — that is, to the right of the

>tical axis. The intersection of tlie two liatti Mejia- W. Ladera

ad N. Guadalupe-W. Ladera is the position of the point

Ladera which was required. This point could have been determined graphti'Ally. On the ae L A B lay off A B - - 3-80. Through B and Mejia draw tie line Mejia-W. Ladera. On the line DFN lay off F E + 2-36, and draw N. Guadalupe-E-W. Ladera. These two line* will intersect at W. Ladera. The distance Mejia- W. Ladei-a, alao K . Guadalupe- W. Ladei-a are scaled from the map and placed in the proper column of the calculation-sheet.

To find the elevation of W. Ladera, or its depression above or below Mejia and N, Guadalupe, the procedure is : — Through the point, B, draw BC perpendicular to B- Mejia, and make it equal to + 0'81 unit. Through Mejia and C draw the line Mejia-C-M. At W, Ladera draw W. Ladera- M perpendicular to Mejia-W. Ladera Then the line W. Ladera-M is the elevation of W. Ladera above Mejia, and it may be scaled and placed on the calculation-sheet.

At £ draw D£ perpendicular to the line H. Guadalupe- W. Ladera and equal to 0'51 unit and at W. Ladera draw W. Ladera-G perpendicular to the same line. Through N, Guadalupe and D draw K, Guadalupe-D-G. Then W. Ladera-G is the de- pression of W. Ladera below N, Guadalupe. Scale this, and place it on the calculation-sheet.

340 UIirK-eURVETtKQ.

To calculate the elevation —

In the right-angled triangle Mejia-A-B, the side Mejiiv-B

COB 10 j6

In the rig li Wangled triangle Mejia-B-C, the tangent ofai'le

at base - '03932 ; the angle of elevation W.

In the triangle Mejia-W. Ladera-M, the side W. L>adera-M 5668 X tan 2° 15' 222-8 feet.

In the triangle N. Guatlalupo-F-E, the side N. Guadalupe E

20-3 „„ . . ,

~s-o-~. 20-4 units.

coa 6 36

In the triangle N. Guadiilupe-D-E, the tangent of angle iit base - — "02 500 ; the angle of depresaion — I' 26'.

In the triangle N. Guadalupe-W. Ladera-O, the side W. LaderaG 6292 x tan 1" 26' 1S7-3 feet.

Therefore, W, Lad era is 222 '8 feet above Mejia, and 167 '3 feet below N. Guadalupe. If Mejia is 500 feet above the datum plane, then W. Ladera is 722-8 feet and N. Guadalupe 880'1 feet above the same plane. In the same manner any , other point on these two photographs maj be determined i grapbically or by calculation.

The point W. Ladera may be determined firom one photograph thus : —

The side Oorruacos-Mejia ie known from the triangulation, and the bearing of Oorruscoa-W, Ladera from the field notes. Then in the triangle Corruscoa- Mejia-W. Ladera, the anglo at Corruacos 139° 46'. From the photograph "VIII. Mejia, the angles 15° 16' and 10° 36' may be found as before. Their sum 25° 51' is the angle at Mojia. The angle at W. Ladera is e<)ual to 180' - (139° 46' + 26" 51') 14° 24'. The triangle can now be solved )iy the ordinary sine-formula, and the distances from Mejia and N. Guadalupe to W. Ladera and their beariAgs ouk be determined.

Photographic surveying has also been euccessfully adopted in other mining districts. Lieut. H. A. Heed in his work on photography applied to surveying reproduces an excellent French pbotograpbio map of an area of 13*6 square miles in the vicinity of Sainte-Marie-aux-JJines, The field work was plotted to the scale of xmre- contours have an equi- distance of 5 metres. The field-work occupied 10 days, the number of photographic stations was 31, of prints 5%, and of points detrmined 1,400.

PHOTOOHAPHIC aOHVEYUJO. 341

In 1880 the Carrara marble quarries were aucceasfully surrey ed by L, P. Fogaaini by the aid of photography, the mouutainoua

'Saracter of the district having rendered the uie of the plane

kble inconTenient. The method was also used by Y, Pollack in 1890 for a surrey required in connection with the construction

a iQQuntaiu railway at the Eiaenerz-Vordernberg iron minea Styria, and in 1 898 by Mr. E. Deville in preparing a niap of

tie Klondyke goldfields from etxteen photographs taken under very adverse conditions from three points at altitudes of 2,870, 3,T00, aud 3,450 feet.

In Canada the method has also been employed on a number of surveys in the Yukon district, on the Columbia river, and in th Kootenay mining district. It was also used by Mr. A. O, Wheeler in Jiis survey of the Crow's Nest coal area. Some diffictdty was experienced in finding camera stations sufficiently commanding to overlook deep valleys. In order to obvttite this difficulty Mr. Wheeler conducted traverses up the main water- ways. The lines of direction were obtained by theodolite readings, and the elevation was carried through by vertical Angle readings at each station. For determining distances some pattern of micrometer or stadia was used. For this purpose a modified form of the Lugeol micrometer was found to give satisfactory results. It consists simply of a telescope, having a bisected object-glass, one of the halves being movable along the line of section by a screw. Two images are formed in the field by the bisected lens. Distances are determined by the number of acre w-re volutions necessary to bring, into optical coincidency, the upper and lower targets of the reflected images. The targets are best made of white opa! glass set in wooden frames, and are fastened to a rod at a known distance apart : say 16 to 20 links (10 to 13 feet) This is called the base; ii is generally furnished with an iron shoe and is stuck in the ground in a vertical position, the targets extending side-ways at right angles. Attached to the screw of the movable half of the object-glass is a graduated head which measures in revolu- tions and hundredths the section of arc passed over in making the coincidence of the targets. It is merely necessary to find the trIuo of a revolution, in order to enable the distance to be determined for each reading. Tables can readily be constructed that distances can be taken out by inspection.

Advantages of Pbotogrammetiy. — From the foregoing de- scription it is evident that, with the camera as a surveying instrument, the field-work may be performed with great rapidity. The reduction to a minimum of the time occupied in field-work is the chief advantaire of the method. Ibe sutv| <:ki

lllNK-aXfVE¥IJff}

of 3 tniles of the Windiicbgarsteu-Spital railway in Austria, covering the entire width of tLe valley and including the heights on the right side, recorded in 24 pictures by H&ti'erl, occupied in favourable weather four and a-half hoars. With the cliicatic conditions obtaining at the Arlberg in ISSD, it was absolutely ioi possible to use any other method of surveying the precipitcns peaks. It is thus evident that the method is sjiecially useful in the unhealthy malurious districts that a mining engineer is often called upon to survey. It is also veU adapted in mountainous and difficult country for laying out rack-railways or aerial wire ropeways. The successful photographic surrevs of the Arlberg and of the Roastraiipe mountain in the H&rs show that inaccessible regions may easily be surveyed. It follows that it is posisible to survey regions that cannot ba traversed without danger, such as railways in operation, glMlH ground above mines where subsidence has set in, or areaH which access is forbidden by the owners. There is, too, the further advantage that additions may at any time be made to the plan without a fresh survey being necessary. The plottang of tlie survey is not Bttend(>d by difficulty, as the plan resolls from an application of the simple method of intersections, whilst the representation of aurface-forroa and of height* Ir effected either mechanically or by the use of tabular values that are easily applied. With carefully constructed instruments, the results exceed in precision those obtained with the compaM ur with the plane-table. As addenda to the plans, the photographs recording the survey will, for the purposes of mine reports, oftea supply useful information.

Appendix I.

EXAIIINATIOH QUESTIONa

The following exauuDatioD questioiu will be found useful to thoae itudeuta who hkTB not the advantage of regular metmotioD in tuiuo-Burveying, affidding them a uieanB of peraooallj testiiig their knowledge : —

1. Uiv the length of a link, &nd of a chain. liow many ohoiiu are there ' In a mile, and how miuiy aaroB in a square mile 1 ICollierf Mcmagert'

JSKOminiUion, Briatol,]

2. In chai ning over eloping ground, how do you ooireot for the inclina- tion t Give a mrnple rule when the inclination ia expressed either in angular meMUie n h a gradient, e.g., 1 in 6, 1 to 15. {City ami OuiUt qf London Itutitute, Bxamination in MiiK'Sureeying, ISSS.)

3. Ltesohbe the miner'a dial, and Dot the improvemeata recently intn>- dnoed into ita ooDstrnction. (Royat School of J/inea, HjamiiuUion in Mm Stoning, 1B84.)

4. Give a opy of a page of a aarvey-book recording an imaginary under- ground-BUrvey. How may yon approximately ascertain tbe date of the workings of an old undated plan ? {CoiUer}/ Mawtgert' STomimiUim, XajtciMtSire, lo87.)

5. Oeacribe the Uenderaoo dial, and atate ita snppoaed odvaatagoa over tbe rack inatrument. {H.6.M., t$!i3>.)

6. Give a short description of the miner'a dial, with its uaual appliance*, aipciaUy when it is used as a theodolite, the needle being thiown off, ifiitt) (hattU, 16S0. )

7. Describe a Guoter's or land measuring chain. (City , 1881.)

S. What is meant by the term true meridian t Desiirib a aimple method for approximately determining it. {CUi/ Ouildt, 1885.)

9. State tbe present deviation. In what maooer ia tbe deviation osnally found to vary from year to year, also in travelling from one looality to aoothr at a considerable distance T {City Oitildt, ISSS.)

10. Sketch on paper tbe following bearings of a survey : — K. 83° E., OS links J 8. 51° E., 115 links j N. 63° E., 73 Unki ; N. 20° E., B7 links ; N. 35* \V„ 87 links ; N, 87" W., 140 links; a 52* W„ 140 links ; S. 48° K, 86 littlu. iColliery Managers, Derby.}

11. Explain the traverse tables, {CoUient Manager* South Waim.)

Mine-Sorvktino.

12. Snppom yoa were driving towards an old waat, which u iowa oa ft ]i!an 20 yea-n old, ezplaiu the precaatioQa to be takn m reganli the meridian. {Oolliery Manager*, Derby.)

13. YoQ >re required to traverse over a level id which c&ila are Uid down. Hoiv would you proceed to use an ordinary miner's dial aader the ciroumstances, the di being without a rack, but sapplied with two wti legs t The only true bearing was one taken in a crosa-cat north, at a dia- tice of, say, 5 fathomti off the main level, where the traverse ia being made ; tiiis croas-out oocnrring about half way in the traverse. Role a mp- posed page of your miderground book suited to this gurpoBe, sud gire, say, sis drafts or bearincs all Ruppoised to be alfijctod by the attraction of t£€ roila, the polarity of the whole being veraed by the tme bearing in the eroBs-cut north. If time will permit, UMert dintnnpea and prove your work by plotting. {(My Omlda, 1883.)

14. Explain by writing and sketching how to make a loose needle aurrey .

(Yorkshire ColUge, , 1S86.)

15. The three sides of s tritukgle measore 144, 192, and 240 links recpee- tively. Find the area of the triangle tn square yards, and the angi* cpposito to the shortest side. {City Oiiiidi), 18S5.)

16. What is the area in Btatate acreage of a ttionguUr Geld whose aidet measure 2420, 1860, and 2005 links respectively t A. sketch m&y given, but not to scale. Logarithms are recommended for the caloaUtion. (Cily Ovililii, 1S83.)

17. Explain by writing and sketching how to make and book a fast

needle survey. {Torkthire CoUtgn, Leeds, 18S6.)

18. The area, in acres, roods, and poles, is required of on irregular fleld, which was surveyed by ronning one Une throogS it fniin end to end (A to

B), with offsets taken as under :—

No plan to be drawn.

Appendix I.

19. Give a general deacriptioji of the theodolite, uid exp}ii the method in which yoa wotild use it in making Aa underground-siirvey. {City Qtiiidi, 1S87.)

20, What Are the special adviLntges and diaadTantages in the use of the ordinary miDer'i compass aa oompared with the theodolite T iOity OuUdi,

31. Lay down the undergrouod-aurvey given oii page 39, on the acale of 3 chains to an inch. Trigonometrical calculationa may be uaed. iCiiy Guiidt, 18S7.)

22. Find the horiEontal diBtanco and direction of the Station H (page 39] from the shaft. Also the approximate difference of level betweeu thees potnta. (Ct(jf GttUdii, 1S87.)

23, Work out the following aeries of levela, showing the height, above the Station A of each jmint taken ; —

SbtUM.

Buk-aiffat.

A

eio

I'M

2ie

4'M

9-Oti

,..

G-15

B'Oo

10*16

11 '20

.,.

Is-Oo

..,

u-eo

3 '23

HIKE-SnRTETlKO,

SMi Exptun by trritiiig bow to level and pUtt a lection. (TorbKir*

CiAUgt, Utdt, I8Sa I

25. Find the quiiutity of ooal In 1 aore of seam of the following leotion : — Top coal, 2 fet 4 inches ; band, feet 10 inches ; bottom ookl, 1 feet 8 inobes ; total, 4 feet 10 inches, taking the specific gravity of coal at im. {CoUifry M an- <ijm, Newcattit-oa-Titne.)

SBL Find the quantity of coal in an acre of a aeam 5 feet 61 inohe* thiok, teking the ipecitio gravity at 1'25. {NaectutU-onTytm.)

27. If pillars are left 30 bj 21, and wimungi :i2 by 26, wtut percentage Is got in the brat working T (OoUirry Majtageri, NetBcatdt-on'Tie.)

28. B.OW much coal might be expected to be available in an area at ISO erea of a 4-feet seam, allovring one- for fanlts and waste f {Seinee and Art DepaHmeiU, Sxamtnalion an Mining, 1884.)

£9. The solid con tents of a lode are in volume per cent. ; —

Galena, ,,, ... ... ... ... SO

Zino-blende,... ... ... ... ... 15

Iron pyrites, ... ... ... ... 20

Quartz, ... ... ... ... ... 35

What is the weight per oubic fathom of the staff and of iln different eon* stitnents {S, and A . D., 18S4. )

30. A copper lode is 14 tnchea thick, oontaining oopper pyrites and fluorspar in the proportion of 2 porta of fluorspar to 1 part of coppet pyrites. What is the weight of a square fsthum of ibe lode, alio wing one-tnirtietli for hoUowa I ( Siclard, )

31. A level 7 feet high is driven on a tin lode 8 inohea thiok, of which oue-teoth is oxide of tin, the remainder being uarta. How many tons of tin stoif will be obtained per fathom in length, if the lode is quite solid ! (Mieiard.}

32. In working to the iiill rise of a seam of which the inoliuation 1 in 12 you meet with a rise fault of 10 yards. What will be the leogth of a rise tunnel to be drawn at the inclination of 1 in 6 between the seam at ths low side of the fault, and the seam on its rise aide, sapposiag the fault to ba vertical T {Colliery M ana , tKwi ZrfineeM Aire, 1887.)

3S. Plot on a scale of 8 fathoms to the inch the foliowiog under. ground traverse, taken with the ordinary miner's " left- hand " dial : —

Nck

Lijkriug,

A

355° aff

tea ft. lu.

From centre of pp shaft

B

84' 26'

,..

92-04'

C AtxoutN.

[d.

342*09'

D- EKD do.

B

96* 05'

e

End.

— (jCitij GuiWs, 188S.)

Appendix I

34. Describe the ordinary method of using the thcodulite in making ixa ondeirDDDd-Bunrey. Also imy niecial method wbioh may be adopted where great nccnraoy is required. {CUi/ OtiiliU, 1887.)

35. Lav down the foUovdog undergroond-aurvay on the male of 2 ohaiui to &n inch : —

DMui, Obttni.

YnrUnl iDellDntJun

Horilaatil Auilo.

to A

1-So

ff" 0'

A 145' Is'

Ab

6-7fi

4° 85'

B 17r sc

Bc

13'

C 213° 54'

Cd

0- 0'

D 97° 20'

De

6° 4C'

Ei'

Of 0'

F lersff

Fg

T 20'

Tha horizontal angles are those on the left bemd of a persoa travel ling in the direction of the survey, and tbe magnetic bearing of the line F G ia 30* cMt of north. (City Guilds, 1887. )

36. Tlie dijfereitee of level of two points several tniles apart ia required with great exaotnesa, and a laTeUingHastrament of high power it naed for the purpose.

Under what oiroumstanceB would it be ueccasory tu allow for the sphericaj form of tbe earth, and in what manner would yoa make the proper correo* tions I {CUy OuUdi, 1887. )

37. A coUiery waggon way in laid down in a straight Une from A, near ths 1 haft, to a point B. in a direction 40° east of north, and is to be extended to I join B m&tn line of railway towards the east, running dne north and south. J The distance from B to the main tine ia 'SO chains, measured due esst, and] the junction is to be made by a curve 64) chains radius.

Show how the waggon way must be set out, and find what length of line will be required beyond the point IS.

In setting out tbe curve from the straight portion of railway, what of&et must be made at tbe end of the first chain F {City Gvildt, 18S7.)

3S. It is intended to sink a shaft on tbe end of a level driven from Fendarves' shaft, and tbe following ia the survey by J. Budge from the centre of the shaft to the eastern end of the level : —

HlKG-eORTEYINO.

No.

Briiij.

DUtuM.

A

asrow

from ueuti-e of ahAft

B

82° 45'

81' ,W

D

woe

8 t 1

E

ithr otf

F

90*45'

Iwoo'

H

85° (W

J

77° 45'

K

351* 00'

End.

As absolute accuraoy wu required a reverse or proof courM of duJliag was made from the eod book to the shaft, with the loUowiag results : —

No.

Benrlug.

Olatimoe.

A

171' 30'

fnu. (t. Ina.

from eaitera ESD,

B

eso-oo'

265° 15'

3 1 S

D

28.r 15'

K

279' 30'

F

aw 45'

O

263° 00"

H

280° 16"

J

177' 46'

centre of ahafc

Calculate the distance and bearing, from Pendarvea' abaft, of the pointat tb taiiace at which the new a'baH muafbe eouV.

Appendix I.

39. Sketch and desoribe t, hangiaj; compon, ette ia which wy it is tested and repaired, &nd describe the m&nner of Ita appUcation. {ToMo l/niveriUy, Japan, 1679,)

40. Give B short deaoriptioo of the OermBQ dial, and what 70a ooniidsr to be its merita or demerits aa compared with tha English mlner'a diaL {City Gvilda, ISSO.)

41. Describe the continetitBl method of sarreying mines by means of the banging compass, giTiDg sketches o( the fnatrnmenta employed. IR.S.JIS,, ISSG.)

42. What methods have been used to determine the deviation of bore- holes from the vertical ! {Sdenet and Art Departmaat, 1887.)

43. At the Scotchman's United Mine, StaweU, and In varions other

S laces, it has been foimd that bores made by the diamond drill have e via ted so seriimsly frotn their initial direotton as to imply errors amount- ing to from 30 to 75 feet in bore- holes of 500 feet. Deaoribe a method of making a snrvey of boreholoa, and aesuminK the errors to have been detected, how is it possible to straighten a bore which baa been so deflected as to endanger the safety of ths driU t {Jt.S.M., 1836.)

44. How should theoompaes be used in exploring for iron oroit {H.S.M., 1887.)

45. Two parallel lodes were discovered at the surface, which was level, 90 yards apart nnderlying south, the sonth lode maUog an angle with the horizon of 65 decrees, the north lode of 52 degrees. Eefolred the per- pendicular depth from the surface to their point of interseition ; and how tar south of the sonth lode would the centre of a perpendicular shaft have to be placed to come down to the same ]K>int! nlnstrate by a sketch, not necessarily to scale, but a scale is reoom mended in order to ronghly teet tho accuracy of the calculations. {City Quildt, ISS3.)

46. Illastrste in oolours the following parts of a finished plan, scale $ fothoms to the inch ;— A road 26 feet wide bounded on each side by a hedge or bttlik 6 feet wide, Hhoving a gateway, with a croea hedge or two, also a lionse 30 feet by 20 feet abutting on the road, with a pond adjoining open to the road, but with the hedge continued round its other aides. The pood not to be leas than 58 feet Ion a and 2.5 feet wide, and of an oval but irregular shape. A shaft 10 feet by 6 feet to be shown in one of the fields, aurronnded by a burrow or mbbidi heap which ia to be aketched in with pen and Indian ink. The whole drawing to be about 1 foot in length. i,€Uy Ouiltls, 1883.)

47. Without the application of a protractor, lay off the following angle* from the same base, viz. : — 20, 30, and 6'i degrees, using a table of nataiat lines for the purpose. Describe the prooees. [Cit;/ QiMd, 1883.)

48. In the triangle ABC, the angle A 37° 45', B 72" 16', and th* aide A B 437. Find the sides A C, B C, tad the perpendicular distance from C to A B. {City Guild*, 1887. )

49. In the triangle A B C, the side A B 365, AC 180, and the angle B 26' 30', Determine the angles A and C, and the side B 0. [CiCy Guilds, 1887.)

60. What do you nnderstand by the word traversing T Where is thii form F lurreying necessary t How would you use an angular instrument in th*

oparatioa, and how would too check the aocancy of the plotting of the work by trigonometry I {City GuiUU, 1833.)

51. Describe the true meridian, aa compared with the magoetic meridiui, now does the Bdontion of the latter aSect plaiu made from oonipasi olHst-'rvations and added to, as in mine plana, nni year to year T iCitjt OuiliU, 1682.)

BS, It is dMired to know the exact dittance and beexiug of an imaginary Una between the centre of a perpendloaUr shaft A and a point B in tevd imdergnHmd, over wbich it is intended to sink another perpendicular shaft, the dialling of the level cammenuing from A. Sketch the sapposed dimfta uuderground, marking each with its leogth and bearing, uid proceed to describe the beat and most aocnrato of laying down, at t£ aoAot, the line required, and the poaitiain of the proposed new shaft oTer B.

63. Deaciibe the ordinary process of leveUing, staUng any precautions required to ensure aoeuraoy. {City OuUdt, 1885,}

64. Work out the following series of lerels and plot in the fomi of a sec- tion. Horizontal scale 1 chusin to the inch, vertical scale 20 feet to th inch. Datum-line 50 feet.

Diilaem

Back-

loie-SlKkt

OMiu.

Foet. 8 '86

8-8£

13 '96

5'40

8'So

6 '80

I Is

9 '40

9'%

3*34

B'87

n-3&

fl-87

S-10

—{OUf Oviidi, 18S&.) 66, Plot, on a scale of 2 ohoina to on inch, the following aurvey :—

Af FEKDIX I

Clwlni.

.

IneUutfDB. IUh.

A

7-

137* 16'

rtv

141° Sff

D

196" Bff

K

6S0

189- 24'

F

111M

268' 36'

rao"

272*22'

— (Otij, OuUd*. 1885.)

M. A ctraiKtkt draft u required to be driven of ouifonn iaoluistion betweoD C Mtd G. How ntut it be aet out from each end I (CUu OuUdt,

1885.)

57. DeMribe the method of niing the tnuuit- theodolite in order to MMnre horizoatal and vertical sogles with great preolHion, {City (hildi,

ISSe.)

58. ExpUiu the prinDiple of the vernier, and describe the muuier in which yoa wonld coiutrtict vernier for a circle to read 30 seconds, when the uo ii divided into quuter degrees. {S. S. M,, 1884.)

59. How msy the andergroond. and turfifMe. surveys of & tnine be am- neotedl (if. A/., 18S7.)

60. In s 20>{athoin level driven on an east and west lode, ODderlving north, a wiiue has been commenced bearing doe north, and it is dctermuiea to pitch a rise against it in the 40-fathom level ; the SO-fnthoni level not havuig been driven far enough east for the parpow. Bow would yott detefmloe the exact point In the 40 iW thorn level to start from ? (B. B.M.,

isae.)

01. Calculate trigonometrical ]y the beuing and distanoe of C from the centre of the shaft m the following traverae : —

M&

Aarie.

BerUig,

DUtanoa.

A

0"00'

351° aff

rma. a is.

10 4 e

From centre of shaft.

B

90° 21'

176' ly

End.

—{R. S. M., 1888.)

H

UIKS-SORTeTIKO. 1

62. Lay <Iown, on a, sc&le of 1 chain to the intvh, the snrvey dten va H nag Sfi, representing four-tided Geld connected with the BhaftotK nuag. H H CalcalAte the area. (Cifi/ (TuiMi, 1S85.)

69, Plot the following survey, by W. Rick&rd, of k Conusb mine : — From pp. line in WilliKms' ahkft the 60-fathoni level.

H

Mo.

Bearing.

DlnuiM.

InaUBathtB.

InollDtd

Langtta.

Rnurkl,

A

176* 00'

fm. ic in.

bB. a In.

i.

B

It 30-

82° 45'

D

97° 15'

to Vivian't wlniBb

4° 15'

P.76* 45'

10 G 6

285" Off

M3° Oo"

6 3 S

to WiUiama' thaft.

171* Off

R.74' 11'

Up ebaft to pp. line.

E

79" 15-

3 D

F

57' Off

a

H

6S° 30'

183* W

—

At X cat drirs to

regain the lode. On lode.

J

94-45'

to John't rie.

aer nv

Up rise to SO fm. levcL

84'' 15'

M'

75° 3ff

6 S 8

to MitcheU's shaft

K

79° 10'

End.

64. State the nature of the dlelocations or heavfi of lodee, their probablt iriin, their appearance vertically and on a horizoDtal plane ; uid th< mnona rules that have been recommend for reeaiBitig the lerered portion Ji.S.M. Examination m Mining, 1879.)

65. A, B, and C are three bore-holea ; the depths of which from the sanu Dorizootsl plane to a Beani of coal are respectively 100, 106, and 108 yanU

t

Prom A to B u 100 ;arda, and from A to C 130 yards. The aogte in a horizontal plane between A B and A C ia 3ff*. What is the direction of the dip oi the aeani, and the angle of dip T {MerivaW* Note and Fo/nnula.)

66. Name the permaaent adjuetmeata of the transit theodolite, and state how they are nude. (Edinburgh Univtrsity, l&SS.)

07. Explain folly the procesB of setting ont a tonnel in the driving of which a noinber of ahaJte have to be employed. {Bdinhurgh Univermty, ISSSv)

68. Suppose yon were required to take levelt along an underground roadway m order to plot a section showing iwth roof uid Boor, state what instrnmenta you woald ose and how yoa wonld proceed, {Colliery Manager*, Lancwliirr, 1887. )

69. State approximately the decUoation of the magnetio needle for the you 18S8, and the average annual variation. How is the deolinatfon found tOTHV hi amount as you travel northwarda or eaatworda? iCilg Qaitdt, 1SS8.)

TO. Describe the Hedley dial Ouiidt, 1888.)

71> Explain what is me&nt by the true meridian. How may the true mstldiMi be determined by gimple obaervationt of some well-known stars t tCUg OviliU, 1888.)

72. Describe the metiiod of meaanring horizotital angl<?R with the theodolite the prosa of repetition, and point out the special advantagei of thi* mode of usiog the imtrumeat, iCUy Quiidi, 1888.)

73. Explain tho inetbod of reducing ond plotting a survey by rectangolar OD-ordlnatea. What are the advantages of this method as coilipare4 with the ordinary mode of plotting with the scale and protractor 1 {Uity Quildt, 1889.)

74. What is meant by the term " error of collitnation" an applied to a traDBit>theodolite 7 How may this error be detected and rectified ? Assum- ing that a coosiderable error of ooUimation is allowed to remain nnoorreoted, is what manner will it affect the measurement of an angle? Can the instrument be used in such a manner as to nentralise thi error? (Gity GvUd*, 1889.)

75. It is required to determine the position of a distant point, C, in the workjns of a colliery, with reference to the surface. For this purpose a mrvey is made with the theodolite above and underground, from the shaft A to 0, and also to a second shaft B, by which means the underground and snrfaoe-sur'eya are connected. .Show now you would carry oot the survey to as to obtain the most accurate result.

Give yonr idea as to the degree of accuracy attainable by this method ; and how far it will dei>eud upon the relative positions of the points A, B, and C, and the uatore of the surveys between these points. {Qit)/ Omldt, 1S89.)

70. Describe the slide rule. {QUji (Hitd*. 1890.) .

77. A line is measured on a uniform slope of 1 in 17. What alio wanes

pr chain mutt be made for the inelination 1

S3

Hink'Sorvetiko.

78. What meant by the declination of tbe needle, Kod u tb iiiouDt nf it At Greenwich now, and wM it ten yaav ago ? What prcL-iiutioiu rooBt be conatiiDtly taken to insure the aoenracy of mining ploDi in consequence of tbe vari&tion of declination t {City Outtdt, 1893.)

79. In the case of a mine with only one shaft, which is vertical, and where there iron, which cannot be removed, in every part, explain how to connect tbe andergroimd with the lorfaoe survey. {City Ouuds, 189)

tiO. The sides of a triangle are 1,200, 1,100, and 1,000 links in Uuetb respectively, what is its area in acres, roods, uid perches T Supijose this area to be m a horizontal plane, sad to be covered by a seam of coal lyiS); at an inclination of 34* from the horizontal, tbe thickness of the coal being uniform and measaring, at right angles to the dip, 3 feet in thickness, what is ihe tonnage of coal in the seam over the above arsal {Cily Ouildt, 18S4.)

61, What errors in direction itre likely to arise in surveys made with tbe magnetic-needle, and how can sach erron be ooutrolled and corrected t iS. and A. 1885,}

S2, In what manner and on what principles can the meaanrentent of the dlitancea and the levels of a series of points in ragged coontry be expedited ? Give examfilea with iketchas of the application of the meUiod. ( Univtr*itif OolUyt, ltJ95.)

B3. What is the declination of the needle at the pneent time at Green- wich or any other plaoe with which you ate acquainted ! Will there be any difference, and if so, about how much, between the decliuation of tbe neelle at Liverpool and at Hall ! What was the declination at Greenwich (or other place) ten years ago (approximately) ! iCity Ouildt, 1S96, )

M, Explain with sketches the oonatruction of a dial sack as ii generally used in surveying mines. {Ciljf Ouildt, 1806.)

85. What are the requirements of the Coal Minn Regulation Act to colliery working plans ! What further infortnation should they afford in addition to what is legally required t (Colliery Managua, Wat LaiKO- thire, 1896.)

86. On a seam dipping south 1 in 6, what will be the gradient of a road

driven north-east 1 (S. and A. D,, 1896.)

87. What is the declination of the magnetic needle at Camborne at tbe present time, and to what extent does it dtifcr from tbe declination at Greenwich T What is meant by the secular variation of the needle T {Gambome JUininff ScIibbI, 1S97, )

68. A coal seam is feet thick, with a dip of 1 in 7. What tonnage may be expected from an area 50 chains square T (& and A. D., )H97. )

89, A beading driven due east in a team of coal rises at tbe rate of S iDches per yard, and a oross-beaduig at right angles to tbe former dips at S inches per yard. Find the direction of the steke of tbe seam, ( Um- vtrsitg o/ Waia, 1898,)

90. Draw an open scale of feet to a scale of 1 7 feet 3 inches to tbe inch, and loni:; enough to measure 100 feet; and beneath it draw a scale of meftei hewing decimetres on the same scale, (Oily Ouildt, 189S.)

Appendix I.

n. Plot the foUowins seotion to a vertical scale of 10 feet to the fawh, and a horizontal icue of 8 chain* to 2 inches : —

HnmlMT.

ToUl Dtatsaee.

Bukslgfat.

Inter- mediate.

POTMlght.

Notoa

Link!.

B.8. on peg A.

3M

Is

im

Is

F.8. on peg &

Find the angle of slope from peg A to peg B. (Otfy OvUcU, 1898.)

98. What methods have been proposed to obtain the greatest amonnt of light from a safety lamp, where onlv this kind of lamp can be need, by vndargrooBdsiirveynsT INea South WeUe§, \8&S.)

n. What are the benefits, present and future, of having the levels of ' Toada put on the ooUiery plan T {Ntw South Walei, 1808. )

04. In a dosed traverse, how could yon prove that the interior angles wenwnreetT [New South Walt*, 1898.)

06. Oonstmot a diagonal scale of 5 fathoms to the inch, long enough to measure 30 fathoms, and showing fathoms, feet, and inches. {OUy GmUU, 1904.)

3d6

Uink-Suryetiko

96. Caloolftte the oo-ordinates, Mid plot by oo-ordinftte* the foUowing thaodoUta surrey of a crou-oat ; theodolite gr&da>ted to the right-iuud, et originaOy pomticg due north ; meAsnrenieDta ia links. So&le, 3 cbaiiu to the ineh, CftlouUte length and be&ring of line required to ctoae tb turrey :—

Ko.

Maridlu Angla.

DlltUIM.

Ho.

Herldlw Atiglt.

DMmoBt.

*2l'2e'

307*40'

42*40'

468 -S

306° 20"

989 '5

43° 00'

306° 17'

448 '4

42° 64*

306° 34'

42° W

306° la-

279-2S

S

43° 43'

221° 11'

eso-s

310° 03'

2-20° Sc

S

31!f 58'

Is

180* 22'

(City Guilds, 1B98|.

07. Plot the (allowiDK aarTey made with a right-banded theodolite, the Inetmment being pointed dne north at the first station. AU meaiuremetita In feet and inchea. The month of the npfter level vrati fotmd to be I17'3S bet above the lover. Scale, 40 feet to the inch ;—

Stntlon Unci.

U arid Ian Angle,

Dlstues.

KUDarlu.

Ab Bo

340*23' 316° 05*

Ft.

Ins.

B is at mouth of lower drilt, 4 feet wid.

Cd

343*20'

in vein, 4 feet 3 inches wide.

Db

67*22'

ae

Vein 4 feet 6 inches wideu

£F

Vein 5 feet 9 inches wide.

Fg

27° 38'

at centre of winze, 4 feet

Ah Hj

Ib* 32' 0*27'

9 JDchea Equare. H is at naoutb of upper drift, 4 feet 3 inobea wide.

Jk

346° 49'

K is in vein, 3 feet fi inobet wide.

Kl

22° 29'

L at centre of wince, 4 feet iscbea iquare.

Dttennine direction and angle of dip of winie. (City Oviiiii, IbS&J

AFPENDIX t.

98. Dnw an open aotM, loos enough to meaimre SO feet, o[ 4 inchei to th inch. {City GviiiU, 1S99.)

99. Draw a diagonal scale of 2 feet 3 liiebes to the inch, long enough to BieMnre IS feet, and showing feet and inches. (Gity Omldt, 16U9. )

100. The three aidea of a triangular lield nveaanre 197, 125, and 89 yards respectiTely ; caloalate ite drea in acres, &c. {City Ouild), 1899.)

101. Plot the following traverse siirvey, and determine the lenh mod bearing of tii line joining points A and £ : —

IterldJun AnglB. .

A B . . . 2-26° 3 chnina 78 links.

Bc . . . 123° 2 „ 40 „

C D ... 242° 1 „ 82 „

Dk ... 172* 2 „ 85 „

Plot to a scale of 2 inches to the chBin. (CVty Ouildt, 1899).

102. Explain how you wonld set oat a right angle by means of an ordinary anrveyor's chain. {City GuiliU, 1899.)

103. An embankment on level groand is 100 yards long, 17 feet wide on tp, and 10 fet high, the sides have a batter of 1 in 3. Calculate its cabio contents. (City Ouiids, 1899. )

104. A coal seam dipping 1 in 10 is thrown down by a fault, inclined 80' to the horizontal, the vertical throw being ISO feet; a drift ia started from the upper portion of the seam to tbe down-throw portion with a (all inches to the yard. How long will the drift be T {City Oviid, 1899.)

105. A msn S feet 10 inches high walks from an obeerver lying on tha CTOund towards a obimnej nntil the tcp of hie head is seen to be exactly in line with the chimney top ; his distance from the observer is 16 paces, Kod from the chimney 107 paces. What is the height of the chimney} [City Quads, 1899.)

106. A lighthouse U Mn on an ieUnd about balf-a-mile from a Hat sandy shore. How will yon determine its eiaot distance using only a surveyor's chain and ranging poles! {City Ouilds, 1899.)

107. A tunnel driven into a hillside rises 1 in 15; it outs a coal seam dipping 20° towards the tunnel mouth ; the width of tbe seam measured along the floor of the tnnnel is 19 Hnka. Mow many tons of ordinary bittuninous coal will the seam contain per acrel {City Quilda, 1899.)

108. A seam of mineral dips 2U° towards N. W E.; at what bearing honld a road be set out in the seam so as to have a grade of 2§ inches to the yard T {Ciiy OuUdi, 1899, )

109. How would you survey with a plain miner's dial In a nunc in which there are much iron machinery, rails, pipes, &c, T Oive a page from an imaginary survey book with at least eiiiht drafts, and show how yon would calculate the traverse from them in iUustcation of your answer. {Ciiy Ouilda, 1899,

110. Explain the subtense method of determining distances. {Oitf Ouild*. 1899,)

HI. A curve of 15 chains radius is to be set out to connect a main level with a cross-cut at right angles to it ; describe in detail how tbia should be done. [City Ouildi, 1899.)

MIHK-SURVETIira.

Give ft from an imagiuury level book, showing Kt leut twdra readiDgs abtaiosiibf four aettiaga of the inatrument ; work oit and plot th section to sny ooavenient Me. {City OvUdt, 1899.)

113. The following aurrey w&a made by doabla foretigbt raathod with

right-handed theodolite, the uutrument pointiiig due K. at the fir*t

station and being brongbt book to zero after each readinc. MeaanMmaiita

In links. Calculite the sarvejr and plot it by co-ordinatM< Soak 3

ea I

L

fcqnired to close the survey, and the area enclosed by it and by the

traverses. {Ciiy Ouiidt, 1809.)

1 14. Work out the following series of levels and plot in the form of a

section. Horizontal scale 1 chain to an inch. Vertical scale 20 feet ta

an inch. Datum line 50 feet.

inobea 1 chain.

UbBurviiJ

ObiAtnd

TbMjiloHio

TtaeadoUM

Na. BwdlugiL

DLitsQcea.

No.

BMdillL

DUiaasaa

1, . 180° 00'

6,

fll'ir

2, , 176° 21'

170' 21'

3, . umv

7,

196*21'

4, . 183* 54'

8,

121* ay

DlitMCO.

Ouk BlgbU

Fors Sight

OluiDi.

rt

0'70

1'60

8 '65

13 Sb

5 '40

0'S2

4-Os

12 '63

s-so

fi-40

e-40

{Nova Scotia ManoQtrif Bxam., 1899.)

110. Lay down the following andergronnd tnrrej on the scale of tw ehalna to 1 inch x'

Ulitutea

Ubshu.

UoriXflntAl Aljfld*.

Shaft to A A „ B B „ C „ D D „ E E .. F F „ G

0'77 3 '90

eis

A 145° If,' B 177° 30' C 213'' 54'

E 130' i.r F 167" 30-

d

Appendix I,

Tia horizontal soRles ue tboie on ths left huid of a penon travelling bl the direction of tbe inrrej, and th* mapieCio bearing of the line F G ii 30° eat of north. Alio reduce the above readings lo one meridian, and plot joor proof. Explain how jon would carrvdt the abOT BUfrej it made in a aeam cooaiderablj inclined.

[Notxt Scotia Manager*' Sxam., 1899.)

116< Plot ths following to a acale of 1 chain to an inch : —

N SI' W, 276 linki.

N 60° E, 610 „

S 30° E, 280 „ Find ths length of " ti* " line, and aaloalate the area, in acrei, of th* nclofled figure. {New Sovih Walta Department of Public Imirvction, 1 899. J U7, Down a shaft underlying foutht the following were maaiured : —

Dii Uncle

Hida.

Fust.

lO'Sff

Ibs

16° 45'

DLHiBcs.

Bid*

TmL

20° 00"

6° axe

SfiS

Ton are required to find [a) the depth of a yertial abaft propoaed to be nnk on the eonth aide to interaect the termination of the imrrey, and {by the horizontal dittaoce betwesQ the tops of the two shafti. Scale 132 feet to an inch. (Aew Soiah Wales, lS9d.)

lis. Plot the following to a eoale of 2 cbaiii)) to an ineh, and find the bearing and length of the seven tb set to tie with the begincing of the

N 621° W, 710 link*. N41 E, 230 „ N 624° W, 340 „ SotUh Walee, 1899.) 119. Find the uniform gradient of a road in which the following lereli wn taken i—

S 471° B, 340 links. 8 nV W, 160 „ B SOj* K, 424 „

ewk 3iti(.

Fore Slghi,

OHttuca.

Feel

reel.

LiDki.

4'Os

12 '03

6-0.*.

6 '72

1-J2

Expreu the gradient in inches per yard. {Netc Sovth Walts, 1S09.) ISO, The three sides of a triangle meaeare 370, 295, and 466 yards

reipectivel; ; draw the triangle to a scale of 100 feet to the inch, and

oalcnlate its area in aeres, ie. {dti/ Gvildi, 190O. )

121. An embankment is 30 chains lon, the top is 10 feet wide, one side

has a slope of 6S* and the other of B0° to the Tcrttcal. The ground and

HIKB-StTBTBTlilO,

lupof the embuikment are level, the embaukineiit ia 13 feet higb the centre. Calculate it* coDtenta in cubic yrda. {Oitjf Ouildt, 1900.)

122, A scftle of to show feet, kad long enoagh to 90 teet. {City OuUdt, 19U0.)

123. Plot the following truTerM line*, [lointf eckle 2S feet to 1 inch

1, . . . N. 77°K,

2, . . . N. 21* 30' W.

3, . . . N. 15* Is' E.

4, , . . 8. 29*20' W.

5, . . . 8. 5° 46' E.

cterting from one centnJ

64 feet.

1 chain 1!! lioka.

IS yardt.

187 link*. 14 fu thorns.

iCUy &uild*, 1900.)

124. Bow many tons of oo&l per acra will there be in & eeam 3 feet S iDChea thick, dipping at au aogle of 9°, aUowicg 20 per cent, dednctiou for faulte, Ac. ! {City Uuiidi, 1900.)

125. In tbe ordinary mioec'i dial the £. to the left of the N. Why is this t {City QtUdg, 1900. )

126. £xpUia tbe ternu diuriial variation, dip, declinstion, and eeoDlAr variatiOD of tbe magnetic needle, (CT(y Guilds, 190O.)

127. Yon have to meaaure the width of a deep river about 150 yard* wide, and your only meaanring inatinient is an ordinary chain. How would you proceed ! {City Cfviidi, 190O. )

12i(. A vertical shaft ia 400 feet deep. Half way down it an incline atrt* from it, which meets a drift diiiiiing towards tbe shaft bottom at a gnde of 2 inches to tbe yard, at a distance of 4 chains from tbe shaft, tbui distance being measured along the floor of the drift. Find the leDitb and inclination (in degrees and minutes) of tbe incline, (City OtaMt, 1900.)

129. A theodolite is aet up iu line with two telegraph poles, 150 feet from the nearer pole and 450 feet from the further pole. The top of the farther pole subtends an aDgle of 18°, the line of sight passing through a hole exactly half way up the nearer pole, lleouired tne heights of Uw two poles, the theodolite standing 5 feet above tbe ground. (Cuy OaUdt, 1900.)

130. A seam of mineral dipping 12° is thrown down 200 feet by a vertical fault; an inclined drift ia started from the top of the down-throw and cuts the seam 400 feet horizontally from the faolt. Required length and dip of the inclined drift. {Oiiy Otiiidt, 1900.)

131. Calculate the co-ordinates of the following traverse survey, calcu- late the length and bearing of the line G A, and plot by co-ordinates to a scale of 1 chain to the inch ; —

Traverse aunty oj polygcaujl area made, by dorMe foraight mctAoct tuith a right-lianded theodolite reading to 30 ttcortd*; lAe thtodoltU was originally set in the true tneridian, true nortA reading S80' Off Off.

. A B Bc Cd De

Anglo.

14° 48' Oo"

Ibs 00' 30"

284" 01' 30"

200* 12' 30"

Line. EF FG GA

nlZka t30

288" 01' 30" 607 —{CiiTi QuUdg, 1900.1

132. Cklcnlkte the of the above polygon In *cres, Ac, by the method of co-ordinatea. idly Ouijdf, 1900.)

133. & bed of miner&l dipa 58° (to the horizoDtal), the direotion of full dip beina S. 24° 56' E, What will be the dip of k road running N. 80° 2(/ W'.t Otiildt, 1900.)

134. Two horixontal levels are drivto in a vein dipping 77° towards N. fiO* E., the levels being 200 feet apart vertieallj. A dat winze in the vein connecttns the leveU is 446 feet long, Wbat is its dip and bearing! {Gilt/ OuilfU, 1900.)

135. How would you proceed to level along an inclined drift about 3 feet 6 inches high, and inclined about 40" J (Ci/y QuUds, 1900.)

136. Draw a eectiou of the teleacojie used io the ordinary dumpy level, showing clearly tbe path of the rays oi light through it. (City (Juilda, 1900.)

137. Under what ciroumBtAiicea must a correction for the enrth's cur'a- tore be applied in la veiling I 8tte ft formula for tlua oorrectioa. {Citjf GtiUda, 1900.)

138. Sketch and exi>lain the action of the tangent screw and clamp, m applied to any part of a theodolite. {City Quildt, ItlOO. )

139. Describe a metbnd &f counectiog underground and surface traverses through a single shaft, the uac of the magnetic needle being inadmissible. {Ciiy Omidt, 1900.)

140. A eoal seam it proved by three boreholea, A, B, and C, the following depths :— A is 200 yards deep, B 290 yards, and C '2§0 yards. The distance between A and B is 430 yards, between A and C 740 yarda, and between B and C 960 yards. Find the direotion and iDcliuation of the fall dip of the eeam, assuming that the surface of the ground at the bone- bolea is level. {New Soxilh Watts, 1901.)

141. Bow would yon proceed to mark a survey atation underground where the roof is badl {Univtrtity of tVala, 1901.)

142. Make out an imaginary page from a level book, abowing twelve readings taken with four settings of tbe ioatrument over undulating ground. Work out and plot the section. {City QvHcU, 1901.)

113. Three boreholes, A, B, and C, interseci, a eeam of ooed ; tbey am ntuated at tbe anjles of an equilateral triangle, whose sides are 300 yards in length. B is N. 17° 30' E. of A ; and C is tt. the westward of the lino A B. A outs the seam at a depth of 173 feet, B at a depth of 342 feet, and C ab a depth of 240 feet. Determine the direction and amontit of din of tbe coal seam. {Cily OuUdt, 1001.)

144. What is meaiJt by a traverse aurvey ? Illnstrato your reply by ft diagram. Show the system you would use for the field book of a theodolite traverse. (Gold Coael Kxamiiialitmt /or Hurveyor'a Lieence, 1902.)

146. Describe the conatructiou of a, prism3.tio eompaas ; state its uses and fiie objections, if any, to ite employment uudorground. [City Guilde, 1902.)

146. Explain how and whv the aneroid barometer can be used for rough levelling. {City OtiiltU, 1902.)

147. Describe the process ot setting out, with accuracy, a long tunnel in a mountainous region. {C'ambomr Miiiin;/ School, 1904.)

145. Desoribe a method of connecting underground and surface traverses through B. single shaft somowtiat out of repair. ICatabbrne Miitii A'choot, 1904.)

Mine-Sub Vet I No.

149. The oo-ordinatw of two pointa A luid II are as follows; — (A) Latitude N. 463 links. Dopirture \V. 249 Uaks. (Bj Latitude 8. 167 links. Departure W. 1,348 links. Calcaliit the length &od boariog of the line A B. {CUy Guildn, 1904)

1.50. You have n miner's dial, and you tind that when one end of the noodle nmrke due N., the other end roads .S. 3° 30" VV. To what fault* of conatniotion may thia tte due? Cud you nae the dial in this state for urveyins, and, if so, how? [City OUd, ISOi,)

161. Explain the principle of the vernier tm applied to an ordinary theodolite. (CUy OiM/<b, 194)4.)

1.52. What ii meant bv the "line of coUitnation " ! lUuEtrate t-otir answer by giving an imaguiaiy page from a level-book, showing 9 readings taken with 4 eettinge of the dampy level, redoced by the method of colUmation. {CtVy Out/ifo, 1904.)

153, A, B, and C are three bore-holes pieroing thu same bed of coal at depths respectively 390, 900, and 474 feet. The height at A above eommon <latum is 150 feet, of B ISO feet, and of C 114 feet. Prom A to B is 2.4110 ynrda, A to C is 880 yanb, nd B to C is 2,300 yards. At wb&t depth would a main shaft X, put down within the triingfe formed by the three bore-hotee, intersect the seam; AX being 1,953 yards, BS 450 yard, and the height of X 423 feet above the datum T {Colliery ifanagtrt,

Wafeni A iLflrtilta, 1904.)

154. A mineral vein dips due south at an angle of 67° to the borixantal ; an incline is set off running S. 34' VV. What will be its gradient in inche* to the yard ? {CStu OuUdt. 1 905. )

1C5. Two straight lengths of a railway track make with each other aa anj;le of 147°. Snow how you would oonncol tiiem hy meuna of a carve of 12 chains ratlius, the ground being praeticaUy level. iCi(y Guilds, 1905.)

156. Work out and plot th? following section on a horizontal scale of 60 links and a vertical scale of 6 feet to the inch : —

Nnmlivr.

Boek Sight

tuumediat*.

Fore Sight.

Dlitance.

CllBllU.

,..

..,

U'59

BdZ

13'81

It

ttf

5 '99

t+4

1*0

6 '59

{City ChUdty 1906.)

187. What are the provisions of the Coal Mines Hegutation Acts aa to

Slans and surveys, and as to plAos o( abandoned mines I [OoUiery fanagert, S. Dinlritit, 1906.)

Appendix I.

158. Deacribe fully the methods of making an onderground survey with the magoetio needle and also with the fixed needle, and show your methods of booking in each ease and how you would oonneot the underground mrrey with the surface plan, and the precautions you would take to avoid errors through a variation of the magnetic meridian, including a survey of MW workings upon an old plan, and how you would find u>e magnetic Mridian at the time of such survey. {CoUtery Managers, 8. District, 1905.)

159. In making an extensive levelling, what amount of difference per mile should be allowed for the curvature of the earth t {Colliery Managers, 8. District, 1905.)

3G4

ArPENDIX II.

Bibuography-

The fdlovring ii a, list of the priooipbl treatiiM pnbliBhed oa

iUTV eying : —

AoKKOLA, G. — "De re metallic Ubri duotteiMui," folio. Basel, 155& Rkinhold, E. — " Grundliolior uiid warer Bericht von Feldntwen."

Sivalfeld, 1574. HonoHTON, T. — " R&r avis Id tenia, oi the oompleate mmer," 12ido. i

London, 16SI. VoiOTZL, N, — "Geometria anbtemaea," folio. Eisleben, 1680. Alaoj

Leipzig, 1692, 1714. BoBH, A. — " Grundliohor Anleitung Kur Markaeheideknatt." Frankfort

and Leipzig, 171S, 17&0, 1TT9, 1S07. WElSLta, J. F. — " Inatitutiones ceometrice Bubterraneie," Sro, Witteaberg,

1726, Also German translation, 1765. Stiolbb, J. S. — " Anleitimg Eur UarksclioidekuDst." Municti, 1717.

Jt'OEL, J. Qeometria subterranca,*' 4to. Berlin, 1744. 2nd EiHtion,

Leipzig, 1773. 1

Bkter, a. — GrOndlicher Untemcht von Bt<rgbau nach AnlMtong der

Marksohoidekunst," 4U>. SchneeVrg, 1749. 2ud £dition, 4ta.

Edited by C. P. Lempe, 17S2 and 1785. Oppel, F. W. von. — " Anloitung zur Markwsheidekanst," 4to. Dresden, J

1749. " Anhang." 4to. Dreadeu, 1762. Ualer, J. F," Geometrie und MarkBoheidekunst," Svi>. Carlaruha, ,

1762, 1767. 1811. Gk-'Sahnk, M. bb — " GAjmtrie aouterraine." Paria, 1770, 1776. KASTNBB, A. G. — " Anmerkungen tibor die MarksobeidBkuiist." Gotlingeo, I

DuHAMKLi J. P. F, G. — " Gtomtrie Bouterraine," 4to. Paris, 1787. Fenwick, T. — "A Theoretical QTid Practical Treatise on Subuerrane

Sun'eying," 8vo. NewoaBtle-upon- 1 yne, 1804. Sod Edition, IS

A reprint of this work is uublished with additions bv T. Baker. Hboht, D. F.— " Lehrbuoh der JlarkBchcidekunai," 8ro, Froyberg, 1S29. BCDOK, J. — "The Practical Miner's (iuide," 8vo. London, I82S. 2ai

Edition, 184G. 3rd Edition, ISM. Eamstadt, J, N. L. VON. — "Anleitung sur MarkaeheidekunaL," 4t.

Pest, 1836. Weisbaoh, J. — "Ke neue MarkBclieidekaiigt,"2 vok., 4to. Brunswick,

AssiAKT, J. — " Leitfadeii seiner Vortrago flber Marksobeideknnde," 8to. '

Vienna, 1862. 2nd Edition, ls6l. , A. E. — " Lehrbncli dor Markacheidekunst," 8vo. Prague, iSSS. HoBKOU), H. D, — "A Praoticnl Treotiae on .Mining, Land, and Railway- Surveying, " 8vo. London. 1863. Sarkak, M. E,— "Mamiel du gomitre souterrftin," 3 voU., 8vo. Paria,

ises.

Muj-er-Hacenpsls, a. von. — " Huhore Markscheidekutut," Svo. Tiennk,

Appendix Ii.

BoKCHJtas, E. — "Die pruktischa Markselieidekanst," Svo. Hanover, 1870. LiNTXRN, W. — "The Mineral Surveyor and Valaer'a Complete Guide,"

ISino, London, 1872, ItlXBBKAM, A, — "Lehrbuoh dor Markchei(iekunBt," Svo. Leipzig, 1876. BRATHiraN, O. — " Lehrbuch dor praktiBoheii Markacheidekuost," 8vo.

Leipzig, 1884. 2ad Edition, 1S94. 3rd Edition, 1902. VruLBT, F. — " TraiW pratique du luvor des plana aonterraini," 8vo. St.

Etienne, 1886. Soon, D. D. — "The Evolution of Mine-Surveying Instruments." {Tram.

Amer. Inst. M.E.) Now York, 1899. Louis, H., and G. W. Cao.vt.— " Traverse Tabloa," 8vo. London, 1901. Crlick, p.— "Lehrbuch der Markacheidekunat," 8vo. Pwihiarg, 1901. LtrPTOtf, A. — Praotioal TrBatise on Mine-Surveying," 6vo. London, 1902. HAANEii, E. — "Examination of Magnetic Ore Deposits bj Magnetometrio

M eaEU re men ts. " 8 vo. Ottawa, 1 904. Fatkb, a. K,, and others. — Proc6edi7iga of thi InalilitU qf Mine Snrityart

(Transvaal). Jolianneaburg, 1905.

The following works contain chapters on Mine-Surveying : —

RSSai.EK, B. — "Speculum metallurfiie politissimum, " folio. Dresden, 170Q. CaI-toh, H. — "Acta lustorico-chronologioo-mechanica," 2 vole., folio.

BrunsTick, 1763, CuiciBlKcrs, F, L, — " Erate Qrtinde der Berg- nnd Salzwerkskunde, " 10 vols.,

8vo. Frankfurt, 1773, jAEta, G. — "Toyagea metallurgiques," 3 vols., 4to. Lyons, 1774-81. Fbtce, W,' ' Mineialogia comubiensie, " folio. London, 1 778 (pp. 202-2 1 3). Hausmann, J. F. L. — "Raifledttrch3candinBvien,"5vola., 8vo. Obttingen,

1811-18. [An account ia given of the methods of atirveying mines

in Sweden, vol. v., pp. 115-126,] Rkhshold, C. L. — "Geometria Foren3iE,"3 vols. Munater, 1781-82, BruDKR, J. G. — " Beachreibung der veraohiedenen Zeichnea- und vorziiglioh

beim Bergbau niithigen Vermessunga-Listrumentei," 8vo. Dresden,

ViLLKFOsat, A. M, HiRON DE I.A. — " Oe la rioheaae mindralo,"3 vola,, 4to,

with folio atlaa. Paris, 1819. BopwiTH, T. — " A Treatise on Isometrio Drawing," 8vo, London, 1834. WlLLUue, B. — " Practical Geodesy," 8 vo. London, 1842. COMBES, C. — "Traits de I'exploitation des mines," 3 vols., 8vo, with 4ta

atlas. Paris, 1844. Dboous, J.—" Guide du aondenr," 2 vols., 8vo, Paris, 1947. 2nd

Edition, 1861. PoHBON, A. T, — "Traits de I'erploitation dea minsa de houiUe," 4 vols.,

8vo, with folio atlaa. Li%o, 1853. 2nd Edition, 1870. BAtTERriFEiND, C. M. — " Elomente der Vennessungskuude," 2 Tola., 8vo.

Munich, 1856. 7t(i Edition, !890. RiOKARD, W.— " The Miner's Manual of Arithmetio and Surveying,

containing the usual Calculationa Employed by the Miner," 8vo.

Truro, 1859. OiLLEBPiE, W. M, — "A Treatise on Levelling, Topography, and higher

Surveying," 8vo. New York, 1871. ADft6, G, O. — "The Draughtsman's Handbook of Plan and Map Drawing,"

4to. London, 1874. Htslop, J.—" Colliery Management," 2nd Edition, 2 vols., 8vo. London,

see

MINK-aUBTBTINO,

ReviBod bv X H.

Davies, C. — "EleraonUof Surveving and Levelliog.

v&Q AmriDge, 8vo. New York, 1SS3. Habits, a. — Coura de topographie," 8vo. Liige, ISS3. 3rd Edition, 1902. Bunt, 11. — "British Mining, a rteatise on the Metalliferooa Mines of the

United Kingdom," Svo. London, 18S4. Cban'CE, H. M. — " Report on Coal Mining. PeniiBylvaiiia Second Oeologieal

Survey," Svo. Philadelphia, 1S85. JoHMSON, J. B.— "The Theory and Ptaoiioe of Surveying," Svo, New

York, 1886. Wabsue, W. — ' ' ReEerenoe Book on PiaetioiLl Coal Mining," Svo. Loadoa,

1887, CUfWAHT, D.—" Plane Surveying," 8vo. Boston, 18S7, Staslet, W, F. — "Surveying and Levelling Instrttments," Svo. London,

I.SfM). 3rd Edition. London, 1901. PLLETAS, A.— "Traits do Topographie," 8to. PariB, 18W. ISELA, W. — "Lehrbuch der Verraessungakunde," Svo. Sttittgart, 189*. Kavmo!(d,W. G. — " Text-book of Plane Surveying,'' 8va New York, 1S96, Buna, VV. G.—" Instruments beat euited for kogineering Fieldwork in

India and the Colonies," Svo. London, 1S99. Dbsny, G. a.—" Diamond Drilling," Svo. London, 1900. KniLR, G. L.— " Practical Coal Mining," Svo. London, 1900. 2iid Edition,

ISOS. NcoiNT, p. C.—" Plane .Surveying," Svo. New York, 1P02. pEfiouaoif, T. — " Automatic Siirveyiug InstrumentB," Svo. London, iSCM.

J

"1

Index.

ABSsr's level, 189.

Bratbuhn, 0., 11. S, 203, 213, 304, 33a 1

ADCuracy obtainable in spirit levsl-

Bridges-Lee, J., 333. Brooks T. B., 311.

lirig, 189.

, , of linear measDremeotfi, 24.

Brough, B. H. , 239, 307.

Aiiit level, 6,

Brunton, D. W., 137.

Ad}tiBtments of the level, 172.

Bunning, C, Z., 193, 325.

„ of the theodolite, 101.

Burr, F. L., 89,

Agricola, Q., 3, 28.

Burt's Bolar compaas, 106.

Ain% W., 239.

AiU. L.. 192.

CALCl7Li.TlNO machines, 1S3.

Altoximuth, 197.

American mining claime, 132.

Calculation of areaa, IdQ.

,, transit, 9S.

Gallon, J., 2S3.

Amaler'B planitneler, 169.

Candle-bolder, 2S3.

Anallatiani, 230.

Aneruid barometer, 199.

Casella's altazimuth, 197.

Angular meaeares, 8.

,, gradient telemeter dial, 240. B

Apex, 5.

,, photollieodolite, 'i34.

Arrows, 12.

theodolite, lOO.

Artificial horizon, 223.

Ashbumer, C. A., 291, 301.

„ in trigonometrical surveys, 20.

Azimuth, 59,

„ only, Biirveying with the, 18. M

Back-observatioks, 31.

Chains converted into feet, 12.

Balancing, 153.

Charlcton, A, 6,, I6S.

Ball and aocket joint, 31.

Barometer, aneroid, 199.

Chorobates, 191.

,, mountain, 19S.

Chrce, C, 51.

Base-line, 123.

ChristmAr'B, 0., 114, 200,

Baae of verification, 123.

Chriatmir's theodolite BUnd, 111.

BMMt, S.

Circumferenter, 62. 1

Baoennan, H., 303.

Beanlandu, A., 217.

ClnimB, rurvev of, 130. Clark. E., 216.

Bearing of a line, 31.

, 6.

Clinograph, 3S2. V

Bench-marks, 186.

Clinometer for bore- holes, 322. 1

Bibliography, 364.

„ forexploratory work, 198. 1

Bioyole-BUrvcying, 1 M.

,, German, 82. H

Boning staves, 1 7U.

,, G, P. Evelyn's, 251,

Borchers, E., 327.

Clinostabs, 323.

,, measuring roda, 200,

Coal minee regulation acta (1887 kod 1896), 238, 293.

„ portable magnetometer, S2S.

„ vane rod, 177,

Coal-seams, produce of, 166.

Tord, 73,

Colby's compensating tHirs, 21, Colliery surveys vith the dial, 37. 1

Bore.holea, etrtke and dip of a seam

found from, 263.

„ with the rank -dial, 70, 1

,, Hurvej'ing, 322. Bowie, A, J., 20/.

with the thiiodolite, 1 15. H

CoUimation, 102, H

Boys, C. v., 153.

,, method of levelling, ISfi, H

BrunweU, Sir F., 16&

Ikdsx,

GombeB, C, 52.

Coiu[ieiisiUing bars, 21.

Cumpuiiiig lliviiduf trtanglWt 126.

CoruiL'ssioTi, 7.

Condv.T, C. R., 258.

OoniifciKid of uiiilerground- wid Hr-

fftce iiurvevs, 'illM. Coutour liuea, 'JOU, 272, 291. ConvoutioDal eigu? for mine plana,

2S9. 202. Cooke. I.. H., 238. 2K9. C-o-orflinates, plotting by, 146, 157. Copying plans, 297. Correotiou for chaining tin stapoa, 14. Corresponding altitudea, 45. Country, 5. Course, 5,

Coxe, E. R, 22, U7. Craven , A., 257. Croaaooiirse, S. Cross-cut, 6. OnMiB-actions, 249. Croa-8tff, 15. Crototi aqueduot, 2i>B. Curvtiture of tba earth's tirfc6, 178. CurvM for engine places, 251.

„ riuiging, by mourn of angUa

at the oiroomferenoe, 247. „ , by offecU. 245. Ctuiiing'a reversible levoi, 173. Cyclograpb, 196.

Datum line, 181.

Dasns, J, B., 106.

Davis's dinl, (Sti.

Dawson. W. B., 238.

Deolinaliun of magiietio-needUi, 40.

Deelina meter, 225,

Dempster, H. fi , 2.'?9.

Depth of ahafts. 199.

Deville, K., 23S.

Diagonal eye piece, 2S1.

„ soalea, 142. Diiil joint, 67. Dialling hook, 35.

„ ,, for sufvoying in pre-

enoe of iron, S6. „ definilioD of, 1. Dickinson, J.> 6, 394, Diopter, 2. iDip. 5, 261.

I Direction of mineral dopoait*, 261. ~>irect vernier, 63.

)tlocatod lodea, 276. bislance-iaeaiaring by toleioopoi 'J37.

Distonoes, measurement of. 11. Diurnal variation of the maguecto-

needle, 42, Divining rod, 3. Dixon, .1. S., 280. Down-throw, 27*. Drawing plan, 2!)4. iJrih. 7-

Driviug Itvyls uiitlergnmnd, 24!1, DumpTitsup, culiitial content of, !S7S. Duuijiy luvel, 171. Dunlmr Soott'a taobeonieter, 212. Dyke, 278.

Earth's magnetism, direotim actio

of thy, 26. Ecocntric'teleacoiw for transit-i

dolite, 22L KwpntriHty of magnetionoadle, : I' niieter, 227.

J.l.-'-iilU U.litrjl.ia, 01.

,, light for survey tog purpiMW,

m.

Elirl. 8.

Enlarging plana, 299.

Kquaiising, 161.

Errors in compasssurvvrs, 59,

r-r-- ' "I"g. 189.

Evelyn 'ml '"i|.

Everest ih- Exuniitmliuii qii' Eiiilyrlng for If

Fac, 74.

Feet oooverted into Unka, IS.

Fennel, A., 60. 32o, 243.

FiTirason, t., 156.

Field-faook for chain larrAyB, 20.

Field-oompaasei, 22.

Fixed-ueadle lurveytn 92.

Fioor, 5.

Flying levels, 18f).

Frtllowr>r in chaining, 18L

t jtL'i-ntswrvaticma, 31

Sir C. Le .Vrvu, 5. 883. 292.

Oakrtkkb. B. O., IM.

GallrTvmv, T. L., 193

HnWgnojS.

Hughes, H, W., 167, 1S6,

iCWMtt. H.. S3.

' Ost roadn, 7.

>iia], 81,

Gilbert, K., 198.

Giving and taking, 161.

Gnomon, 45.

Itluminatiun of crots-irirea of theo-

Gordon. W. E.,216.

dolite, 114,

Gothan'a stratameter, 326.

Inclination of ootltcry rood 250.

Orfulient telemeter diAl, M).

,, magnetic-needlo, 50.

Ortilieiiter screw, '2'27.

Inclined sliofta, surveying in, 78.

Interior angles of a traverse, US,

Gnratt's level, 171.

Intennediate sighta, IH2,

Inteneotion uf two reins, 373.

. Sir H., 80.

Gorden, K. L., 164.

Iriarte, C. de, 332.

Gurley's soUr attaohroeot, 107,

Iron ore, exploring for, 307.

Guthrie, J. K., 325.

rails, inUuenoe of, 52,

,, surveying in the presence of, S6. Irregular dejiosite, S.

Hade, 5.

Hu'ldoD, A., 33<K

„ variations of the magnetio-

Hammer- Fennel tncheometer, 263.

needle, 44. H

Hanging compaw, St ,

Irregnlarities of seamii and beds, 27S.

wll. 5.

Isogionic! lines, 42,

Hftrten. J, H., 97.

Isonietrio plana of mines, 300.

0. B , 304.

Hill tniiie pUns, 304,

J.tCKSOM, L, D., 249.

' H.iuH>f. R., 2412.

1 Heading, 7.

Johusoo, F, R., 207.

lleailwftv, 74.

Be(ltt:.v'adia.l, 34.

BenderaoQ, J., 35, 51.

J. B., 238, 239.

,, diat, 65.

Jordan, T. B., 303.

rapid traverser, 156,

HenrcttA, C. M., 119.

HenwcKxl. W. J., 278.

Jariscb, C. L. H. M., I<i5.

Hero oE Atexandria, 2.

Juatioe, J. K., .726.

Hildebrand's compass, 223,

History of the miner's dial, 36.

IvAY, 8. R., 284.

,, mining theodolite, 90.

nurveying, 1.

Koehlor, U., 279, S80.

Hitch. 74, 278.

Hoffmann joint, 67,

Lamdis, e. K., 284.

tripod head, B6.

Holing one excite&tioD to mi-

utliur,

,, use miigiiet in, 327.

Uooaac tunnel, 257.

LeMt'i dial, U.

llortxontol circle of theodolite, 91.

Least reading of a vernier, 83.

Uokold, U. D., 210, 2-20.

Hakld'4 transit-theodolite, 94.

Lee. J. B., 333.

Houghton, T., 27, 192.

Lehigh Valley Coat Co. , Sm.

Howard, W. F., 79, 112, 304.

Haebuer, U., 112.

Leuz. W., 33, 61.

LtteriDg of the minor'B dial, 33.

MouItoD, M.. 302.

„ on pUaB, 296.

Murphy, J. G., 167.

LevfUing, 170.

., -book, 181, 183, 1S4, 186,

Natural Bo&le, 140.

186, 187,

Navarro, L., 332.

-ataff, 173.

Namecek, L., 212,

Levels of a mine, G.

NewaU, R. S., 225.

Limb of theodolite, 92.

Newt-on'B tripod, 31.

Lighting Ternieni, It 3.

Nevr York target rod, 17

Linear measurements, &oouracj of, 24.

NicUel steel, 21.

„ rolling planimeter, 166.

Nolten, G., 324.

Little, J. C, 169.

Liveiug, E. H., 217.

Norria, R, 119.

Local attraction in the mine, 55,

Lodes, S.

pBUQITKoBBatB, lU.

Long comfia.B9-box, 223.

Longwall, 7.

OQset rod, 16.

Lorber, F„ 24, 166.

Louis, H., 12, 164, 197.

Liigeol micrometer, 341.

Oldest mine plan, 1,

Lyman, B. S., 239.

Optical square, 15.

M'Farlase, G. C, 326.

Ordnance branch mark, 1861,

Maogeorge, E. F. , 323.

survey, 126. Ore. reserves, odouUtion of, 187. V

Magnet used in oae8 of unoertain

holing, 326.

Orientation, line of, 50. 1

Magnetic meridian, 40.

Osterland's hanging company I

,, -needle, declinsition of, 41.

Outcrop, 5. 1

„ „ for exploring for

Owens, W. 0., 49.

iron ore, 307.

„ „ shape of, 29.

Magnetometer, 225.

Pantograph, 299.

M.1U, determination of meridian by.

Parallax, 101.

Passometer, 2a

Marquard, L., 157.

Pedometer, 23.

Marquaia BcdleB, 191.

Penkert's hanging oompaw, S8a

Percy, R. P., 143.

Marriott, H. F. , 326.

Maaon'B Sevel, 170.

Physical levelling, 197.

MaascB, 6,

Photogrammetry, 332.

Measures of ftrea, 160,

Photography, 298, 333L

„ length, 7.

Pierce, J., 129.

Measuring- tape, 15.

Plane table, 129,

wheel, 23.

„ theodolite, 92.

Menzel, C, 284.

FlanimBteis. 164.

Meridian line, setting out, 49.

Plans of oollieriea, 288, 800.

Meri™l, J. H., 167.

,, metalliferous mines, 2SSL 1

Meyer. Wiesmann tacheoraeter, 243. MiddletoQ, B. E., 239.

Plato of theodolite, 92, M

Flotting-Bcales, 142.

Miller-Hauenfels, A. von, 83.

Mine modolB, 301, Miner's dial, 28.

,, surveys, 139.

„ „ with the Gennan 1 ilial, m. 1

Models of mines, 301.

,, the undergraimd travriia 1

Moinot'i laebeometer, StSl,

on the Burfaoe, 24& J

Morg0a, 137.

-

.YVutiiWiV), U(J, 103, 2561, 1

Index.

Hiiininet-]amp, 112.

Point at omoe, directly above one

nndergroand, 266. Fole atar, determination of meridian

by, 48.

PoIUtnr, S. J., 215. Pook, W., 239. PotroB lens, 230.

„ taoheometer, 231. Post and stall, 7. Proeervation of plans, 293. Prismatio oompaas, 114, 129. Prolongation tn base line, 124. Protractor, 146, 232. PITO W., 28. Pnybonki, M., 26, 113.

Quick lerelling tripod, 98.

Rack dial, 62.

Backing, 63.

Bailways to mines, setting-out, 246.

Bsmaay, J. A., 186.

Ranges, 137.

Ranging rods, 244.

„ straight lines, 244. Bankine, wTjTm., 249. Rapid trvrenea, 166. Raymond, R. W., 100, 280. Record of colliery sorrey, 30.

„ „ with fixd needle, 71.

„ snrface-snrvey with the dial, Rednoing plans, 299. Reflecting level, 189. Relief plana, 301. Repetition, 104.

Reservoir, onbioal content of, 272. Retrograde vernier, 63. Rhodins, A., 274. Ridding, 74. Rise, 6. Rods. 21.

Roessler's hanging oompasa, 84. Rolley ways, 7. Roof. 6. Royalty, 7. Rfioker, Sir A. W., 62,121.

Satok, a. H., 258. Scales, 139.

„ for mine plans, 202. Schmidt, M.. 176, 212. Schmidt's rule, 276. Sootlaod, jiottijtg surveys in, 166.

' Scott, D. D., 3, 222, 242. Scale, H. P., 239. Seam, 5.

Section comer, 137. Secular variations, of the magnetio-

aeedle, 41. Seibt, W., 189. Sett, 7.

Setting-out, 244. Severn tunnel, 218. Shadow-method of determining the

true meridian, 44. Shaft, 6.

,, surveying, 78. Shafta, depth of, 199.

„ sunk from several levels, 27L Short, J., 240. Siloam inscription, 267. Simms, F. W., 253. Simplon tunnel, 265. Simply divided scales, 139. Slide-rule, 161, 232. Slope, ratio of, 249. Slopes, chaining on, 13. Smock, J. G.,320. Smyth, H. L.,311.

„ Sir W. W., 4. Solar attachment, 106. Sopwith, T., 301, 302. Sopwith's atefif, 174. South Africa, surveying in, 137, U7 Southern hemisphere stars, 49. Spherical excess, 124. Spirit-level, 171.

Spirit-levels of the miner's dial, 30. Split-sieht, 65. Spring balance for tapes, 26. Stadia, 228.

,, and theodolite, 236. Stamfer's distance-measurer, 227> Standard chain, 12. Stanley, H. M., 336.

„ W. F., 114, 176, 233, 30a Station-lines, 19.

„ meaaoring, 81.

Stations, 19. Steel band, 22. Stanton, 74. Stepping, 16. Stockwork, 6. Stokes, A. H., 288. Stope, 6.

„ plans, 138, 169. Stoup and room, 7. Strike, 6.

SluaMonteath, P. W„ 6.

Truulile, 278.

Subsidence and draw, 280

Trijili;lit.an'9 level, 173.

Subtenne Barveymg, 227.

SurTi]), 6.

True meridiaa, 40.

Sarfaoe- plana of tninea, 289.

,, determination itf. M.

Surfftcv-BUTTeyB with the dial, 35.

Tabular compaaa, 223.

„ ,, theodolite, 123.

Tunnel, 6.

Surveying, dsfinition of, 1.

„ driven tlirougb a hill, 2TU.

,, with chain only, 18.

Tunnels, eettiAg out, 232.

Suapnded planimotivr, 166.

Sweden, mine inn-ejs in, 130.

UiiDKatJir.TAaui, 319.

V Swedish mine pUni, 304, 300.

Underlie, S.

United StAtes, magnetic deolinolion

Tabdlaa dspoaits, 5,

in, 5.1.

Tncheometer, 2,'?3, 243.

Units of length, T.

Tamarack ahafls, 44, 216.

U|t-throw, 278.

Telemeter, '236.

Teleeoope, 93.

Variatiov of Lhe BManeUo-neadK

Tlecopia tQeasuremetitof dictaaees,

Veins, mineral, 6.

Vernier, 62.

P 238.

1 Thak'n, a., 312. 320.

1 Tbeodotite knd coinpaai conipared,

soalca, 143.

1 12!.

Verlioal angles, Rieaaurmat of, 13.

,, levelHog with, 1!)3.

sDrvey* in Peiuisylvuiia,

m 117.

Voiglel, N., 154.

Thill, 74.

Volume excavated, SSi.

Tlwwpson, G. R., 60, 217.

ThomaoD-Thaln magnetometer, 322.

Walti., v., 305.

Thornton's dial, 69.

VVordle. W., 231.

,, lining ftighlB, 251.

VVitter-levet, lai.

„ Bta; 175.

Thwit, B. H., 299.

Wtitt, J., 22S.

Tiberg. E,, 317. 320.

Tie-line, 10.

Wavrie, T, H. U., 210.

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I leiMTi.— V. Motion Work.— VI. Crank Shafla and Pednato.I —VIl. Val>M Uear.— VIU.

I l,ubri?ati!>D,— IS. UtKetlanaoui Detalla — Ivnitx.

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Bv WILLIAM NICHOLSON .

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AND ON THl!

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Br LEONARD ARCH BUTT, F.I.O.

Obeailtt to Dm UUUknil EivUww Oamrmnj,

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Clitef UKntuallfe 8u]iBtilitMlitclit, Hlillmnd BaUvi Companr.

ConlKBTa.— 1. Frictl'jii of SoliJa.— II, LUniid Friction or VUcoilty, nd Plutlt CrtcUon.— III. Superfleinl Ta>lun.~IV. The TliMrj of Lnbrlcmtlon.— V. Lnbricmntt, thett SouTCN, Preparation, and Fropertlei.— VI, Fliyiieal Pimnrtlu and Uetbodi of Kxamlnatlon of Labriimita.— VII. Chemical Pmpenlei and llethods at Ktuclnatleo ot Labrl!iiu.— VTII. The Steiuitlc Tatliia of LubrlcaaU hj Yttftlomi and CTwaliMl Uethoda.— IX. Tha Mochanicai TctLlnsof LabrtcaDta.— X. Tbe I>slgii and I<ubrkaUi o( Bearlngn.— XL Tha lubricntlon o( fluotilnety.— Index.

" Diffltined to become a OLiSSIO on Uio iiibject."— /mlialriM and Iron.

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Fourth Ed in oh. Very/uU TUustraled. Ololh, ed.

Steam - Boilers:

Their Defects, Mana&Ement, And Oonstbttotion.

Bt R D. MUNEO, Vhi EnqinBeT of ihf ScoUUk Boiler /fuuranw ami ITiifw liupeetfon Comp

GRlKitAL .— 1. ExrtostofiS caused (i) hj Overheating c.f Plates — (*J By Defective .nd Ov>?rloaded Safety Valves — (3) Dy CEfrrosioTi taterDai or ExienuJ — 4) By Defective and Cotutruciion (Unitppartctl FUie Tubes: Unstnngthencd Ma&Jbctles; Defective Slaying ; Sireiith uf Rivcited Joinii; Factor of Safety)— 1 1. CoK&-rftUCTiOM of Vbhtiial Bnii.RRs: bell — Crown Platci aod Uptake TubcsMao-HoTes, Mud-Hfo, and FireHoles Firebojces— Mountitjgi— Manafitmenl, —Cleaning— Table of BtmCnst Presiteres of Steel Boi] — Tab3c of Rivetted JoiniiSpecificiitJons and Drairis of Lancasbire Boiler for Working prcuurci (a) So lbs, ; aoo iW pet tqoarc iacb respectively.

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Kitchen Boiler Explosions

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Emery Grinding Machinery.

A Text-Book or Workshop Practice In General Tool Grinding, ' and the De$U[!i, Construction, and Application of the machines Employed.

Bv R. B. HODGSON, A.M.Inst.Mech.E.

Introduction.— Tool Grinding. — Emery Wheels. — Mounting Emery Wheels. — Emery Rings and Cylinders. — Conditions to Ensure Efficient Working,— Leading Types of Machines.— Concave and Convex Grinding. —Cup and Cone Uacbines. — Multiple Grinding. — "Guesl" Universal and Cutler Grinding Msicbines. — Ward Universal Cutler Grinder. — Press. — Tool Grinding. — Latbe Centre Grinder. — PoIishing.lNDEX.

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PART I.— THE PETROL CAR. 5s. net. Contents.— .Section I. — Tub Mechanism of thk Petrol Car. — The EniTie. — The Engine .cceisorics. — Electrical Ignition and Accessories, — Multiple Cylinder Engines,— The Petrol. — The Chassis and Driving Gear. — Section II. — The Management ot the Petrol Car.— The Engine. — The Engine Accessories. — Electrical Ignition, — The Chassis and Driving Gar.— General Management. — Glossary.— INDEX.

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Tbose who [uto CLxpericDC: in eacact Sukvky-work wilt beat knaw haw to apprccute |h(r enonnoui amount of labour rcprcKQted hy thi& valuable haost, Thf compuluitio&s eoabte the user to uceruin the sias aiid cosines for a dtstaace of tweUe miles to wjthJD balf XD. VLLh, and thh sv HKraHcit to bu't Onc Table, in [ikcc 01 uic usual yifteen feomutc computatioru required. Thu aloue Ls evideuce of Che assuUunce which the Tables easure to ererr user, and As every Surreyof in active practice has felt the want of fucb usutance fkw kkqwing or thkik pukUCATiOH will nsMAm witkovt THUt/'

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Applied Mechanics & Mechanical Engineering.

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Unqinebrino And Mechanics, 35

Works By

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Hydraulic Power

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Hydraulic Machinery.

Bt

HENRY ROBINSON, M. iNST. C.E., F.G.S.,

rZLLdW Qt r.Tf9XfB COLLVGS, LONDON: PROT. EMIRITL'S OF CIVIL EHGtHiSSi1iG,

king's COLLVGV, vtc. e-tc COMTBifTS — Diichargc through Orifice*. — Flow of Water through Pipes. — Accumulators. — Ppesae* *nd Lifts.— Hoists, — Rama.— HydrauUc EnBvnt-V— Pumpbg trtgijc-— Capstans. — Traveraere.— Jacks, — Wdching Machines. — Riveters and Shop Tools. — Punching, SheTtrrni;, and Flanginc Machine*. —Crants. Coal DJAchnrEnng Kfjichincs. — Driit* ma Oit.'cr,.— Pile Drivers, Excavators Jtc— Hydraulic Machinery applied to Bndae, Clif..", Wheli> and Turbine?*— Shields, — Vanoiia S>>tciiu and Powrer Installationi —

"The standArd work on the application of wa.\et power," — Cauitrt Mii£rme*

Stcond Edition, OrtaUy Enlarged. Wiih FroTiiiapUce, several Platfi, and aver 250 IlluitTalionn. 21s. ntt.

The Prihciples And Cobsthuctioh Of

Pumping Machinery

(Steam And Water Pressure),

With Practical Illiutr&tionB of Enoiniss aod FuMPii applied to Miiriira,

Tows Water Sippi.v, Drainaob of Lands, *o., also Ecoaomy

and EfficisDcy Trials of Pumpiog Maobinery,

bt henry davey,

MAtabar of tbe InBCltutloa of Civit EanoBrEt, Mmbor oT tb InitltotlaD ot Mechutlul EnDcsri, F.O.S., Ac.

CoNTEfTS — Early History of Pouipiug EiiKines— Steani Pumpmg Eii(j!nt— Pumps and Pump Valvca— General Prjnciploa of Non-Rotative Pumping SngineH — The Comitih Ennf, Simple ancl Componnd — Types of lining Engiiiea — Pit Work— Shaft .Sinldntr— UydrauUc Transmisgioii of Power ia Mines — Electric Tranamiseioii i.t I'DWer— Valve (jfcara of Pumpingr Engines — Water PruBMnre Pnrapiaj; Enjea — Water Works Engines — Pumping Engine Economy ami Tnols of Pumping Machinery— Centrifugal and other Ixiw-Lift Pumps — Hydrjiulic Ksnu), Pmaping Mains, &c. — Index,

" B J tbe 'oao EnfUjih Enijlneor who pT'"'b'Al)ly Icnovn more about PampLoiBt MKcblaer; Ul>m AJ(T oTUfut/ ... A voLuai lueooaDUfa tus aasbi.'n or toso KxrmsUMoi aitd STOTJi."— rA* Ungiiutr

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Sir Edward J. Reed, K.C.B., F.R.S., M.P.,

miGHT OP THE JMrSKIAU ORDEKS OT ST. STAKILAtrS 0' ; nJlffClS

AVSTUtA ; KEDJIdlK Of TURKW : AMD RltlNG £UH OT |Ai'Aid j Vl PRESIbRhTT OF TH INSTlTUiriOM Or HATaL ARCHITXCTS-

Sif Kdwaho RaiDS ' Stabilitv of ' u ittvaluablk. The Natal Archttbct wiU find brought tsgctnci' and rdy to Ki& hand a mu of LMofmaUOD whidi be vould odier- wiM have to Ki ui almost endli&s variety of pubUcftdoni, and lome vrtiich wdoU possibly DfM be able to obta.ui at all el&ewheref" — Sktattuhip.

THE DESIOH ANJ> OONSTBtTCTION OF SHIPS. B; JoKii

Harvaki> Biles, M.Inst.N.A,, Professor of Nivil Architecture m the University of Glasgow. [/w Pnparatien,

Third Ewtjon. IUiistrare<3 with Plates, Numerous Diagrams, and Figures in the Test. iSs. net.

Steel Sh I Ps:

Theib Consthtiction And Maintenance.

A Manual for Shipbuilders, Ship Superintendents, Students, and Marine Engineers,

Bv THOMAS WALTON. Naval Architect,

AirxHOH OP "WKOW VUUR OWM 5H11'."

OONTEHTB. — I. Manufacture of Cut Iron, Wrought Iron. And SteL — Oom- poiition of Iron and SttH>l, (.Quality, Strength, Ttste, &c. II, Classifiottan oE ateelShips. III. Cotuideratiariitianiakiiigcbok'eof Typeof VeiseL — Fnunina of Shipg. rV. Strsoni! experienced by Ships. — Methods of Compiltdiw uud ComMring Strenha of Ships, V, Construction of Ship- — AltematiTo jilodea of OonstrfiDtion. — Types of \reaulB. — Turret, Self Trimming, and Trunk Stesineri. &o. — {tivets and Bivetting, Workina.uship, YI. Pamping Amiige- menta, VII. Mainten&nce.Prevention of Deterioration in the HuUa of Ships. — Cement, Paint, 4c— Indi.

'So thorouith and veLI written U OTQrj ebik|]ier [u Ibe book tbktH !iUiflcatl toiolnl inj of tham blRg wontij o( oxcepticmiU ppriiie, AJtoeother, Uae work li exoatloQI, Bd will proTO of greftt v-luo to tbono for wboni tt Is lutended?'— rA £nginefr.

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Present-Day Shipbuilding:

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Bv THOS. WALTON, Author of *'K-Movr Vour Ovu StUji."

Gehekal CoKTENTS, — Classification. —Matertala used in Shipbuilding. — Alterutttive Modes of Construction. — Details of Conatruction. — , Plating, Rivettingi Stem Frames, Twiii-Screw Arrimgements. Wator "Ballast Arrangemcnu, LoaJThii and Discharging Qear, fto. — Types Vessels, including Atlantic Liners, Cargo Steamers, Oil Oftrryiag Steamen, Turret and other Self Trimming Steamers, Ac. — .

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AXD Wsimtt, )UIH|,T, bf Saooib for SULOM.

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The British Mercantile Marine: An HUtorioai Sketch of its RUe

ind Devolopmeot. By lbs Bi-iiOB, Capt. BLiOKMORt. Si. M.

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Dsmentary Seamanship. By D. Wilson-Barker, Maaur Mmriner, r.IUa.E,, y.R.O.S. with nmneroui Plstei, two In Coloun, uid FFontUpieoe. F(jrKTH EniTiUN. Thori'U{;hlj Keirlsed. With ddltluoil IDiulntUoni. (I, "ThU jaiMiKALX KiNUAL, b; On. Wilson Bareeh, uC the ' Wurcwtar, eeen

toummCTLC [>E9ia![EU."~>lCJlnHtUrn.

Kjiow Tour Own Ship : A Simple Ezpluiation of the Stability, Ccn- ctrnctlon, TonnsKe, end Freebou'd of Ship*. B; Tno. WALToM, NiTHl Arohttect. With nntnerout lllustritlcini and Additional Chipten on Buayunc;, Trim, md Oalcnlatloni. Ni?iTEi Shitton. Ti. fki. " Mk. Waitun b book will be {ound veht cseful."— THe ETtgiiittr.

avlsration : Theoretical and Practleai. By D. Welson-Babees

dJ WlULliM Al/LISOUAK. SKCOKI> ElllTIoN, Rerlsoil 3. fid. Prkpiselt the kind of work retnlred for the New Certlflcatet of oompeteniTJ. t:udiilsti will dud It, mVAiDABLE. "— ihjiK*!! Adveriittr,

Marine Heteoroloerv- : For Officers of the Merchsmt Navy. By WauAH ALLtNiiHAH, Flrit Ctui Hoiiourt, NtrlntloD, Science sud Art Department, With nioitntttoni, Hapa, and Dlagnuua, and jaaimile rettfodiMtion of log pB(e. 7*. M. "Qnlte the best tTsMOATiON on tlili >ub}eot."— Qautu.

Latitude and Longrltude : How to find them. By W. J. Millab,

C.B, SECfjNE Enino."*, Reylied. i%.

"Canuut hut prove aoquLiltloD to ttaoae itudirlDK HaTlgatlon."— JTorfn' Bnginetr.

PPftCtlcat Mechanics : Applied to the requirementa of the Sailor. By Tao9. aJackkszie, Master Mnrtner, P.a.A.!i. Sboond EtirrioM, Reriaed. 3*. W.

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AIDS iisr PRACTICAL GEOLOGY;

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Eliphic Stone, Quartz and Opal, &c., fto.~pTed(nM Stonec and Qeni — Stnktifid Bpoeits: Coal and Ores— Mincru Veiua and Lodes — IrreffuLw Deptwita — DvTiainics of Ixnlej ; Fftulta, Jtc, — Allurial Dc|K)aits— Noble Mitala ; Gold, Pffttinn"?) Silver, &c— Lead — llercury— Copper — Tin — Zinc — Iron — Nickel, 4c.iilnhur, Antijnony, Arsenic, Ac.~Combuatible Minerala— Petrtileum— Gcaenl Hint* on ProapectiugGlossary — Index.

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METALLtraGICAIj MACHINEBT : the Application ol Engineering to Metallurgical Problems. By Hbnry CharlbsJbnkins, Wh.Sc., Assoc. R.S.M,, Assoc M. Inst. C.E,, of the Royal CoUeg* o( Science. (See p, 64)

COPPER (The MetaUurgy of).

R.S.M.

AIiLOYB. By Edward T. Law, Assoc R.S.M. Otlier Volumes in Preparation,

J

By Thos, C. Cloud, Assoc.

iOmmi CHAflLES QRIFFIH A CO.. LIMITED, EXETER STREET, STRAND.

Mbtallubqwal Works,

Qbiffin'S Mftalltjroicai, 8Ebiss.

Fifth Edition, ihcronghly Revised and considerably Enlarged. Large

Svo, with numerous Illustrations and Micro-Photographic

riates of different varitlieg of Steel. tSs,

An Introduction to the Study of

Sir W.ROBERTS AUSTEN, K.CB., D.C.L., F.R.S., A.R.S.M.,

liMe Cheiatst and Aiuyir of ihe Royil Mint, and Pnilcssoi o( MclaJlufgr ia the Royal College of Science,

Gekkital Comtints.— Tii: Rcbdon of Meiallurgy to Chcniistry,— Miysical t'npertia of UtAl$. — Alloys. The Thermal Trcaltncni of Welal*,— Fuel nnd 1 hernial McjisuTeirent, — MteriaU Alid t'roducts of Metallurgical ProctiWJ. — Fumacei. — Mcaoi of Supplying AiJf to Funitt£*.— Thertno-Chemislry.— 'lica] Metallurgical Processes.— The Micro-Structore of MetalK and Alloys. — EcanQiniC Coosidttatjotii*

'' No English text-book at all approaches this in the cohfleteneSiS with

which the most taodem views on the subject are dealt with. Professor Atisten's

I to ltimg will be lrvALUAeLK, not only to itie student, but also 10 those whose

powledge of tbe art is far advanceil " — Chtmical Nans.

Lt

itH EuiTtos, Revised, ConBiderably Enlarged, and in part Re.written. With Frontispiece antl numerotu Illuatratioua. 2l£.

The Metalldrgy Of Gold.

. KIRKE ROSE, D.ScLond.. Assoc.R,S.M.,

Cliemuit and Attauer qf On Rouai MinL

aKSIRAL CO.TEKIS.— The Prcipertiei ot Gold ind lt Alloy.— (.hcttjiJlry o( the Compounds o( Gold.— Mode ol Occurrence and Distribution of iJcild.-SJiIlow Pliipel Ilepoalti.— Iiect> Flkcei ItuiKilU.— QuaH4 Cruattiag in the taitip Batti7.— Anrnlgant- ACloQ In tbt! :itan]p Uattery..— Other >'onna ot CruAttlng tnd AnialgmmaLinff Machinery. — ConcentrBtion In Gold MUla.— Dij Cnuhlng.—Re-giinditig.— Roosting,— thlorinilion : Hie Plattuer PructM, The Barrel Froceo, The Vst-Solutlon PrweM.-The Cyanide Fnwen.— ClicnilgtTT of the Cyanide Proce.— Beflulnm and Pittltig ot Gold Bulltun. — Aiiay ol Oulfl "Itbs.— Asmj ot Gold Bullfon.— Statlsilcs nt Cold PrcptlncHon.— Blhllo- gisphy,— IKDEX. 'AcH.upRKutirsivi raACTice. TataTUK ou thli Imponaat eubjeot,"— 7% Timtt, 'The ufjn aoHFLara dMonpUoD of the anijiiivAT]oK paocKn irbtob tuMrnt basa pntH bab 6."MiAintfJo umal

"Adapted lor all who ht lolorentad la the Gold Mining ludoitrf. !m> From teoB- nJealltifrs at far its poaiUlo. but ia more partioalarly ol Talkie 10 those enf&ed In the tndoatrf ,' — Capi .

Lohdon: Charles Griffin A Co., Limited, Exeter Street, Strand.

Charles Qriffin Co.'S Publwations.

Qbiffin'S Metaixubgicai, Sebies.

Edited av SIR VV. ROBERTS-AUSTEN, K.C.B., F.R.S.. D.C.L.

/rt Largi Soo. Hatidiiome Cloth. With lUiulraliont.

In Two Volumea, Each Complete in Itself and Sold Separately.

The Metallurgy Of Lead And Silver.

Bv H. F. COLLINS, AsaoaR.S.M., M.Inbt.M.M.

Part I.— U£:JLD:

A Complete bad Exhaustive Treatise oa the Blknufacture of Lead, with Sectlona on Smelting Kad DeBilyaria.tioQ, and Cbaptera on the Aawy and Aaalysij oi the Materials involved. Price 16s. S

BuMMAHT nr CoNTEsi'ta.— SumplliiB and Aiiajlng Load aod SllTor.— Propertlei and CompouDJs III Loml.—LeaJ Ores.— Lead 8moltln.—aevorbrtorlei ' "" "' ' Heartha. — The Biutlikg of Lead Oru. — Blast Furnace SmelUug;

;.'— Reverberatorlei.— Lead ameltlng In „ : PrindplM, PraoMce, and Bxampln; ProilncU.— Klus Dusl, Iti Campoaitloii, CoUeetion and Traatment.— CmU and Purchiie o( Orea— Treatment of Zinc, Lead Snlpliidei, DMllTBriaation, Sortenlng anl BaOnlug.— Ttie FutUiitcin FroceH.— The Parlcea ProoeiL—ODpellatloa aod RefluLng, dc, Ac

'A TEJOsairaaLT iOtlNs and nielul digest. Uaf with IVUir DOMrroSHQt recomnieuded."— JfAiiiv Jwrnai.

Part II,-

Iiv£:R.

c i

Carapriaing Details regarding the Sourccii and Truatment of Silver Ores, together with Descriptiona of Flant, Machinery, and Prooesaes of Manufactare, ReQning of Bullion, Cost of Working, &c. Price 16i.

acTMMAKY or CoSTBXTB.— ProperMea oi Mlvar aod Ita Principal Corapouudi.— Silvei Ores,— The Putlo Proeesi.— The Kaiio, FondOD, Krtbnke, and Tiui Proqeie>.-The Pan PtocBM.— Roast Amalgamsliaa.— Treatment ol TaiUikga and Concentration.— Rcirtlng, Melting, and Aasaj'Ing — Chlortdialni-Bautlng.- The Auguitlu, Claudet, and Zlervogel ProcMsua.— The Hypu-Sulphite Leaoiilng ProooM.—Eean[ng.— Matte Stdeltlng— Pyritie Bmeltlug.— Matte amcLtiiig in EeverberntarlsB.— SUTer<Copper Stueltiiig and Heftnlog.—

Iniiex.

" The author hni tociUHd A LAKOs AKoirKT OF vALCAaLR raroRMAiiDS Into a ci>i)venit:nt form. . . . The author haa evidently oonsiderabto praetleal eKperlanea, and deflcrilwi the varlum prooewH ciearly and well. ' — Jtiainff /oumtU.

t N

Preparation.

Metallurgical Machinery:

The Application of Enilneertng to Metallurgical Problems.

By henry CRAIILES JENKINS, Wh.Se., A>ioe.R,S M., AssocM.Init.C.JS.

LONDON: CHARLES GRiFFIN i CO., LIMITED, EXETER STREET, STRAHtt

Mstallusqioal Works.

QBIPFIN'S METAZiLirSGICAIi BEBIS8.

DND Edition, Revised, With Ntuneroua IlluBtrfltiooB, Large 8vo. H&DdBome Cloth. '25a. net. With Ailditional Chapter on The Electric Smelting of Steel.

The Metalldrgy Of Steel.

By F. W. HAREORD, Assoc.R.S.M., F.I.C,

Ooiuiiltintf Melallurfiitt ami Analylical Chtmi4t to the Indian Oovtmnent, Hoyal Inilian Enijiiiteriny ColUgt, Gooptn Hill.

With 37 Platea, 2S0 lUastrations id the Text, and aearly 100 Micro-

Sections of Steel, and a Section on

Tbs Mechanical Treatmbst Of Stesl.

By J. W. HALL, A.M.Ikst.C.E.

Absiikeji CoTKrra.— The Plsuit, UiicblnsrT, MetboJa otl ChBiiiJstrj of tha Beusmer nd of etas Open Hurt PnxoMai (Aclit .nd BiLilci.— T'bo U7bi,i)lcBil Tre4tni9nl ot Steal oomprlaliig lIUl PnctUw, Plant mad UanhtDory. — Tbe InflDSDce at Ustklloldi, Uatt Treatmao SpeoEaL SUals, ULoroBtmctiire. TaatlDg. m4 SptclilCjiilonfl.

"A work which we reutura ta DMniaend h an iDTftlnablo compendium of intnmMtlob upon the metallnrsT of ttteL" Iran and Ooal Trodt Btviiw.

The SgitutrtAji, et the eunclniton of mnrlaw of ttila book ;— "We cuinot coDclnda wltbiKlt wiintlT rDcnmiDcnib nil who mer he luteretted us mekenoi- tLHre of ilee}. which pnctlolljr meanfl the 1lhoJ( nf (iMicnpliieetlojf prrofAvSon, toniake thetneelrei ecquelntetl with It m ipeedllr and this may the more done u the pnbllihed price, conilderfng the etvi ttKnk. iHextreiuot; juodente/'

Second Edition, Revbed, Price 16a.

E Metallurgy Of Irom.

By THOMAS TURNER. Assoc.R.S.M., F.I.C.,

Frofeuor of Mftalhirt)!/ in the U-itirertilti of Birmingham. Labok Svo, Handsoue Cloth, With NcraiERocs tLLCHTRAiTDiri

(MAN'T rBOU PHOTOOKAFHS).

(7on(fii.— Early Hlaiory of Iron.— Modern Hleioir of Iron —The Afro of Sieel — Ohlaf Iron Orel.— Preparation of Iron Orel —The Bint Fumaco— The Air used In me Blast Pumaca.- BeacUciDt of the Bleat Parsaoe.- Ttie Fuel used In ihs Fumaie — SlMii aad Tuxei of Iron Smelting. —Propertin ot Oaat Iron— Foundry PrKtfcG,— Wrauftbl Iron — Indlrsct ProdaetloQ of Wrought Iron,— The Fuddling Proceu -Further Treatment of Wrongtat Iron. -Gorrobton of Iroo and Steel.

A MOiiT TALUABLS suhhart of knowledge relating to every method and stage in the mannfactUTt of cast and wrought iion , . , rich in chemical detaila, . . . ExHAUBTTvs and TBOHOUOHLT iTF-TO-DAi:!!." — Biillttin o/ the Aintrican Iron and St<el Auociation.

" This is A DKUGM-. book, givinj;, as it doea, reliable infonnation on a anbject I becommj; overy day more elaborate. " — ColUcry Guardian.

I " A THoafjiiOHi,T uasrvL, book, which brings the subject dp to dati. Of

I OBB4T TALEIK to tboM engaged in the iron indnatiy," — Mimnji Jaiimat.

For Profe9or Tamer's Leeturei on Irt/ifFoanding, see 68.