A Text-Book of Mineralogy; with an Extended Treatise on Crystallography and Physical Mineralogy Manual of Determinative Mineralogy; with an Introduction on Blowpipe Analysis Elemente der Mineralogie, begründet von Carl Friedrich Naumann (1873†)
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Nature
Thursday, February 23, 1899.
The New Mineralogy.
A Text-Book of Mineralogy j with an Extended Treatise oil Crystallography and Physical Mineralogy. By Edward Salisbury Dana. New edition, entirely re written and enlarged, with nearly 1000 Figures and a Coloured Plate. Pp. vii + 592. (New York : John Wiley and Sons. London : Chapman and Hall, Ltd., 1898.)
Manual of Determinative Mineralogy; with an Intro duction on Blowpipe Analysis. By George J. Brush. Revised and enlarged, with entirely new Tables for the Identification of Minerals, by Samuel L. Penfield. Fifteenth edition. Pp. x + 312. (New York : John Wiley and Sons. London : Chapman and Hall, Ltd., 1898,)
Elemente der Mineralogie , hegriindet von Carl Friedrich Naumann (i873f). Dreizehnte Vcfilstandig umge- arbeitete Auflage von Dr. Ferdinand Zirkel. 11 . Halfte : Specialler Theil. (Leipzig : W. Englemann. London : Williams and Norgate, 1898.)
HIRTY years ago the science of chemistry passed through a great revolution ; new points of view were occupied by some investigators, and fresh lines of inquiry opened up by others ; a general revision of the nomenclature and notation of the science became neces sary, and thus arose what has been called “the New Chemistry.” The last few years has -witnessed a similar crisis in the history of mineralogy ; crystallography has been reconstructed on a revised basis, and new views concerning the optical properties of crystals have rendered much of the old terminology of the science obsolete if not actually misleading.
It is a fortunate circumstance for English-speaking students and teachers of the subject that, in the first two volumes placed at the head of this article, we have a presentation of the science of mineralogy, in its modern aspects, which leaves little to be desired in the way of simplicity, precision and completeness. Prof. E. S. Dana, who is Professor of Physics as well as Curator of Minera logy in the Yale University, gave the world in the year 1877 his “Text-Book of Mineralogy”—a very admirable introduction to the science. But as time passed on, and new methods of inquiry were invented, or old ones became obsolete, the necessary modifications and interpolations in the text of the book, when successive editions were called for, could not fail to mar the symmetry, and to some extent destroy the value of the work as a scientific treatise. Now the whole book has been rewritten, and, as its author is equally familiar with the methods and literature of physics, as well as with the technicalities and nomenclature of mineralogists—and these are by no means always in harmony with one another—a book has been produced which may be confidently recommended alike to students of the physical and the natural sciences.
Prof. S. L. Penfield, the Professor of Mineralogy in the Sheffield Scientific School of the Yale University, has similarly rewritten the well-known “ Manual of Determin ative Mineralogy, with an Introduction on Blowpipe Analysis,” of Prof. G. J. Brush—a work which first NO. 1530, VOL. 59J
appeared in 1874, and since that date has passed through no less than fourteen editions. It is not too much to say that, wherever determinative mineralogy has been taught to English-speaking students, the work of Brush has been adopted as by far the best and most thorough guide to the subject. Originally based on Von Kobell’s “Tafeln zur Bestimmung der Mineralien,” successive additions and corrections have given the work a character of its own ; and without in any way impairing the efficiency or destroying the familiar features of the work, Prof. Pen- field has brought the book up to date, and at the same time added much new matter which will be regarded by all teachers of the subject as being remarkable alike for lucidity and masterly treatment.
It is in the treatment of the difficult subject of crystal lography that teachers and students will first appeal to these works for guidance at the present time : and they will not appeal in vain. During the last decade the six systems of crystallography have undergone complete disintegration ; and an entirely new nomenclature has become necessary, in order to adequately express the great facts of isomorphism, heteromorphism, and of crystal-symmetry generally. The mathematical researhes of Sohncke, Wulff, Schonfliess, Federow, Barlow and others have shown that there are thirty-two—and only thirty-two—modes of molecular grouping possible in crystals ; and, of these, exemplifications of all but three have already been observed, either among artificially crystallised salts or among natural minerals. The great majority of minerals crystallise in one or other of some eight or nine of these groups, however ; while only five or six other groups are at all commonly represented among the rarer species of the mineral kingdom. It is to these groups then, and not to the more comprehensive systems of the crystallographer, that the attention of students of practical mineralogy must in future be directed ; and we are indebted to Profs. Dana and Pen- field for a simplification of the very cumbrous nomen clature hitherto adopted for the crystal groups. It is a distinct gain to speak of the “ Pyrite-type ” rather than of “pyritohedral-hemihedral forms” of the Isometric system, and of the “ Quartz-type ” rather than of ‘ trapezo- hedral-tetartohedral forms” of the Rhombohedral system.
The complicated mathematical questions involved in the derivation of hemihedral, tetartohedral and hemi- morphic forms from holohedral ones, now lose much of their importance to the practical crystallographer. As Prof. Dana says :
“ The development of the various possible kinds of hemihedral (and tetartohedral) forms under a given system has played a prominent part in the crystallography of the past, but it leads to much complexity and is dis tinctly less simple than the direct statement of the symmetry in each case. The latter method is sys tematically followed in this work ; and the subject of hemihedrism is dismissed with the brief (and incomplete) statements of this and the following paragraphs.”
Students of the subject familiar \yith the methods of older treatises on crystallography, will find that Prof. Dana has been able—while giving an admirably clear and complete account of crystallographic methods and results in 144 pages of his book—to dismiss the subjects referred to in less than a single page.
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[February 23, 1899
Prof. Penfield’s introduction to the study of crystallo graphy, in which the subject is admirably treated in sixty- six pages of large print, will prove of not less interest to teachers, as showing how the great fundamentals of the modern presentation of the science can be dealt with in a very moderate space. Questions like those of the pro jection of crystals, and the calculation of axial ratios from goniometric measurements, which are well explained in Prof. Dana’s text-book, are, of course, omitted in the smaller summary of crystallography by Prof. Penfield.
The subject of the optical characters of minerals is one which in the past has always proved to be of peculiar difficulty to students of mineralogy. The important memoir of Mr. Fletcher on “ The Optical Indicatrix,” has recently led physicists and mineralogists to reconsider the soundness of the postulates on which Fresnel based his theories of the action of crystals on light; and there can be little doubt that the near future will witness as complete a revolution in the nomenclature and methods of physical optics, as that which we have witnessed in the case of crystallography.
At the present time, however, it seems desirable to adopt the course followed by Prof. Dana, and to lay before the student both of the accepted methods of interpreting observed phenomena in connection with the passage of light through crystals of various kinds. We feel little doubt, however, that a future edition of the “ Text-Book of Mineralogy ” will break altogether away from the somewhat cumbrous and complicated terminology of Fresnel—hampered as it is by unnecessary assumptions— and that a more simple and rational method of treatment, in harmony with the methods of Mr. Fletcher, will be adopted in its place. The subject of physical optics finds no place in the more elementary work of Prof. Penfield.
The second half of the “Text-Book of Mineralogy” is a very judicious abridgement of the sixth edition of Dana’s excellent “System of Mineralogy,” the most important features of which were described in this journal at the time the work appeared. It is scarcely necessary to add that the present book has been brought well up to date.
The concluding portion of Prof. Penfield’s book is made up of the well-known analytical tables for the deter mination of minerals. These tables have not only been completely revised, but have now had incorporated in them a great number of new species, including not a few which are of very rare occurrence. This increase in the number of species treated of has necessitated a complete rearrangement of the tables.
Prof. Zirkel, in bringing out a new edition—the thirteenth—of Dr. Naumann’s well known “ Elemente der Mineralogie,” has recognised equally with Profs. Dana and Penfield the necessity for a complete change in the mode of treatment of the crystallographic and optical properties of minerals. As time has not yet per mitted him to altogether rewrite the introductory portions of this old standard treatise, he has contented himself with issuing a revised edition of the second or systematic portion of the volume. The excellent features of this familiar text-book are well maintained, and some improve ments are introduced into it, especially in the clearer and fuller treatment of the mode of occurrence of the different mineral species. We trust that the indefatigable editor, who has so long kept Naumann’s book in the first rank
No. 1530, Vol. 59]
of treatises of the science, may before long be able to supply us with that complete revision of the groundwork of the subject which he contemplates.
John W. Judd.
The Theory Of Functions.
Introduction to the Theory of Analytic Functions. By
J. Harkness, M.A., and F. Morley, Sc.D. Pp. xv
+ 336. (London : Macmillan and Co., Ltd., 1898.) NOTICE of the “Treatise on the Theory of Functions,” by Profs. Harkness and Morley, appeared in Nature during 1894 (vol. xlix. p. 477). The object of that work, as of Prof. Forsyth’s book on the same subject, was to present a complete view of the theory as a whole, and to follow out its various develop ments as far as space permitted. It would not be correct to regard either of them as written for a student who could be fairly described as a beginner. What Prof. Klein somewhere calls “ a certain ripeness of mathe matical judgment,” -which is just what a beginner does not possess, would be necessary in a reader who, without previous knowledge of the subject, could study such volumes with profit.
The new work by Profs. Harkness and Morley, the title of which is given above, is stated in the preface, and quite justly stated, to be in no sense an abridgment of their earlier and larger treatise. The authors say that their aim in writing -it has been purely didactic, and that the book is intended to be an introduction to the subject for a student with no previous knowdedge of it. The scope of the book will be best described by giving a short account of what it contains. It commences with an introductory chapter on ordinal numbers. The second chapter explains the representation of a com plex number by means of an Argand diagram ; and the third and fifth chapters deal at some length with the correspondence established between two planes, distinct or the same, by means of a lineo-linear equation between two variables. The fourth chapter discusses the logarithmic function from a special point of view'. Chapter vii. deals with rational algebraic functions. In Chapters vi., viii. and ix. the idea of a limit, the concep tion of continuity, and the definition of convergence in connection with an infinite series are introduced. The conditions under which an infinite series has the properties of an ordinary sum are very completely in vestigated. Then follow five chapters which treat of power-series, and of some of the properties of an analytic function defined by a power-series and its continuations. Chapter xv. considers the representation of an integral function as a product of primary factors, each of which has a single zero. Next come a chapter on the integra tion of a function of a complex variable, and three chapters treating very briefly of the elliptic functions. Chapters xx. and xxi. deal with some of the properties of algebraic functions and with the construction and use of Riemann’s surfaces in connection with them. The last chapter gives some account of the method of Cauchy and of the theory of the potential.
Opinions will and must differ as to what should be admitted into and what excluded from a book which is
© 1899 Nature Publishing Group