lOO 



NATURE 



[June i, 1893 



the coal gives out. An elaborate investigation of the 

 action of electric light circuits ends in a set of rules and 

 restrictions for the electric light engineer so stringent and 

 complicated that it would effectually check all dis- 

 turbances by frightening off a contractor altogether, and 

 a three-wire system would be rendered impossible. 

 However the author recognises that the best remedy lies 

 in the telephone engineer's own hands. 



The book concludes with a reprint of a paper by Mr. 

 J. J. Carthy on Inductive Disturbances in Telephone 

 Circuits. 



The general style of the book is good and intelligible, 

 and the diagrams clear and new, the old familiar text- 

 book pictures being rigidly excluded. The arrangement 

 into chapters and headings is carefully done, though in the 

 endeavour to make each one complete some repetition is 

 unavoidable. The reason of the omission of an index at 

 the end is hard to understand, as its use in a book in- 

 tended to be kept is undoubted, and the insertion of the 

 title of the book on every page instead of that of the 

 chapter does not mend matters. As the author states, 

 the mathematical processes have been mostly omitted, or 

 inserted as footnotes. But the few that are found in the 

 latter place might just as well have been left out. For 

 instance, to quote Lord Kelvin's somewhat complicated 

 formula for the current density at any point in a con- 

 ductor is not so useful as a reference to his original 

 paper would have been, and the formula is not used to 

 obtain any result. Immediately after this follows a 

 remarkable proof that d^\dt=Y.. The use of the term 

 " volume " for " current " is needlessly unscientific, but in 

 general the terminology is accurate and consistent. That 

 comprehensive but dangerous word, " retardation " is 

 used with careful explanation of the component parts of 

 its cause, though in one or two places it is loosely em- 

 ployed for " inductance," or " capacity," with consequent 

 inaccuracy. 



To sum up, it will be found a useful and very readable 

 book, giving information not otherwise easily obtainable, 

 and both practical men and students will find it repay 

 careful reading. Francis G. Baily. 



MODERN PURE GEOMETRY. 

 An Elementary Treatise on Modern Pure Geometry. By 

 R. Lachlan, M.A. (Macmillan, 1893.) 



BY a recent regulation for the Cambridge Mathemati- 

 cal Tripos provision is made for the introduction 

 of a paper on " Pure Geometry " : this to include, in addi- 

 tion to Euclid, the simple properties of lines and circles, 

 the elementary properties of conic sections treated geo- 

 metrically, for which a place has already been found, 

 such questions as may be treated by inversion, reciproca- 

 tion, and by harmonics. It has been for some time a 

 reproach that pure geometry has not occupied a more 

 prominent position in the University curriculum. The 

 University has never lacked able geometers, and 

 amongst the present generation our author has 

 won for himself a good name. He has put 

 together an excellent manual complete enough to 

 meet present wants, and doubtless in subsequent editions 

 he will bring the present work even more up to date than 

 it is. Some of our best text-books are overloaded with 



NO. I 23 I, VOL. 48] 



corollaries and much other matter which it is difficult for 

 the student to retain clearly in his mind. Mr. Lachlan 

 appears to us to have steered a most judicious course, 

 and avoided overloading his book in this way. Mr. Pinto 

 (in "Lothair") speaking of the limited range of the English 

 language (which, however, he admitted to be expressive), 

 said it consists of four words. If this be so, the word we 

 should select to characterise Mr. Lachlan's essay is that 

 it is "charming." It treats of the subject in si.xteen 

 chapters, in which, after devoting the first three to an 

 introduction, measurement of geometrical magnitudes 

 and fundamental metrical propositions, he starts from 

 harmonic ranges and pencils, and carries the student at 

 once to the theory of involution. He then discusses pro- 

 perties of the triangle (giving an account here of the 

 recent additions to this branch of the subject, from which 

 we infer that it has at length got a footing in the Univer- 

 sity) and of rectilinear figures. The reader then has 

 laid before him a clear account of the theories of per- 

 spective, of similar figures (previously introduced to 

 English readers in Casey's " Sequel "), and of reciproca- 

 tion. The properties of the circle are discussed under 

 the heads of the circle as a figure by itself, and then in 

 relation to one or more circles. In this division of the 

 subject our author gives account of his own discoveries 

 and of the many interesting additions contributed by Mr 

 A. Larmor. In two remaining chapters the theories of 

 inversion and of cross ratio are unfolded. The treatment 

 in the text is strictly confined to the line and circle. We 

 believe that a further volume extending the methods 

 herein employed to the conic sections is in course of pre- 

 paration. A few slips have caught our eye, viz. p. s'Sj 

 ex.4; §97 ex. ; p. 55, ex- 7; §116; §262 ;§268,andone 

 or two other easily corrected mistakes. In such a mass 

 of mathematical work there may well be others. Refer- 

 ences are given to the sources whence many of the ques- 

 tions are taken. VVe note that an oversight, which we 

 have had occasion to point out twice before in Nature 

 in reviewing the late Dr. Casey's " Sequel," is perpetuated 

 here. On pp. 68, 71, a question is cited from a "Trin. 

 Coll., 1889" paper, whereas it was given many years 

 previously in the Educational Times (Feb., 1865, and 

 April), and was then by a correspondent carried back to 

 Steiner (Crelle, vol. liii.). Th e figures illustrate the text 

 very clearly, and there is a full index at the end. 



\ 



OUR BOOK SHELF. 



An Analytical Index to the Works of the late Johl 

 Gould, F.R.S. By R. Bowdler Sharpe, LL.D. With.<l 

 a Biographical Memoir and Portrait. (London :. 

 Henry Sotheran and Co., 1893). 

 The compiler of the present work mentions in the: 

 preface that the need for it was originally suggested 

 in the course of a discussion between Lord VVharncliffe 

 and Lord Walsingham as to some ornithological question. 

 They decided to refer to one of Gould's plates, but could 

 not readily find the volume in which the figure was 

 given. It occurred to both of them that " such a diffi- 

 culty would not arise if there existed a complete ' Index' 

 to all the folio works issued by Gould," and Lord 

 VVharncliffe asked Mr. Bowdler Sharpe whether he would 

 undertake the preparation of the kind of volume that was 

 wanted. As Messrs. Sotheran were willing to publish 

 an " Index,'" Mr. Sharpe set about the task, hoping to be 



