January i. 1903] 



NA TURE 



201 



of logarithms, algebra and trigonometry required as a 

 preliminary, the work is self-contained. 



The author says in the preface that he would " like to 

 have added chapters on surfaces of revolution, centroids 

 and radii of gyration "— subjects which are usually con- 

 fined to treatises on the integral calculus. It is high 

 time, however, to take them out of the exclusive control 

 of the severe exponents of pure mathematics and to 

 bring them more into contact with practical needs by 

 means of arithmetic. More especially is this true with 

 regard to what are called '' moments of inertia" — a term 

 so wide of the thing intended to be signified that it is a 

 perpetual stumbling-block to perception in the mind of 

 the average student. What can be the meaning of the 

 " moment of inertia " of a mere area about an axis ? 

 Is not the notion of a mean square of distance, 

 whether of a material body or of a mere area, from an 

 axis something the nature of which is more readily 

 grasped and firmly retained than the ordinary term 

 square of the radius of gyration? The square root oj 

 the mean square of distance is what is universally called 

 the "radius of gyration." No doubt, the expression 

 sounds strange at first to the student, but the strangeness 

 rapidly wears off; and the notion of a mean square, 

 whether of distances or of velocities, is one which so 

 often occurs in various branches of physics that benefit 

 to the student would result if a "radius of gyration " 

 were presented to him in this way. The notion is one 

 which preeminently lends itself to arithmetical illustration 

 and treatment ; it is found, for example, to work admir- 

 ably with certain engineering students, and we commend 

 it to the consideration of Mr. Edwards when he prepares 

 the second edition of his useful work. 



OUR BOOK SHELF. 



Traile encyclopedique de Photographic. Third supple- 

 ment. By Charles Fabre. Pp.423. (Paris : Gauthier- 

 Villars, 1902.) Price 10 francs. 



THIS supplement constitutes the seventh volume of Prof. 

 Fabre's work, and covers the period from the date of the 

 second supplement, 1897, to May of the present year. 

 On turning over its pages, one cannot but be struck by 

 the very large amount of space devoted to apparatus. 

 More than 230 pages are so utilised, while negative 

 making has but 54, direct printing methods 41, and 

 photo-mechanical methods II. It is needless to add 

 that while lenses, cameras, shutters, &c, are dealt 

 with in full detail, the progress of photography itself 

 is inadequately treated. Some important matters, 

 concerning which one would naturally turn to such a 

 work as this, are omitted, and others are only referred 

 to. This tendency to neglect photography for the sake 

 of photographic apparatus is more or less general in 

 the larger treatises on the subject ; perhaps, therefore, 

 this kind of manual best meets the general demand. 

 But it is difficult to understand why the photographic 

 student should desire a full technical description of every 

 variety of objective and be satisfied with little more than a 

 popular summary of work done in the science itself. We 

 know of no treatise that gives any approach to a complete 

 survey of the science of photography. And seeing that 

 the present position of the science is so largely due to work 

 done during the last ten, or at most about twenty, years, 

 the need for a comprehensive treatise written from our 

 present standpoint is obvious. 

 The character of Prof. Fabre's work is too well known 



NO. 173 I, VOL. 67] 



and appreciated to call for detailed reference in connection 

 with a supplement. The author might perhaps have been 

 a little more up to date in some respects. He might, for 

 example, have stated that the Royal Photographic Society 

 has at last withdrawn its unit of/' 4 for lens apertures and 

 recognised that the natural unit is//i. On the other 

 hand, he could not have recorded the similar step taken 

 by the International Congress of Paris, as their accept- 

 ance of the natural unit was not announced until after the 

 first part of the supplement was published. The table at 

 p. 43, showing the various series of empirical numbers 

 that have been used for indicating apertures, is therefore 

 now almost wholly a matter of history. 



Astronomy Without a Telescope. By E. Walter 

 Maunder, F.R.A.S. Pp. xii + 272. (London : Know- 

 ledge Office, 1902.) Price 5.?. net. 

 Bv collecting these papers on " Constellation Studies," 

 "The Zodiacal Light," and other subjects for the amateur 

 astronomer, Mr. Maunder has directed attention to many 

 interesting observations which can be made without 

 instrumental aid. 



The book is divided into three sections, (1) constella- 

 tion studies, (2) astronomical exercises without a tele- 

 scope, and (3) astronomical observations without a 

 telescope ; and it is illustrated by 44 charts and photo- 

 graphs, and 12 excellent star maps. The object of the 

 book is to encourage naked-eye observations, and this is 

 kept in mind throughout, though for some parts of the 

 subject an ordinary field-glass is allowed. 



In " Constellation Studies," the reader is introduced 

 to the constellations and their units, an intimate know- 

 ledge of which the author counts a sine qua non in the 

 prosecution of the exercises and observations mentioned 

 in sections ii. and iii. This instruction is given in a 

 readable and interesting form, and seems to deal with 

 all the objects which are of interest to a naked-eye 

 astronomer. With the aid of frequent quotations from 

 Aratus and some of the ancient rhymesters, the historical 

 and mythological allusions to constellation and star 

 names are explained in an instructive manner. 



In sections ii. and iii , the observer is given assistance 

 for the scientific observation of some ten different astro- 

 nomical phenomena. For instance, in the chapter on 

 " Meteors," a list of questions is given which observations 

 of the meteor should answer, and, further, the un- 

 necessary, but usual, complicated remarks are indicated. 

 In the chapter on " Auroras,'' also, there are hints on 

 what to look for and what to note ; whilst such sug- 

 gestions as an apparent connection between the apex of 

 the "Zodiacal Light" and the Pleiades will encourage 

 amateur astronomers to make patient and persistent 

 observation. The chapter on "New Stars" indicates 

 another field of possible usefulness. 



With the exception of the introduction of "■ Columbia " 

 for "Columba" on map 12, the book seems to be free 

 from typographical errors, but we would express a 

 regret that the names of the letters of the Greek 

 alphabet, when used to designate a star, were not 

 printed in a different type from that used for the proper 

 names of the stars, because, despite the explanation of 

 the alphabet given as an appendix, this is likely, at first, 

 to form a stumbling-block to readers who are not familiar 

 with the names of the Greek characters. 



Aids to the Analysis and Assay of Ores, Metals, Fuels, 



cW. By J. J. Morgan, F.I.C., F.C.S. Pp. viii + 105. 



Students' Aids Series. (London : Bailliere, Tindall 



and Cox, 1902.) Price is. 6d. 



This little book is intended for the use of students and 



others to whom the more expensive standard works on 



analysis and assaying are inaccessible. It is entirely 



devoted to quantitative estimations, and some two 



hundred methods are concisely described. It contain 



