144 



NATURE 



[October 8, 19 14 



naturally to the problem of determining orbits, 

 which has received a new and admirably clear 

 treatment, and is now placed in its logical order 

 as an illustration of the application of the pre- 

 ceding- theory. Even so, the fourth chapter, 

 which deals with attractions, seems to some extent 

 out of place, as it interrupts the study of those 

 parts of the subject which depend essentially on 

 particle dynamics. An interesting chapter on the 

 problem of three bodies leads up to the final 

 section of the book, in which the subject of 

 perturbations is discussed both geometrically and 

 analytically. These two methods will scarcely 

 appeal with equal force to the same class of 

 student. 



The book is probably better adapted to the 

 requirements of the American than of the English 

 student. In this country it would be assumed 

 that a reader who was capable of really profiting 

 by the last chapter, for example, must have a 

 considerable mathematical equipment. One would 

 therefore expect a more thorough treatment of 

 some points for which room might be found by 

 omitting some of the more elementary explana- 

 tions. In America, on the other hand, there is 

 more chance of appealing to some immature but 

 keen student who will be induced to pursue his 

 studies further. 



Numerous examples are given, and an index. 

 An excellent feature is to be remarked in the 

 historical and bibliographical notes. With the 

 dictum that Galileo was a man of greater genius 

 than Kepler we are tempted to disagree pro- 

 foundly; but when genius runs in such distinct 

 moulds, who is to decide ? H. C. P. 



OUR BOOKSHELF. 

 The Practice of Navigation and Nautical 

 Astronomy. By Lieut. H. Raper. Twentieth 

 edition. Pp. xxv + 934. (London: J. D. 

 Potter, 19 1 4.) n.p. 

 It is possible to keep the most valuable educa- 

 tional treatise too long before the public ; methods 

 grow obsolete with lapse of time and in altered 

 conditions, but later editors, fettered by the spell 

 of tradition, fail to use the pruning knife with 

 sufficient freedom. As a pioneer instructor, 

 seventy-five years ago, Raper 's work was admir- 

 able. He raised the standard of accuracy, he 

 appreciated the necessity of systematising pro- 

 cesses, of shortening calculations, and of ensuring 

 correctness in working. Others occupying the 

 more advanced outposts that he made tenable 

 have improved on his methods, benefited by wider 

 experience, and have aimed at greater efficiency. 

 Of course there is nothing wrong in Raper's book ; 

 too many critical eyes have examined its prin- 

 ciples, and too many practical hands have tested 



NO. 2345, VOL. 94] 



its usefulness. But accuracy of statement is not 

 all we look for in modern treatises. We expect 

 to find placed at the service of the student all 

 that has been achieved by science, analytical or 

 practical. 



Tested by such criteria, the treatise that guided 

 admirably the navigators before the age of steam 

 or of iron and steel built vessels is a little dis- 

 appointing. In a modern book one would scarcely 

 expect the explanation of Sumner's method of 

 finding a ship's position at sea tucked away in an 

 appendix or limited to a few paragraphs in the 

 text. So far as we can see the student would not 

 suspect that the time-honoured noon sight for 

 latitude, and the morning or afternoon sight for 

 longitude, are but special cases of this most 

 powerful method. The theory of the Sumner 

 Lines of position is so easy to understand, and at 

 the same time is so widely applicable^ that it 

 should be made the basis upon which the whole 

 theory of practical navigation depends. Again 

 there is no mention of the desirability of observing 

 time signals sent out by wireless telegraphy, and 

 of the opportunities thus afforded for obtaining 

 accurate Greenwich time. The practical methods 

 suggested by Darwin for deriving improved tidal 

 tables receive but the scantiest mention. These 

 may be slight defects, but we think they indicate 

 the inadvisability of attempting to accommodate 

 an excellent book in its day to the requirements of 

 another generation, possessing enlarged facilities 

 and seeking more scientific instruction. 



W. E. P. 



Memorabilia Mathematica, or the Philomath's 



Quotation Book. By Prof. R. E, Moritz. 



Pp. vii + 410. (New York : The Macmillan Co., 



1914.) Price 125. 6d. net. 

 Prof. Moritz has brought together more than 

 two thousand passages from the writings of 

 mathematicians, philosophers, and others, and has 

 grouped them under twenty heads, as well as 

 indexed them under nearly seven hundred topics. 

 Among the subjects of the groups of passages 

 which make up the chapters of the book are : — 

 the object, nature, value, and teaching of mathe- 

 matics ; study and research ; persons and anec- 

 dotes ; logic, philosophy, and science in relation 

 to mathematics ; arithmetic ; algebra ; geometry ; 

 the calculus and allied topics ; concepts of time and 

 space ; paradoxes and curiosities. All the pass- 

 ages are in English, having been translated when 

 the original extracts were in other languages. 

 Full references are given, so that the originals 

 can be consulted by the inquiring student when 

 desired. 



The preparation of such an extensive collection 

 of notable utterances of some of the world's great- 

 est thinkers must have involved enormous labour ; 

 and many writers and teachers will be grateful 

 to the author for providing them with this antho- 

 logy of mathematical philosophy. The extracts 

 are of varying length and merit, but they are all 

 interesting, and the grouping, as well as the index, 

 enable selections upon particular aspects of mathe- 



