I02 



NATURE 



[April 5, 191 7 



p. 303 the fat resynthesised in the intestinal wall 

 is stated to be different from the original fat 

 hydrolysed in the cavity of the intestine. This 

 is not the case. 



(2) Dr. von Fiirth's book is well known to 

 many of us in the original as a valuable presenta- 

 tion of the facts of the subject at the time it was 

 written. The use of the word " problems " in the 

 title may cause a little disappointment to those 

 who look for assistance in attacking difficult ques- 

 tions; something resembling Leathes's "Problems 

 of Animal Metabolism " may have been expected. 



It seems doubtful to the reviewer whether the 

 translation of a general text-book is worth the 

 trouble and expense unless the translator is pos- 

 sessed of the knowledge and capacity to bring it 

 up to date. A new edition of the original work is 

 almost certain to appear before the translation is 

 exhausted, so that the latter prolongs the life of an 

 antiquated edition, which is undesirable. The con- 

 tents of the present book date from some time prior 

 to 1913. On the whole, it is questionable whether 

 any real necessity existed for its translation, since 

 there are other books in the English language 

 which serve the purpose. W. M. Bayliss. 



SOME MATHEMATICAL TEXT-BOOKS. 

 (i) Dynamics. By R. C. Fawdry. Part i. 

 Pp. viii+ 1 77 + ix. (London: G. Bell and Sons, 

 Ltd., 1916.) Price 3s. net. 



(2) Differential and Integral Calculus. By Dr. 

 Clyde E. Love. Pp. xviii + 343. (New York : 

 The Macmillan Co. ; London : Macmillan and 

 Co., Ltd., 1916.) Price gs. net. 



(3) Engineering Applications of Higher Mathe- 

 matics. By V. Karapetoff. Part ii. Pp. iv -\- 

 103. Part iii. Pp. v + 113. Part iv. Pp. v-f 

 81. Part v. Pp. vii + 64. (New York: John 

 Wiley and Sons, Inc. ; London : Chapman and 

 Hall, Ltd., 1916.) Price 3s. net each. 



(i) 'X'HIS is a text-book of elementary dynamics, 

 ^ leading up to circular motion. One 

 naturally turns first to see how the foundations 

 are treated, and here we must confess to some 

 disappointment. Various experiments with a 

 "trolley-apparatus" are quoted, and are used as 

 a basis for the fundamental inductions. As a 

 matter of fact, dynamics did not begin in this 

 way, but with the testing of hypotheses. Such 

 experiments are useful and instructive enough, as 

 verifications, at a somewhat later stage; but they 

 are too rough and too liable to error to serve as 

 the basis of dynamical faitH. They are also 

 necessarily indirect, and various assumptions 

 have to be made before they can be regarded as 

 bearing specifically on the points they are meant to 

 illustrate. The article on " mass " also is vaguely 

 w-orded, and scarcely adequate to its purpose. 

 Nevertheless, the book has points which may 

 make it useful to a teacher who takes the theory 

 largely into his own hands. The examples are 

 well chosen and of the right standard of difficulty, 

 and there are good exemplifications of such things 

 as relative motion and centrifugal force. 

 NO. 2475, VOL. 99] 



(2) This book gives an account of the calculus 

 from the first elements to the theory of ordinary 

 differential equations. It includes also chapters 

 on the applications to geometry and mechanics. 

 Since the whole takes up only some 300 pages^ 

 it will be seen that the treatment is necessarily 

 concise. It can, however, be recommended as a 

 good introduction to the subject, and it is doubt- 

 less intended that it should be supplemented by 

 plentiful oral comment. The examples are of a 

 simple character, and bear directly on the text. 



The book, naturally and properly, having regard 

 to its scale, does not attempt to deal with the 

 more abstruse logical points which present them- 

 selves in the beginning of the subject. The 

 author is, however, to be congratulated on the 

 practice he has generally adopted of stating ex- 

 plicitly when he makes an assumption which it 

 is not convenient to stop and prove. There are 

 two respects in which he has, we think, been 

 unduly conservative. The treatment of the ex- 

 ponential and logarithmic functions and of their 

 derivatives scarcely brings out the special import- 

 ance of the former function, the logarithm being 

 practically used as the primary conception. The 

 proof of Taylor's theorem, again, is of the usual 

 indirect and artificial character. One cannot but 

 feel sympathy for the type of student whom Tod- 

 hunter tried (vainly, we hope) to placate with the 

 somewhat cruel remark that "he must not,, 

 while engaged in the elements of a subject, expect 

 to be able, as it were, to rediscover the theorems 

 for himself." It is no doubt difficult to present 

 these matters in a way at once natural and fairly 

 rigorous, but the attempt should be made. 



(3) We have here four parts of a work on the 

 application of higher mathematics to engineering. 

 In the words of the author: — "The book may be 

 called a summary of the most common engineer- 

 ing applications of higher mathematics, or a 

 mathematical cross-index to engineering text- 

 books. It fulfils its purpose if it saves the 

 teacher the trouble of consulting many engineer- 

 ing books for the purpose of selecting a few 

 mathematical problems for his students. The 

 author also hopes that the book may stimulate 

 interest in higher mathematics among his fellow- 

 engineers." It should be said that the term 

 "higher" is used in rather a restricted sense, 

 and that the reader will find many quite elementary 

 things explained to him. For example, it is 

 formally proved that the minimum value of x + y 

 subject to the condition :>;y = const, occurs when 

 x = y; this with the help of the calculus! 



The four slender volumes before us deal with 

 hydraulics, thermodynamics, elasticity, and elec- 

 tricity respectively. The treatment is, on the 

 whole, sound, though the diction is often rather 

 loose. For instance, it is not easy to justify the 

 offhand statement that the internal stresses in a 

 cross-section of a beam are proportional to the 

 bending moment, " since the action of these forces 

 is to bend the beam." The mathematical work is 

 not distinguished by neatness, and one finds 

 awkward and cumbrous proofs where often quite 



