REVIEWS 137 



practical student. In this respect Mr. Rose, in the second part of his 

 Mathematics for Engineers, has been more successful than most of his pre- 

 decessors. 



This second part, with the exception of two chapters on Spherical 

 Trigonometry and Mathematical Probability, is devoted entirely to the 

 Differential and Integral Calculus. Though the volume is complete in itself 

 it assumes a knowledge of certain principles, such as the properties of the 

 Exponential and Hyperbolic Functions, dealt with in the first volume, 

 which are usually comprised in any textbook on the Calculus. This allows 

 the thread of the argument to be better maintained, but prevents the book 

 being so readily comprehended by a student not possessing such previous 

 training. 



The author claims that the treatment is based upon algebraic principles, 

 graphical proofs or constructions being utilised for amplification or explana- 

 tion of the subject. This may have been the author's intention, but we do 

 not feel that the object has been attained. The introduction of the ideas 

 of differentiation and integration is based very largely upon graphical methods 

 — and, as far as that goes, the exposition is clear and adequate — one simple 

 and little-known method of graphical differentiation being given. On the 

 other hand, the development of analytical rules is treated with considerably 

 less care and is not free from error. For instance, in obtaining the rule for 

 differentiating a power of x, the proof given, though valid only when the 

 index of the power is a positive integer, is not qualified in any way, and the 

 result is in fact tacitly assumed for any index. Although allowing that for 

 practical purposes elaborate demonstrations are not necessary or advisable, 

 we believe that the passing over of such points is not to the advantage 

 of even the practical student. 



A short treatment of the simpler forms of Differential Equations and 

 of Harmonic Analysis is a useful adjunct. 



The most valuable feature of the book is the field covered by the ex- 

 amples, which are chosen from all branches of engineering. A very large 

 number of these are worked out in full, and, besides serving as illustrations, 

 provide a useful training in the application of the Calculus in practice. 



The book should prove of considerable value not only to the student 

 of engineering, but also to the practising engineer, as a work of reference. 

 It supplies a need for a treatise on Mathematics from a practical standpoint, 

 comprehensive in its range, whilst omitting the less essential and more 

 academic parts with which the average technical student need not be 



concerned. 



Bevan B. Baker. 



A Treatise on the Mathematical Theory of Elasticity. By A. E. H. Love, 



M.A., D.Sc, F.R.S., Sedleian Professor of Natural Philosophy in the 



University of Oxford. Third Edition. [Pp. xviii-l-624, with 75 



figures in text.] (Cambridge : at the University Press, 1920. Price 



37s. ^d. net.) 



The second edition of this standard treatise on the theory of elasticity was 



published in 1906 : the first edition was then so substantially altered that 



practically a new book was the result. No such extensive alterations have 



been deemed necessary in preparing the present edition, which is essentially 



the second edition revised where necessary to bring it up-to-date by the 



incorporation of new researches. The most important of the additions are 



an appendix to Chapters VIII and IX, which deals with Volterra's theory 



of dislocations and a new chapter at the end of the book, following the 



chapter on the general theory of thin plates and shells, dealing with the 



equilibrium of thin shells. The numbering of the articles in the second 



edition has been retained, the new articles being specially numbered. This 



