May 24, 1906] 



NATURE 



7-> 



mathematical theory, the 21-constant hypothesis is as 

 legitimate as its rival and conversely; the question 

 that interests physicists is which of the two, if either, 

 best corresponds to the properties of elastic bodies. 

 Saint-\'fnant rightly argued that this could not be 

 settled a priori, but only by experiment; and at the 

 present day his justification on this point is complete, 

 although he was led to adopt the rari-constant theory 

 bv relying upon inconclusive experiments. .\s Prof. 

 Luv<' points out (pp. i.\, 15) our views of the ultimate 

 ■■tructure of matter are being profoundly modified, and 

 until they are cleared up it is premature to propose 

 an " atomic " theory of elasticity. Meanwhile we can 

 make a working hypothesis by assuming the existence 

 of a strain-energy-function which is a quadratic 

 lunction of the components of strain. In all proba- 

 bility the ultimate theory, if we could only reach it, 

 is kinematical; the stresses set up in a strained body 

 being an aspect of a new distribution of kinetic energy 

 in space. 



The results of the theory, as applied to the arts, 

 are, of necessity, only approximate; and great care 

 must be taken to see that, when an approximate solu- 

 tion has been obtained, it is really applicable to the 

 concrete case. An excellent example is given on p. 

 i-l-o, relating to a sphere strained by its own gravita- 

 tion. If we put in the numerical values of g, r„, p, 

 and any reasonable values for \, /j., when the sphere 

 in question is the earth, we find that the condition 

 that U/r should be small for r„>»'>o cannot be 

 satisfied, although this is one of the assumptions on 

 which U has been calculated. This point was brought 

 DUt in the previous edition (i. 220); it is a pity that 

 this warning has been suppressed, though another, 

 equally instructive, has been given. 



.Again, take the condition (or conditions) for 

 rupture taking place (pp. 117 sqq.). This cannot be 

 given by the ordinary theory, which is only applicable 

 when the elastic limit is not exceeded. Nevertheless, 

 attempts have been made to express the condition in 

 terms of the components of stress. This is entirely 

 illogical, and hence, as usual, a contest between rival 

 formulae. It may, of course, happen that one formula, 

 as against the other, may have a wider range of ap- 

 plicability; but it ought to be treated as purely em- 

 pirical, and not rashly applied to untested cases. On 

 this point the author might have been more dogmatic 

 than he is. 



A very interesting section is that on the deforma- 

 tion of plates. This is a famous problem, historically, 

 and even latelv gave rise to a controversy, now 

 satisfactorily settled. To get a reasonably simple 

 approximate solution some kinematical assuinption 

 must be made, and this must be compatible with the 

 boundary conditions. Prof. Love pointed out that, 

 strictly speaking, a vibrating plate with free edges 

 cannot satisfy the condition that the middle surface 

 is unstretched ; Mr. Basset and Prof. Lamb showed 

 that the boundary condition could be satisfied without 

 supposing any considerable stretching except near the 

 edge. .An interesting statical illustration due to Lamb 

 is given on p. 521. On p. 506 Prof. Love obtains, 

 by a method of his own, second approximations for 

 NO. 1908, VOL. 74] 



stress and strain in a curved shell, agreeing to that 

 order with results of Mr. Basset's. 



In this, as in other parts of the book, the analysis 

 is very elegant, and is given in sufficient detail for 

 really competent readers to follow. But the author 

 follows the general tendency now in vogue, of sup- 

 pressing details of calculation, and eni|)h.-isising results 

 of practical value, rather than examples of mainlv 

 a-sthetic interest. In his preface he expresses a hope 

 that his book will be useful to engineers ; how far they 

 do so depends, of course, upon them as well as upon 

 him. They will find among the subjects treated the 

 buckling of plates, the collapse of boiler-ffues, the 

 whirling of shafts, the stability of slender columns, 

 and other such things; it is to be hoped that they will 

 also appreciate the general theory, as the author 

 presents it. Every student, not an expert, should 

 follow the advice given in the preface of proceeding 

 to chapter v. as soon as possible. 



It is a great advantage that the author of this book 

 is a mathematician of wide as well as accurate attain- 

 ments. As an illustration, it will be enough to refer 

 to p. 306, dealing with the torsion of a rectangular 

 prism; it is at once clear that the author's knowledge 

 of Fourier expansions is quite different from that of 

 the average physicist. Similar examples of rigour 

 free from pedantry may be found throughout the 

 volume. 



At the end of the introduction occurs the sentence : 

 " Most of the men by whose re.searches it [the mathe- 

 matical theory of elasticity] has been founded and 

 shaped have been more interested in Natural 

 Philosophy than in material progress, in trying to 

 understand the world than in trying to make it more 

 comfortable." It may be added that most of the 

 comfort we enjoy, and most of our civilisation that is 

 worthy of the name, is due to men who have endured 

 discomfort, in pursuance of ideal ends. Apart from 

 the poets and the philosophers, where should we be? 



G. B. M. 



PROTEID CHEMISTRY. 

 Chemistry of the Proteids. By Dr. Gustav Mann. 

 Based on Prof. Otto Cohnheim's " Chemie der 

 Eiweisskorper." Pp. xviii + 6()6. (London : Mac- 

 millan and Co., Ltd.; New York: The Macmillan 

 Co., igo6.) Price 15^. net. 

 T^R. GCSTAV MANN started this work with the 

 •-^ modest idea of producing an English transla- 

 tion of Prof. O. Cohnheim's well-known monograph 

 on the chemistry of the albuminous substances. But 

 it has developed into a volume of a much more am- 

 bitious nature, and has culminated in a book twice 

 the size of that on which it is founded. The subject 

 in many parts is treated much more fully, and a good 

 deal of new matter introduced. In many places, 

 moreover, Cohnheim's own views are adversely 

 criticised, so that the present volume bears witness 

 to the originality of the English author. 



Those who know Dr. Mann best as a histologist 

 may be surprised that he should have the necessary 

 knowledge to write on a subject at first sight so far 



