62 



NATURE 



[March 22, 1917 



worked and unworked. Beginning with the 

 ordinary definitions of complex numbers, etc., the 

 author goes on to holomorphic functions, contour 

 integration, and power-series; then we have 

 Weierstrass's theory of infinite products, and 

 after this various applications to gamma-func- 

 tions and elliptic functions (both first-stage and 

 second-stage). Finally, there are four chapters on 

 linear differential equations, with applications to 

 Legendre and Bessel functions. Singular points 

 are considered after the manner of Cauchy ; 

 Weierstrass's theory of analytical continuation is 

 explained ; there is a good introduction to the 

 work of Fuchs, Frobenius, etc., on linear 

 differential equations ; and the last chapter shows 

 how to find solutions of aw" + bit)' + cw = o by 

 means of definite integrals, with illustrations com- 

 prising Bessel functions and the hypergeometric 

 series. 



It is a small matter, perhaps, but we regret 

 to see on p. 2 the formula tan^^y/.-v put in 

 such a context that a beginner is apt to take it as 

 a definition of amp {x + jy). The proper defini- 

 tion of the latter is that it is any angle satisfying 

 the tvio relations cosO — xjr, sind = yjr, where 

 r = I :c + ty I = + v/ {^2 + y^). No other definition 

 meets the requirements of function-theory. 



G. B. M. 



PHYSICAL CHEMISTRY. 

 Theoretical Chemistry, from the Standpoint of 

 Avogadro's Rule and Thermodynamics. By 

 Prof. Walter Nernst. Revised in accordance 

 with the seventh German edition by H. T. 

 Tizard. Pp. xix + 853. (London: Macmillan 

 and Co., Ltd., 1916.) Price 155. net. 



'X'HE fact that a fourth English edition of this 

 -•- treatise, based on the seventh German 

 edition, has been called for is sufficient testimony, 

 if any were still required, to the excellence of a 

 work which has made for itself a high reputation 

 for its individuality and lucidity. First published 

 more than twenty years ago, the book was written 

 from a definite point of view, emphasised in the 

 title, owing to the belief of the author that "the 

 theoretical treatment of chemical processes — the 

 most important part of my task — depended, first, 

 on the Rule of Avogadro, which seems to me an 

 almost inexhaustible ' horn of plenty ' for the 

 molecular theory; and, secondly, on the Laws of 

 Energy, which govern all natural processes." 

 The position thus taken up by the author has 

 become increasingly justified with time. 



But although we give a glad welcome to this 

 new edition of a valuable book, we cannot but 

 Yeel some regret that certain sections should not 

 have been made rather more modern, and that 

 little or no attention should be given to some 

 recent and valuable contributions to physico- 

 chemical science. The translator frankly recog- 

 nises that "the character of the work is slowly 

 changing, since it is no longer possible in a book 

 of this size to describe fully all modern develop- 

 NO. 2473, VOL. 99] 



ments of theoretical chemistry." This is quite 

 true, but the reviewer cannot but feel that if the 

 necessary trouble were taken, a certain amount of 

 rearrangement of the matter would allow most 

 of the important new developments to be at least 

 indicated, if not fully treated. It must be regretted, 

 for example, that in a book of this character no 

 mention is made of the recent important work on 

 X-ray spectra and the bearing of this on the 

 atomic theory. Moreover, certain other sections, 

 such as that on osmotic pressure, might with 

 great advantage be rewritten (so far as the 

 experimental work is concerned), in view of the 

 investigations, in this particular field, of Morse 

 and his collaborators, and of Lord Berkeley and 

 E. G. J. Hartley. One table giving the results 

 obtained by Morse and Frazer is reproduced, but 

 it refers to some of the earlier work of these in- 

 vestigators carried out before their apparatus and 

 technique had been perfected. In the case of this 

 subject, moreover, the importance of which the 

 author recognises, something more might be ex- 

 pected than the bare reference which is made to 

 the work of Lord Berkeley and Mr. Hartley. 

 (In passing, one may point out a misprint which 

 seems to have gone through all editions of this 

 work; namely, on p. 133, Flurin instead of Flusin. 

 Likewise in the index.) Defects such as those 

 indicated certainly diminish the value of the work 

 for the general student, and the reviewer cannot 

 regard as complete compensation the interesting 

 treatment of Nernst 's own researches, such as the 

 sections dealing with the specific heat of solids 

 and all that is based thereon, and the Nernst heat 

 theorem. 



Nevertheless, although there will always be a 

 difference of opinion regarding the emphasis to be 

 placed on the various sections of the subject, we 

 cannot but recognise the success with which the 

 author gives, in general, a survey of a very large 

 and growing branch of knowledge ; and this new 

 edition of an inspiring and intellectually bracing 

 book will doubtless receive the welcome it de- 

 serves. We ought also to express to the trans- 

 lator our appreciation of the general excellence 

 of his work. Is, however, one may ask him, 

 " depolarisators " (p. 778) an English word? 



A. F. 



OUR BOOKSHELF. 



The Land and the Empire. By Christopher 

 Turnor. Pp. 144. (London : John Murray, 

 1917.) Price 35. 6d. net. 

 Mr. Turxor is well known as an enthusiastic 

 landowner who firmly believes in the future of 

 British agriculture if only it is properly taken in 

 hand. He divides his book into three parts : the 

 errors of the past ; land settlement and education ; 

 and a sketch of an organised agricultural industry. 

 The keynote to the whole is that a new outlook 

 is wanted. On the rural side the Government, the 

 landowners, and the farmers must all be brought 

 to recognise that the holding of land implies the 



