JAxNUARY 12, 1922] 



NATURE 



39 



A g:ood deal of original matter is incorporated in 

 the book, and, as the author says in his preface, 

 much on which further experiment may be based. 

 The descriptions of instruments and the theories 

 of their actions are clear, but though the text is, 

 on the whole, quite simply written, the mass of 

 material is somewhat overwhelming, and one 

 cannot help feeling that this is due, at least in 

 part, to the space given to certain sections being 

 out of proportion to their importance. It is a pity 

 that the appearance of the book is marred by the 

 very careless printing of the many half-tone blocks 

 with which it is illustrated. 



It is rather remarkable that actual radio-tele- 

 graphic transmission from station to station is dis- 

 missed in these text-books in a very few pages; 

 in fact, their subject is rather radio-telegraphic in- 

 struments than radio-telegraphy. Atmospherics 

 and their elimination, the laws of the trans- 

 mission of power, the causes of distortion of wave 

 fronts, and the relative telegraphic efficiencies of 

 various methods, are the most important problems 

 in radio-telegraphy to-day, and their solution is 

 incomparably more urgent than that of any ques- 

 tion of purely instrumental theory. 



Our Bookshelf. 



The New Physics. By Dr. A. C. Crehore. 



Pp. xii-i- III. (San Francisco : Journal of Elec- 



iriaty, 1920.) 2 dollars. 

 Objection may be raised against the title of this 

 look, on the grounds that it has been used before, 

 and that it seems to imply an exaggerated sense of 

 the importance of the views therein expressed. The 

 physical dimensions of electric and magnetic quan- 

 tities are first discussed, and the author, rightly we 

 think, emphasises the importance of retaining the 

 specific inductive capacity, k, and the permeability, 

 /A, in the equations. He supposes that k may be 

 ronsidered as the reciprocal of a velocity, and 

 Maxwell's relation then automatically determines /x 

 s a quantity of the same kind. This gives a single 

 system of units for all quantities in terms of length, 

 mass, and time, electric and magnetic charges ap- 

 pearing as quantities of the same dimensions. Dr. 

 Crehore 's next step is far more questionable— he 

 assumes that the dimensions of mass are those of 

 a velocity. We cannot attach much importance to 

 the first of the " two equally forceful reasons " he 

 idvances in support of this assumption. His new 

 \pression for Planck's constant may be the resuH 

 merely of a numerical coincidence. His second 

 reason is based on the gravitational equation which 

 he has developed, but this equation has been criti- 

 'ised, and must be considered as still suh judice. 

 As a literary production the book cannot he com- 

 mended, and the habit of stating results " in ad- 

 vance of the narrative " tempts one to suggest that 

 it should be read backwards. 

 NO. 2724, VOL. 109] 



Fermat's Last Theorem: Proofs by Elementary 

 Algebra. By M. Cashmore. Third edition. 

 Pp. 67. (London: G. Bell and Sons, Ltd., 

 192 1.) 2s. 6d. net. 



The first attempt to prove Fermat's last theorem 

 contained in this edition repeats a fallacy to 

 which attention has already been directed in 

 Nature, Oct. 30, 1919. On pp. 18, 21, 

 "quantities" t and w are defined, and it is 

 assumed that these quantities are integers, 

 which is not generally the case. In the 

 second attempt there is a fallacy, pp. 34-35, 

 relating to the divisibility of numbers. The 

 pamphlet ends with a version of Barlow's attempt 

 to prove the last theorem, taken from the 181 1 

 edition of his "Theory of Numbers." Barlow's 

 attempted proof contains a well-known fallacy, 

 which need not be pointed out here. 



In view of the considerable erroneous literature 

 concerning Fermat's last theorem it may not be 

 out of place to direct attention to two valuable 

 additions to the correct literature which have 

 appeared since the last edition of Mr. Cashmore's 

 book was reviewed in Nature. They are : (i) 

 Mr. L. J. Mordell's "Three Lectures on Fermat's 

 Last Theorem," and (2) a chapter in vol. 2 of 

 Prof. L. E. Dickson's " History of the Theory of 

 Numbers." W. E. H. B. 



The Physical Properties of Colloidal Solutions. 

 By Prof. E. F. Burton. Second edition. 

 (Monographs on Physics.) Pp. viii-f22i. 

 (London: Longmans, Green and Co., 1921.) 

 125. 6d. net. 



The second edition of this work conforms in 

 general to the plan of the first, i.e. it gives an 

 account of the properties of suspensoid sols from 

 the point of view of the physicist. The Brownian 

 movement and the electrical phenomena accord- 

 ingly claim the largest share, while the optical 

 properties of small particles are also treated with 

 unusual fulness. The rather difficult investiga- 

 tions dealing with these matters are summarised 

 with great skill and lucidity. Apart from some 

 omissions — among which the X-ray analysis of 

 colloidal particles, Pauli's work on the effect of 

 radiation, and Ostwald's on the protection of 

 Congo-rubin sols must be mentioned — all import- 

 ant advances made since 191 4 have been em- 

 bodied in the present edition. This applies 

 specially to the gradual breaking down of all 

 "valency rules" in electrolyte coagulation. The 

 book is excellently produced, and will be welcome 

 to all serious students of the subject. 



.'In Introduction to Organic Chemistry By D. LI. 

 Hammick. Pp. viii 4-258. (London: G. Bell 

 and Sons, Ltd., 1921.) 65. 



Mr. Hammick 's book provides an introduction to 

 organic chemistry suitable for junior students, and 

 not differing in any notable way from numerous 

 other books of similar standard. Experiments are 

 described. 



