240 



NATURE 



[October 21, 1920 



the Riemann zeta function to *he type of problem 

 to which Waring-'s theorem belongs. In his inau- 

 gural address to the University of Oxford on his 

 appointment as Savilian professor of geometry, 

 I'rof. Hardy gives a most lucid account of the work 

 on which he has been engaged along' with Messrs. 

 Littlewood and Ramanujan. The whole of it is 

 expressed in non-technical langfuage, and many 

 gaps in the theory are explained. We specially 

 note the first few pages as forming a model intro- 

 duction to a professor's inaugural address. A 

 statement on p. 15 needs amendment, integers ex- 

 pressible as a sum of two squares being of either 

 of the two forms 



M2P or 2M2P, 



where P is a product of positive primes 4fe + i. 



W. E. H. B. 



On Gravitation and Relativity : being the Halley 

 Lecture delivered on June 12, 1920. By Prof. 

 R. A. Sampson. Pp. 24. (Oxford : At the 

 Clarendon Press, 1920.) Price 2s. net. 



There is a special appropriateness, as Prof. 

 Sampson points out, in choosing a gravitational 

 subject for the Halley Lecture, in view of the im- 

 portant part that Halley played in securing the 

 publication of the "Principia." The lecture is an 

 able resume of the various speculations on the sub- 

 ject, from Galileo's "Dialogues" and Newton's 

 hypothesis of aether-pressure down to Einstein's 

 theory. The author evinces the highest admiration 

 for Einstein's skill in devising^ a formula which ex- 

 presses his results "without redundancy, defect, or 

 effort, and whose boldness, range, brilliance, and re- 

 sounding successes" have commanded universal at- 

 tention ; but on proceeding to examine the formula 

 in detail he confesses to his dislike of some of the 

 devices employed, in particular imaginary time and 

 the obliteration of the distinction between past and 

 future. He alludes to Newton's experiment of the 

 rotating bucket and to Foucault's pendulum ex- 

 periment as establishing the possibility of detecting 

 the absolute direction of an axis of rotation. It 

 will probably be admitted, even by the convinced 

 relativist, that it is of advantage to students to 

 have the claims of the older "common-sense" 

 kinematics placed before them in an attractive 

 form, which the author has certainly done. 



A. C. D. Crommelin. 



A i'rimcr of Air Navigation. By H. E. Wimperis. 



Pp. xiv+128. (London: Constable and Co., 



Ltd., 1920. J Price 8s. 6d. net. 

 This book provides an interesting and sound 

 introduction to the subject of findings one's way in 

 the air. In many ways the investigation of 

 methods of air navigation is based on nautical 

 experience, but the author points out that the 

 reverse process is beginning to apply. The chief 

 differences appear to arise from the greater speed 

 of aircraft as compared with the steamship, and 

 the considerable altitudes above sea-level reached 

 by the aeroplane and airship. Height in itself 

 gives a wider range of vision, and in clear 

 NO. 2660, VOL. 106] 



weather allows a greater permissible error in dead- 

 reckoning without loss of port than is required for 

 a ship seeking- harbour. These points are clearly 

 brought out in the little book under notice, and the 

 various steps involved, both of observation and 

 calculation, are developed simply. Whilst non- 

 mathematical in character, we suggest that " .\\t 

 Navig:ation " would provide a .suitable starting- 

 point for the more complex studies of advanced 

 works and, what is perhaps more important in the 

 present state of aeronautics, encourage capable 

 students to extend the subject into regions yet un- 

 explored. The main ideas of navigation are illus- 

 trated by examples from the great flights of the 

 post-war period — Atlantic and Australasian. The 

 correction for wind for aircraft is more important 

 than that for tide and steamship, and clouds inter- 

 fere with surface observations to an undesirable 

 extent. Such difficulties, at any rate near land, 

 will be countered by the use of direction-finding 

 wireless telegraphy, a subject dealt with in one of 

 the chapters of the book, which may be recom- 

 mended as covering the essentials of present-day 

 knowledge. 



A junior Inorganic Chemistry. By R. H. Spear. 

 Pp. viii4-386. (London: J. and -A. Churchill, 

 1920.) Price 10s. 6d. net. 



Although this does not seem to possess any 

 features differentiating it from many other element- 

 ary text-books on chemistry, it is clearly written, 

 and obviously the work of an experienced 

 teacher. In some cases the information is not up- 

 to-date, as on p. 128, where it is stated that "ex- 

 periments carried out with the most elaborate pre- 

 cautions have shown that i grm. of hydrogen 

 combines with 798 grm. of oxygen." c3zone is 

 said (p. 177) to have "a faint, peculiar smell." 

 Although molecular formulae and equations are 

 used freely from p. 152, the molecular theory is 

 not explained until p. 278 is reached. Instruc- 

 tions for experiments are given throughout the 

 book, which provides a good introduction to 

 chemistry. 



Part i. of the book, containing the first thirteen 

 chapters, which lead up to, but do not include, the 

 atomic theory, is published separately at the price 

 of 55. net. It provides an introductory course 

 for junior forms in schools. 



Atiiinic (iitd Molecular Theory. Bv D. L. 

 Hammick. Pp. 82. (Winchester : P. and G. 

 Wells, 1920.) 



As an exposition of the simple applications of 

 the atomic theory to chemistry, this account leaves 

 little to be desired in clearness and accuracy. 

 Nothing, however, is said of the recent work 

 which has put the atomic theory on an entirely 

 new basis, and the point of view is that of twenty 

 years ago. One cannot now truthfully say that 

 "Dalton's hypothesis merely restates the facts 

 about the elements and their modes of combina- 

 tion in terms of atoms and, as an 'explanation,' 

 is not very satisfying." 



