134 



NATURE 



[March 31, 192 1 



well's theory that the ultimate seat of electro- 

 magnetic and optical phenomena is in the aether 

 may have to be modified or even abandoned. Ex- 

 periments have proved that natural phenomena go 

 on exactly as if there were no aether. We agree 

 with the author in thinking that "the hypothesis 

 that there is an aether may give a possible explana- 

 tion of the phenomena, but the hypothesis that 

 there is no sether provides an equally possible 

 and very much simpler explanation." Einstem's 

 theory, unfortunately, although it helps us to dis- 

 cover the laws according to which phenomena 

 occur, cannot lay claim to provide a mechanical 

 explanation of them. Electricians know the im- 

 portance of discovering the mechanisms by means 

 of which electric and magnetic forces are trans- 

 mitted through space. When the nature of these 

 mechanisms is discovered, there will probably 

 be a great advance in the practical applications 

 of electricitv. The theory of relativity, a very 

 convincing explanation of which is given in. this 

 book, proves that it is unnecessary to presuppose 

 an ather. This is welcome, as it is known that 

 highly complex properties must be ascribed to an 

 sether in order that it may explain both electrical 

 and magnetic forces. In the kinetic theory of 

 gases, forces and pressures are explained by a 

 flow of momentum, and a similar explanation 

 might be given of electrical, magnetic, and gravi- 

 tational forces. 



From the practical electrician's point of view, 

 the value of this volume would be increased if 

 the ordinary working formulae for the high-fre- 

 quency resistance and inductance of cylindrical 

 wires were given. Kelvin's electrostatic and 

 hydro-kinetic analogies are useful in this connec- 

 tion. The engineer also wants the formula for 

 the capacity between parallel cylindrical wires. 

 The fact that a brush discharge begins at a per- 

 fectly definite value of the potential gradient is 

 the principle on which accurate high-pressure volt- 

 meters are constructed, and it is known that the 

 sparking between spherical electrodes occurs at 

 a definite potential gradient. Kelvin's formulae 

 for the attraction and repulsion of electrified 

 spheres are proved, but no explanation is given 

 of the column headed " Ratio of charges for equi- 

 librium." We doubt whether the average reader 

 would infer from this that spheres electrified with 

 like charges would repel one another when far 

 apart, and attract one another when close 

 together. In conclusion, we can recommend this 

 book to every student who has a sound mathe- 

 matical training, and every man of science should 

 read the new chapter on the theory of relativity. 



A. R. 



NO. 2683, VOL. 107] 



Mathematical Text-books. 



(i) The Elements of Plane Geometry. By Dr. 

 C. Davison. Pp. viii -1-280 (with answers). 

 (Cambridge : At the 'University Press, 1920.) 

 10s. net. 



(2) A Primer of Trigonometry for Engineers: 

 ]Vith Numerous Worked Practical Examples. 

 By W. G. Dunkley. Pp. viii -1-171 (with 

 answers). (London : Sir Isaac Pitman and 

 Sons, Ltd., 1920.) 55. net. 



(3) Pure Mathematics for Engineers. By S. B. 

 Gates. With an Introduction by H. A. Webb. 

 Part i., pp. xi-l-191. Part ii., pp. xi-M79. 

 (The New Teaching Series.) (London : Hodder 

 and Stoughton, Ltd., 1920.) 45. 6d. net 

 each vol. 



(4) A Second Course in Mathematics for Technical 

 Students. By P. J. Haler and A. H. Stuart. 

 Pp. viii + 363. (London: W. B. Clive, Univer- 

 sity Tutorial Press, Ltd., 1920.) 65. 



(5) Elementary Applied Mathematics : A Practical 

 Course for General Students. By Prof. W. P, 

 Webber. Pp. ix+115. (New York: John 

 Wiley and Sons, Inc. ; London : Chapman and 

 Hall, Ltd., 1920.) 75. 6d. net. 



(6) The Laws of Mechanics: A 

 Text-book. By S. H. Stelfox. 

 (London : Methuen and Co., 

 65. 



(7) Elementary Dynamics: A Text-book for En- 

 gineers. By J. W. Landon. Pp. viii-t-246. 

 (Cambridge: At the University Press, 1920.) 

 I05. 6d. net. 



(i) ry-iHIS is a book in the old style, written 

 X by an old hand, and it has all the lucidity 

 that we have learnt to expect of its author. The 

 subject-matter is that of the first six books of 

 Euclid, with the addition of some miscellaneous 

 theorems on such subjects as concurrency and 

 loci. The method and the arrangement are ap- 

 proximately those of Euclid, with some modern 

 improvements. The book is the latest of its kind 

 and probably the best. 



The difficulties of a geometry of this type come 

 mostly at the outset. When we went to school, 

 in a less enlightened decade, we were taught that 

 " a straight line lies evenly between its extreme 

 points," and this elusive phrase, which seems to 

 have a meaning, has haunted and mocked us ever 

 since. Dr. Davison says (p. i) : — 



" A straight line is sometimes defined as a line 

 which has the same direction from one extreme 

 point to the other. The definition is, however, 

 imperfect owing to the use of the word ' direction,' 



Supplementary 

 Pp. xi-1-20i. 

 Ltd., 1920.) 



