.'4 



NATURE 



[February 2, 1899 



advanced student ; it is full of hints and references, 

 gathered during the author's long experience as a teacher 

 and observer, and which will be valuable to all who seek 

 to interpret the history of our stratified formations. 



H. B. W. 



THE MATHEMATICAL THEORY OF ELEC- 

 TRICITY AND MAGNETISM 



A Treatise on Magnetism and Electricity. By Andrew 

 Gray, LL.D., F.R.S. In 2 Vols. Vol. I. Pp. xv + 

 479. (London : Macmillan and Co., Ltd., 1898.) 



IN the preface to this book Prof Gray defines his aim 

 to be the presentation of the whole subject of 

 electricity and magnetism from the point of view of action 

 in a medium, and his method to be a preliminary con- 

 sideration of the phenomena, followed by a development 

 of the consequences of assuming that the medium is a 

 receptacle of energy according to certain laws, and a 

 proof that among these consequences the observed 

 phenomena are included. .\t the same time, it is pro- 

 posed that the work should not deal with theory alone, 

 but should take account of its applications to questions 

 of practical interest. 



In following out the first part of this scheme the author 

 commences with magnetism, reviewing the elementary 

 facts, and showing how they are related to the condition 

 of the media occupying the field. Then, as applications, 

 come chapters on terrestrial magnetism and on the 

 deviations of the compass in an iron ship. Next, the 

 elementary facts of electrostatics and the theory of this 

 part of the subjec are dealt with in a similar manner ; 

 they are followed by a treatment by the ordinary mathe- 

 matical methods of a number of electrostatical problems 

 and of the steady flow of electricity in systems of linear 

 conductors. 



.•\t this point, in order to provide suitable mathematical 

 equipment for the student of electromagnetism, two 

 chapters are interpolated : one on general dynamical 

 theory, in which Lagrange's and Hamilton's equations 

 are explained ; and one on hydrodynamics, which extends 

 to the consideration of vortex motion. 



The experimental results relating to mechanical actions 

 between magnets and currents are next described, and 

 their theory worked out ; then, after a short account of 

 the fundamental experiments on electromagnetic in- 

 duction, the application of general dynamical principles 

 to the treatment of a system of circuits is explained, and 

 some problems on circuits with capacity and inductance 

 are solved. A chapter on general electromagnetic theory 

 follows, touching upon electromagnetic waves, the trans- 

 ference of energy in an electromagnetic field, and the 

 behaviour of moving electric charges, with a short account 

 of the Zeeman effect. Part of the subject of contact 

 electricity next receives treatment, and the volume con- 

 cludes with a short chapter on thermo-electricity. 



It is the misfortune of an author with the reputation of 

 Prof Gray that general commendation must pass him by. 

 To hint at his authority as a teacher, or to insist on the 

 industry, learning and research displayed in his books, is 

 wholly unnecessary ; and, at the risk of appearing un- 

 gracious, it may be of more utility to bring forward 

 NO. 1527, VOL. 59] 



objections, and to reveal blemishes for consideration and 

 removal in a subsequent edition. 



First of all, then, it is possible that after vol. ii. is 

 written the author, having quarried the whole of his 

 material, may find himself able to improve its general 

 arrangement in some respects. In particular, we would 

 plead for an early treatment of the phenomena of mag- 

 netisation in iron and steel, which surely is more germane 

 to the plan of this treatise than the precedence given 

 to terrestrial magnetism and ships' magnetism, for re- 

 arrangement and further elucidation in the domain of 

 general electromagnetic theory, and for the postponement 

 of contact electricity until it can receive fuller discussion 

 in connection with electro-chemical phenomena and 

 theories. 



.Secondly, as the book is clearly intended for the use of 

 students, it may be urged in their interest that, whenever 

 it is necessary to state a result which cannot be deduced 

 from what precedes it, great assistance would be given 

 by drawing attention to the fact. For example, the con- 

 scientious student will be discouraged by his failure to 

 obtain the expression given at the end of § 498, and there 

 is no hint that it must either be accepted as an article 

 of faith, or traced to Prof. J. J. Thomson's " Recent 

 Researches." -Again, when he reaches the beginning of 

 § 500, and reads concerning a perfectly conducting wire 

 that " there would be no dissipation in it, but energy 

 would enter it," he has not been supplied with the know- 

 ledge which would enable him to insert before "energy'' 

 the word " no,' which has been omitted by the printer. 

 Also, he may well be pardoned for complaining that the 

 next sentence but one is a very hard saying indeed. 



A few inaccuracies may also be pointed out. The 

 numerical example on the torsion balance (§ 16) would 

 present a difficulty to any one, if such a man there be, 

 who is not familiar with problems on this instrument, 

 and the difficulty would be intensified by the remark 

 (§ 17) that "no account was taken of the earth's field in 

 determining the forces acting on the magnet." In the 

 description of Maxwell's dynamical model illustrating the 

 induction of currents (§ 451), the long bar is wrongly 

 stated to be rigidly attached to the axle of one of the 

 wheels, when it is, in fact, free to rotate about this axis ; 

 but the analysis, which follows, exposes the oversight. 

 A more serious error occurs in § 232, which states, and 

 sets out to prove, that the actual distribution of currents in 

 a net-work of conductors containing internal electromotive 

 forces corresponds to a minimum rate of production of 

 heat, i.e. that with the usual notation, 2(RC-') is a 

 minimum. The conclusion reached, however, is that 

 5(RC'^-EC) has a minimum value which is zero, a 

 plausible result, but due to an algebraical lapse, by which 

 a term is omitted in the final equation. If this is cor- 

 rected we obtain the true law, namely, that 2(RC*-2EC) 

 is a minimum, which is demonstrated in a foot-note to the 

 third edition of .Maxwell's " Electricity " , vol. i. p. 4o8\ 



These suggestions are put forward in no spirit of dis- 

 respect towards an author who has earned the grati- 

 tude of so many students of electrical science, but with 

 the conviction that, in the case of a text-book, absence of 

 errors is as great a recommendation as excellence of a less 

 negative character. L. R. W. 



