January 25, 1895.] 



SCIENCE. 



103 



toi-s who liavo extended the field of the 

 Hertzian method of investigation. But it 

 should be observed that the experiments of 

 tlie pre-IIertzian epoch receive their full 

 share of attention, as, for instance, the ex- 

 periments of Rowland, Riintgen, and others. 



The work will undoubtedly exert a very 

 strong inlluence upon the future develop- 

 ments of tlie electromagnetic theory, and 

 deserves, therefore, more tlian ordinary at- 

 tention. This circumstance should, in the 

 opinion of the reviewer, excuse the length 

 of this review. 



General Theory. — Poincare's discussion di- 

 vides itself naturally into two parts. In the 

 fii-st part an electromagnetic field with con- 

 ductors at rest is considered. In the second 

 part the discussion extends to electromag- 

 netic fields with conductors in motion. 



The Hertzian method of presentation is 

 adopted in preference to the Maxwellian. 

 Two distinct differences between these two 

 methods should now he pointed out. The 

 fii-st difterence is essential, and may be 

 stated briefly as follows : — 



Hertz described jMaxwell's electromag- 

 netic theoiy as the theory which is contained 

 in Maxwell's fundamental equations ; he 

 stated, however, very clearly that the sup- 

 pression of all direct actions at a distance is 

 a characteristic feature of this theory. But 

 if it is not a sufiicicnt hypothesis, and if no 

 other hypotheses are clearly stated by iMax- 

 well, then his deduction of the fundamental 

 equati(ms which form the heart and soul of 

 his theory must necessarily lack in clearness 

 and conii>leteness. This is the difficulty 

 whicli Hertz discovered in Maxwell's .syste- 

 matic development of his own electromag- 

 netic theory, and Hertz obviates this diffi- 

 culty by starting from the equations them- 

 selves as given, proving tlieir correctness by 

 sliowing that they are in accordance with 

 all our experience. 



The second difference is formal only. It 

 mav be stated briellv as follows: Maxwell 



considered the elect rot onic state, discovered 

 by Faraday, as of fundamental importance. 

 The matliematical exjjression of this state, 

 the vector potential, was considered by him 

 as the fundamental function in his mathe- 

 matical presentation of Faraday's view of 

 electromagnetic phenomena. Hertz, just 

 as Heaviside did some time before him, 

 considered the vector potential as a rudi- 

 mentary concept which should be carefully 

 removed from the completed theory Just as 

 the scaffolding is removed from a finished 

 building. In place of the vector potential 

 Hertz substituted the electric and the mag- 

 netic force as the fundamental quantities. 

 This enabled him to state the fundamental 

 equations of JIaxwell in a more symmetrical 

 form than Maxwell did. 



It seems that it is principally this second, 

 the formal, difference which decides Poin- 

 care in iavor of the Hertzian method. But 

 there is still considerable difference between 

 the presentation of the electromagnetic the- 

 ory given by Hertz and that which Poin- 

 care gives in this book. For whereas Hertz 

 proceeded fi-om the symmetrical form of 

 Maxwell's fundamental equations as given 

 and by deducing from them and from .several 

 clearly defined assumptions the general ex- 

 perimentally established laws of electrical 

 phenomena pi-oved the correctness of these 

 equations, Poincare deduces them from the 

 following experimentally established facts : 



1. The energj- of the electromagnetic 

 field consists of two parts, one due to the 

 action of the electric and the other to that 

 of the magnetic forces. They are each 

 homogeneous quadratic functions of the 

 two fundamental ([uantities, that is of the 

 electric and of the magnetic forces respect- 

 ively. This experimental relation defines 

 the units of the electric and of the magnetic 

 force and also the phj'sical constants of 

 the medium, that is the specific inductive 

 capacity and the magnetic permeability. 



2. Having defined the meaning of mag- 



