104 



SCIENCE. 



[N. S. Vol. I. No. 4. 



netic and of electric induction and of their 

 fluxes in terms of the corresponding forces, 

 Poincare states then the fundamental law 

 of electromagnetic induction in a closed 

 conducting circuit as an experimental fact 

 and deduces immediately the first group of 

 the Maxwellian equations. This group is 

 nothing more nor less than a symbolical 

 statement that the law of electromagnetic 

 induction is true for every circuit whether 

 it be conducting or not. 



3. Joule's law is stated as an experi- 

 mental fact. In a homogeneous conductor 

 the heat generated per unit volume and 

 unit time at any point of the conductor is 

 proportional to the square of the electric 

 force at that point ; the factor of propor- 

 tionality is electrical conductivity by defi- 

 nition. Another quantity is then introduced 

 which is defined as the product of the 

 electrical force into the conductivity and 

 the name of conduction current is given 

 to it. 



By means of these definitions, the prin- 

 ciple of conservation of energy, and the first 

 group of Maxwellian equations, the second 

 group, in the form given by Hertz, is then 

 deduced. This completes the Maxwellian 

 electromagnetic theory for a homogeneous 

 isotropic field in which both the medium 

 and the conductors are at rest. 



Poincare loses no time in commenting 

 upon the physical meaning of these equa- 

 tions, but proceeds rapidly to Poj'nting's 

 theorem, which introduces one of the most 

 important quantities in the wave-propaga- 

 tion of electromagnetic energy. It is the 

 radiation vector, as Poincare calls it. A 

 brief remark, however, prepares the reader 

 for the good things that are to come. A 

 comparison of Maxwell's fundamental equa- 

 tions with those of Ampere shows them to be 

 identical except for rapid electric oscil- 

 lations, when the displacement currents 

 (Poincar6 does not mention this name, but 

 only refers to a mathematical symbol) iu 



the dielectric cease to be negligibly small. 

 For these no provision was made in Am- 

 pere's or any other of the older theories. 

 Here then is the starting point of the radi- 

 cal departure of the Faraday-Maxwell view 

 from that of the older theories. Hence the 

 study of Hertzian oscillations takes us into 

 a new region of electrical phenomena, a re- 

 gion entirely unexplored by the older the- 

 ories, and first brought before our view by 

 the discoveries and surmises of Faraday, by 

 Maxwell's mathematical interpretation of 

 these discoveries and surmises, and by 

 Hertz's confirmation of Faraday and Max- 

 well. 



Hertzian Oscillations. — It is the study of 

 these rapid oscillations which forms the 

 subject of the rest of Poincare's work under 

 consideration. 



Sir William Thomson's theory of the dis- 

 charge of a Leyden jar forms a fitting intro- 

 duction to this study. It states clearly the 

 essential elements which should be consid- 

 ered in the study of electric oscillations. 

 They are the period and the decrement. 

 The relation of these to the self-induction, 

 the electrostatic capacity, and the resistance 

 of the circuit are given by this theory and it 

 was verified by many experiments, espe- 

 cially those of Feddersen, who measured 

 the period of these oscillations and also 

 their decrement by a photographic method. 

 But inasmuch as these oscillations were of a 

 comparatively long period, 10^ per second, 

 they were not apt to furnish a test of the 

 Faraday-Maxwell theory. The waves of 

 the oscillations studied by Feddersen would 

 have been 30 kilometers long and would, 

 therefore, have escaped experimental detec- 

 tion. 



Hertz was the first to produce verj^ rapid 

 oscillations, 10^ per second ; but since their 

 period was too short to be measured di- 

 rectly, another method of testing the agree- 

 ment between theorj^ and experiment had 

 to be devised. This was done by Hertz, 



