Laws of Irreversible Phenomena. 



397 



§ 13. Electromagnetic Dissipation. — In Helmholtz's 

 memoir " Das Princip der kleinsten Wirkung in der Elektro- 

 dynamik " *, it is shown in great generality that the thermo- 

 kinetic principle holds for electromagnetic phenomena ; 

 nevertheless we beg leave to consider here the simplest (but for 

 our purpose most important) case, to which in the second part 

 of the paper we shall have again to refer. Consider isotropic 

 conducting substances, at rest. Let us suppose that energy- 

 dissipation of the simplest or Joulean type is the only possible 

 irreversible phenomenon. Let the components of electro- 

 motive intensity at the point (x, y, z) be E z , E , E^ ; those of 

 extraneous electric forces, F z , F , ¥ z ; and the components 



of magnetic force H , H 



Let C be the electric con- 



ductivity, K the dielectric inductive capacity, and jj, the 

 magnetic permeability. If 



E =- 



dA a 

 ~dt 



E =- 



dk 



3 



dt 



".— ^- • iu 



dt 



then the vector A, whose components A x , A , A^ are, may be 

 taken to represent the " electromagnetic momentum " at 

 We assume that 



(x,y,z). 



dt ~by "dz 



4irO(E 



dt ~dx 



^X 



BH 



> 



(2) 



By 



J 



MH,: 



**,= 



(3) 



Mr. Heaviside and H. Hertz, it is well known, have con- 

 structed the whole of Maxwell's Theory upon two systems of 

 equations, one of which is the system (2) above, whilst the 

 second follows at once from (1) and (3). We shall take 

 A , A , A z to be the independent variables ; that is the choice 



* Sitz. Berl. Akad. 12 Mai 1892; Wiss. Abh. Bd. iii. p. 476. 

 also Boltzinann, Vorlesungen iiber Maxwell's Theorie, vol. ii. p. 7. 



See 



