207-209] The Dissipation Function 177 



209. Happily there is no need to probe into this difficult question. The 

 dynamics of those parts of the ether which do not contain any matter are, at 

 any rate if we assume Maxwell's electrodynamical theory, sufficiently well 

 understood. If Si, S 2 are small surfaces surrounding the molecules, we know 

 that at any point outside these surfaces we have, if E, H are the electric and 

 magnetic forces, 



div E =0, div H = ........................ (423). 



The total energy, electrostatic and electromagnetic, inside any one of the 

 surfaces, say S 1} is known to be 



where P, Q, R a'nd a, /3, 7 are the components of electric and magnetic force 

 respectively. The total flow of energy outwards across the surface 8 : is 

 known, as shewn by Poynting*, to be 



(425). 



Now if 1, 2 ... are the generalised coordinates of position and velocity of 

 the system inside S lt we have at every point inside Si 



div E =/(, & ...)...: (426), 



div H = <(,&..-) (427), 



where f and <f> are functions of the coordinates which are theoretically 

 calculable, the latter being almost certainly zero. From equations (423), 

 (426) and (427) we can calculate E and H as functions of all the coordinates 

 of the various systems, and from these we can calculate the Poynting flux 

 given by expression (425), also as a function of those coordinates. 



Let us, then, regard as the energy of the system inside Si the total 

 material energy of this system, if any, plus the total electric energy, electro- 

 static and electromagnetic, associated with the ether inside Si, this latter 

 being given by expression (424). Then we may legitimately regard expres- 

 sion (425) as a dissipation function of the system inside Si, and the motion of 

 the system will be deducible from a knowledge of the forms of the energy 

 function and of the dissipation function just denned. Taking this view of 

 the system, the interaction between matter and ether is represented by the 

 existence of the dissipation function, which may be interpreted physically as 

 evidence of the radiation of electromagnetic waves and " pulses " into the 

 ether ; and the interaction of the various molecules inter se is represented by 

 the fact that the energy and dissipation functions of system 1 depend not 

 only on the coordinates of system 1, but also on those of systems 2, 3 



* J. H. Poynting, Phil, Trans. 1884, n. p, 343. J. J. Thomson, Eecent Besearches, p. 308. 

 j. 12 



