Partition of Energy between Matter and Radiation. 21 



§ 4. Distribution of Energy in Matter and Radiation. 

 For the aether 



(v*-JJ> + 4.p = o. . . . ri9) 



( v2 -4£) F+4 ^=°- • • • ^ 



<j> and F are the scalar and vector potentials, tt is the vector 

 velocity of electricity of density p. 

 For any electron 



l=J E '^ ( 21 ) 



In (21) p is the true material momentum of the electron, 

 supposed rigid we must remember. E' is the whole electric 



intensity at any point of this moving electron. — f indicates 



differentiation at a point moving with the electron. In (21) 

 the integration is all over the volume of the electron 



E^-^-V^-^tt.CurlF]. . . (22) 



At the perfectly reflecting boundary there is the condition 

 that the tangential component of 



is zero, and everywhere we have 



DivF+i^=0 (23) 



c at 



Now F and (f> are clearly indeterminate to the extent that 

 we may add to F a term of the form V« and to </> the term 



-j-. The electric and magnetic forces remain unaltered, 



but (23) requires 



1 d 2 \ 



(v^S) 



0. 



&) can be chosen to satisfy this equation and to have any 

 assigned value at the surface : we can therefore so choose co 

 as to make the value of </> always zero at the surface. Then 

 the condition that E is normal at the surface requires nlso 

 that F is normal. 



