Partition of Energy between Matter and Radiation. 23 

 also 



|Wf i( *V= j , F 1 V 2 F,.rfV+ ^F^-F^dS, (32) 



-y- denoting differentiation along the outw.ird drawn normal 



dv ° 6 



at the element of surface JS. At the surface Fj and F r are 

 normal, I\ and iv are their normal components. 

 From (25) and (29) it can be shown easily that 





dt\ „ / 1 1 



rfv 



\pi pi) 



Here /?! and p 2 are the principal radii of curvature at the 



surface. These give Fr-rn =F X tt?« 



Using this and (31) we can reduce (32) to 



JF r V 2 F 1 JV=JF 1 V 2 F//V=~47r^%. . (33) 



We now use the value of F by (24) in the equations of 

 aether (20) and the equations of motion (21). First in (20) 

 and we have 



Multiply this equation throughout by ~F r dV and integrate 

 through the volume. By (31) and (33) 



The term involving tfr is easily seen to vanish on 

 partial integration when we recall the surface conditions 



^. = 0, VV = °- 



We have finally 



1 d 2 a r . r u 



c 2 rf* s 



?+*rV= p-F> (34) 



and the integral on the right hand of (34) is taken wherever 

 there is electric charge. 



