ITS L. Page — Relativity and the Ether. 



Consider a point P fixed in the system K. Let dl be an 



infinitesimal line drawn from P in the direction of E, and let 



c, be the component of c in the same direction. Now E is a 



vector function of position in space, which has everywhere the 



direction of the tubes of strain and is equal in magnitude to 



<9E 

 the number of tubes per unit cross-section. Hence ^ dt at 



P can readily be shown to be made up of three terms, 

 namely : 



_C-vE^, the change in E due to the fact that the tubes of 

 strain at a point — cdt from P will reach P in the time dt ; 



\ — Ev c + E ~t dt, the change in E due to the fact that 



the direction of c changes from point to point, and conse- 

 quently the density of the tubes of strain will change in the 

 time dt ; 



E- vc-E J \di, the change in E due to the twisting of 



the tubes of strain in the time dt. 

 Therefore, 



<9E 



-gj =-cvE-Evc+Evc 



Therefore, at any point outside the charged particle, 



|^=vx(cxE) (ii) 



since v • E = 



We shall now turn our attention to the determination of 



St < c x E > 

 It can easily be shown that 

 9 c 



w = " c - vc 



Hence, making use of this result and (11) 



9_ 



9t 



9 (c x E)= -c v(c x E)-(c x E)v c-(E- vc)x c 



= -c 2 vxE+v x(c-Ec)-(E- vc)x c 



-(c x E)- vc + cv (c x E) 



But the most general type of field is that given by equations 

 (7). For this field it can readily be shown that 



v(cxE)=o (is) 



