L. Page — Relativity and the Ether. 179 



and 



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

 Hence 



9t 



(c x E)= -c 2 v x E (13) 



So the ether strain due to a single charged particle is deter- 

 mined, for a point outside the particle, by the equations 



V • 



(c 



x E)=o 



9E 

 9t 



= 



v x (c X E) 



9 

 9t 



(c 



x E)=-o 2 



vx E 



in which the two vectors, E and cxE, appear. Consider now 

 the resultant ether strain due to all the particles whose fields 

 extend to the point under consideration. If by E we denote 



this resultant strain, and by H the sum of the vectors — (c X E) 



due to the individual particles, the preceding equations take 

 the form 



v H=o 



E = cvx H (H) 



H = - c v x E 



for any point devoid of matter. 



If matter is present at the point under consideration, we can 

 resolve E into two components, one of which represents the 

 strain due to the matter at P. Then it is easily shown that 

 the first and third of the above equations remain unchanged, 

 while the expression for E contains the additional term 

 -Vv E. 



So, in general, 



v-H=o 



vx H = ~(E+Vv E) (is) 



vxE^-JH 



Hence we have derived the field equations of electro- 

 dynamics from nothing more than the assumption of the 

 existence of an ether which is in accordance with the Principle 

 of Relativity, and the assumption that a charged particle is 

 the center of uniformly diverging tubes of strain. 



