I 



328 Dr. Pocklington on the Fundamental Equations of 



Taking now the case of plane waves, from VII. Sto-=0, and 

 hence e = 0, giving 



From this, the surface-integral of dr/dt equals the line-integral 

 of go-. From IX. and X. we see that g must be + 1. We 

 must take the negative sign if we chose the axes as usual. 

 Finally, 



£~*. ^ 



which gives S . Vt=0. 



7. From (1) and (2) we get 



d 2 ar „ dr 



m =vS7 di 



— =uVt + const., 



and the constant is clearly zero. 



Finally, then, our assumptions lead to the equations of the 

 field in Hertz's form, 



SV<r=0, SVt = 0, 



da- 2 dr /9 . 



dt =vS7T ' di = -^ < 3 > 



8. We must now consider the case of a moving charge. 

 XI. Assumption. The motion of a hody produces no motion 



in the aether through which it moves. — This has been verified 

 experimentally for the case where the moving body rotates 

 and always occupies the same space. 



Let the charged body move with a constant velocity y. 

 Then d/dt=SyV ( ), and from (3) 



w at 



since S . Vo" = 0, 



whence 



= J(StV-c-7S..V») 



J-'V.Wvr, 



^Vyc+To, (4) 



where t is any solution of V . Vt o =0, S . Vt =0. 



