424 Prof. Rowland on the Propagation of 



Aebiteaby Disturbance. 



In the equations of p. 423 make a=0 and w=l. We then 

 have 



C^cjl-ji-jy}. 



The magnetic induction is then 



P 

 and the components of the electric displacement, 



®'= - Y f sin0 (2C + C 2 )6-^p-vo, 



^""^ 27T&P 2 Vl ' 



Let now a sphere of radius R be circumscribed about the 

 origin, and an arbitrary uniform displacement take place in 

 the interior of this sphere of a value equal to 



^ 6 2tt6R* X 1 bU) 



Taking this value for the displacement inside the sphere and 

 the previous values for the outside, the equation of continuity 

 is satisfied for the electric displacement and for the magnetic 

 induction. If the sphere is very small indeed, we have 



;VKC 



X'= 



2tt& 2 R 3 



Whence we have, on substituting the value of C from this 

 equation in the others and replacing f 7rR 3 by dv, the magnetic 

 induction 



- T// 8b 2 X.' sin 6 C-. .., ™ 7 



w= -^vKr^ e dv> 



and the electric displacement, 



&=s _ SOo+O? ^X' gin e -iK P -vt) dV} 



47T/J 2 



These equations give the complete solution of the problem 



