136 Prof. A. Anderson on Scalar and Vector 



is the solution of 



2A 1 B 2 A (' c + u 



c 2 c^ 2 u °c—u 



p being the density and u the velocity of the electricity at 

 any point. 



If, now, we write 



A=f_ ^ 



27TC log 



SH 1 -")] 



where w is the velocity that ^ had when at its companion 

 point, then 



V 2 A-4|£ = 



at any point where there is no electricity, since u is a 



r 



function of t . 



c 



But at any point where there is electricity it satisfies the 



equation 



13 2 A 



If this is not evident it can easily be shown to be true by 

 using the method of the small sphere as before. In this 

 integral u means the velocity of the element ciq when at its 

 companion point. The companion point of P coincides with 

 P, and therefore there the actual value of u is the velocity 

 at the companion point. 

 In like manner 



2A j. o -a. 



-k 



i^SK 1 -?)] 



is the solution of 



c 2 dt 2 r c 



In this latter equation u x means the x component of the 

 actual velocity at P : in the integral it means the x com- 

 ponent of the velocity of dq when at its companion point, 



which is a function of t . Similar expressions may be 



written down for the solutions of 



_ 2 . l^A Uy l^A U z 



V*A- ?w = -p-f, and V * A - ?w = -p-*. 





