140 HENET A. BOWLAND 



electric conductivity, V the potential, p the volume density of the elec- 

 tricity, and t the time. 



The subtraction of one equation from the other gives 



To introduce the condition that there shall be no electric absorption, 

 we must observe that when that phenomenon exists, a charge of elecr 

 tricity appears at a point where there was no charge before; in other 

 words, the relative distribution has been changed. Hence, if the rela- 

 tive distribution remains the same, no electric absorption can take 

 place. Our condition is, then, 



where c is independent of t, and // and p' are the densities at the points 

 x, y, z, and x', y' z'. This gives 





where c is a function of t only and not of x, y, z, and p is the value of p 

 at the time t = 0. As we have 



1 dV dm dV d /,-. k\ . dV d /, k\ . dV d /, k 



where m = - and n is a line in the direction of the current at the given 



I 

 point, equation (1) becomes 



_1_ d V dm 1 dp 4rr p _ ft 

 m dn dn ~lc ^IT ~ ~^~ ' 

 From equation (2) 



P = f 



and hence 



_!_ dV dm 

 m dn dn 



If we denote the strength of current at the point by 8, we have 



