706 



RICE 



ART. L 



where ^{x, y, z) is the potential at the point x, y, z, and D is 

 the dielectric constant of the medium. In the present instance, 

 since \l/ depends only on z, this simplifies to 



dV 47r , ^ 



This result is introduced into the previous one and in this way 

 solutions for 4^(z) in terms of z can be found. For details the 

 reader is referred to the literature. 



One or two results, however, can be indicated in a general 



L 



M 



Fig. 14 



N 



way by means of graphs. Thus suppose we have a graph of 

 ypiz) before us (Fig. 14), then wherever p{z) is positive, d}\{//dz'^ 

 is negative, i.e., dip/dz is decreasing with increasing z, or the 

 slope of the graph is decreasing. (This means, decreasing in the 

 algebraic sense; so that if the slope is negative as in the region 

 OL in the figure, the numerical value of the slope is increasing; 

 in the region LM, the slope is increasing algebraically although 

 in the first portion of it the numerical value of the slope is 

 decreasing.) Thus in the figure p is positive in the region OL, 

 negative in the region LM and positive once more in the region 



