199] DIELECTRICS AND MAGNETIZABLE BODIES. 383 



During the displacement the distribution of the field varies, 

 but if we use the form of W given in 119, namely, 



we have the important simplification that B V W = 0*, for after the 

 motion as well as before the potential satisfies the conditions 

 180 (8) and (9). Accordingly in considering the variation SW 

 we have to consider only the variation of p and p, produced by 

 the motion, the change of W in other ways being taken account of 

 in the condition 8 V W= 0. The change in p at any point is caused 

 by matter differently charged coming to the point, and we find as 

 in 38, putting dm = pdr, 



d(p&*) 



dp ~~ ~ 



In like manner //, has changed to the value it formerly had at the 

 point xx,y$y,z &z, which has moved to x, y, z, so that 



Accordingly (considering surface distributions as a limiting case of 

 volume distributions) since we have 



I /// J9F98F SVS8V dVSSV\, 

 ~ 4ar IJr \ te" W + ty ~ty + 8J M 



oo 



we obtain the change in W as 

 (4) 



1 [ffify* S/^j ,df**}(fiV\* /dPY 



+ -Q- llnfw+fty + ffor] ^- + ^- 



87rJJJ(dx dy * dz j [\dvj \dyj \dz 



00 



and integrating the first integral by parts, the surface integral 

 vanishing at infinity, 



(To the first order.) 



