﻿Theory of Dispersion. 469 



And if * we agree that / =u« = total current (polarization 

 and convection), we conclude that A = p.%, .... (9) 



x, y, z beingjthe velocity of electrons, as before, and it is 

 easily seen that (7) and (9) are consistent, on the under- 

 standing that p(x — x )=A (say) or e(x — a ) — Adr, 

 e being the unvarying charge in vol. dr, 

 and x — # =the displacement of e in the direction of x. 



Comparing the equations (3), (4), (5), and (6), we con- 

 clude that total polarization in any medium may be regarded 

 as made up of two parts — one involving sethereal (fg h) and 

 the other corpuscular (A B C) displacement. 



Again, comparing (8) and (3), we observe that the total 

 current, is to be regarded as similarly made up and that it is 

 the total current and total polarization that are subject to 

 the solenoidal condition. 



From (6) since, in stationary media, 



oA t oB dO ~dP __ 



ox " r ^ + oz ot ' 

 we get the equation of continuity for electrons in motion, 

 viz. : 



dt ox 

 Again, from (6), we can obviously derive 



d<r 

 where \ is defined by \Tj 2 (j) + p = Q. 



This equation states that </> is the potential of a distribution 

 p, provided 



where k Q is the specific inductive capacity of the medium. 

 Since the medium here is the ?ethereal medium (whose pro- 

 perty is modified by the presence of electrons), k is an 

 absolute constant denning the property of the free gethereal 

 medium. 

 Thus 



A = ^|£,&c., and fi=/+£l*;Ao. . (10) 



47T ox ' 4tt ox 



so that , . , e o /1\ 



in the neighbourhood of an electric charge. «'• 



j\ 



