ON OPTICAL THEORIES. Zon 
From the value of »? we see that 6? must be comparable with m, the 
density of the ether, so that, except when n?/(»?—n?) is a large 
quantity, the ratio of the amplitudes will be inversely as the densities, for 
$?/p» will be comparable with m/u. When, however, n?/(»? — n?) is 
large, the matter motion becomes appreciable, and the phenomena of 
anomalous dispersion arise. 
Part IV. 
THE ELECTRO-MAGNETIC THEORY. 
Chapter I.—MaxweE.i’s THrory. 
§ 1. There remains now for consideration Maxwell’s electro-magnetic 
theory. The fundamental equations of this theory are purely electrical, 
and are established on electrical principles. According to Maxwell, when 
electromotive force acts on a dielectric medium the change of condition 
known as electric displacement is produced. The two are connected by 
the equations— 
ee eriaa edt as htouhel oe 
P, Q, R being the components of the E.M.F. and 7, g, h of the dis- 
placement. K is the inductive capacity. In a crystal the equation 
holds only for the principal axes, and along these K has three different 
values. ert irts 
The rate of variation of the displacement given by f, g, h constitutes 
the current in the medium, and it is an essential part of the theory 
that— F ; : 
df | dg, dh 
de + dy tae 
vanishes everywhere. 
The current is connected with the components of the magnetic in- 
duction a, b, c by the equations— 
} doa dh 4 
——— =4 j 2 F ustedes KPT 
etc., and the magnetic force a, 3, y is given by 
eho ih. 22 aon coh oaheh actiaatat te 
etc., where p is the coefficient of magnetic capacity, 
a, b,c are also given in terms of a quantity known as the vector 
potential, the components of which are F, G, H, by the equations— 
dH dG 
a= dy ‘dz . . . . . (4) 
ete., and from these it follows that 
= A 
, docu f= a net : } J 20@S) 
etc., where 
ya iF dG, dH. 
dee dy * da? 
