THE ELECTRIC AND LUMINIFEROUS MEDIUM. 
289 
as the absolute temperature : in intermediate cases it would not vary so rapidly as 
this. The circumstance that in gaseous media and some others, the dielectric 
constant is exactly equal to the square of the refractiv^e index, favours the former 
alternative (§ 21 ). 
Mechanical Relatiuns of Radiation reconsidered. 
t 6. The results given in Part II., §§ 28—9, as to the mechanical forcive exerted on 
a Tnaterial medium by a stream of radiation passing’ across it, require amendment in 
the light of these principles, of which they also form an apt illustration. Consider, 
as there, two media separated by the plane of yz, and a system of plane-polarized 
waves advancing across them, with their fronts parallel to that plane, the electric 
\ibiation parallel to the axis of y, and the magnetic one parallel to the axis of z ; we 
may generalize by taking K and p, to be in each medium functions of x. The 
electrical equations are 
ilTV = 
clQ (7c 
dx dt ’ 
V = o-Q + 
K , dQ 
— ^ • 
Ttt dt 
■^PP^y^^o formulae found above 38), the force acting on the electric polarity 
comes out to be null, while the electromagnetic bodily force is, per unit volume, 
X = v'y, being ’wholly parallel to the axis of x : its periodic part has double the 
fiequency of the radiation. Now there is no mechanical elasticitv associated with 
matter w-hich is powerful enough to transmit in any degree the alternating phases of 
forcives connected with a phenomenon which travels so fast and with such short 
wave-length as radiation, long Hertzian waves being excluded. Consequently when 
X is wholly alternating’ it is not transmitted by material stress at all; and it is only 
when its value for each element of the medium contains a non-alternating part that 
we can have a material forcive. When the media are perfectly transparent, and are 
traversed by a steady train of waves, there is therefore no transmissible material 
forcive either on surfaces of transition or anywhere else, and the JX dx previously 
calculated has no relation to material stress. But if we consider a stream of radiation 
passing across a transparent medium into an opaque one, and for simplicity take the 
latter to be homogeneous so that for the transmitted waves c = CqC"^-^ cos {iit — qx), 
the expression for X, viz : {v — ~ c“" y, contains a non - periodic term 
“ 2^2 -f ^ 2 j 877 ^^ when integrated over the medium gives a pressure on 
the opaque medium of intensity 9 ^ 3 where E is the energy per 
unit volume of the incident radiation absorbed. Unless the opacity is so great 
that the intensity of the light is diminished in the ratio e~^ in penetrating a few 
wave-lengths, that is when p is negligible compared with qf this pressure will be 
* This will not usually be the case for metallic media. 
The sign of this mechanical force may be negative in a region of intense absorption. 
VOL. CXC.—A. 2 P 
