a eee eS ey ee eee eo ee ne i> 
pee ee 
nae , 
hy 
Dispersion of Colors in perfectly transparent Media. 265 
We may go farther in the determination of the quantities €’, 
’, ¢’. For in view of the very fine-grained structure of 
medium, it will easily appear that the manner in which the gen- 
eral or average flux in any element Dv (represented by &, 7, 0) 
distributes itself among the molecules and intermolecular spaces 
must be entirely determined by the amount and direction of that 
flux and its period of oscillation. Hence, and on account of the 
superposable character of the motions which we are consider- 
ing, we may conclude that the values of €', 74 C’ at any given 
point in the medium are capable of expression as linear func- 
tions of €, 7, € in a manner which shall be independent of the 
time and of the orientation of the wave-planes and the distance 
of a nodal plane from the point considered, so long as tbe period 
of oscillation remains the same. But achange in the period may 
/ J 
ment. Let us examine each of these quantities, and consider 
the equation which expresses their equality. 
6. Since in every part of an element Dv the irregular as well 
as the regular part of the displacement is entirely determined 
(for light of a given period) by the values of &, y, ¢, the 
Statical energy of the element-must be a quadratic function of 
14; 7 Say 
(AE? 4+ Br’ + Ce? + Ene + F2é + Gn) De, 
where A, B, etc. depend only on the nature of the medium and 
the period of oscillation. At an instant of no velocity, when 
- t 
sin on’ =0, and cos" 27-=1, 
P P 
the above expression will reduce by equations (1) to 
(Aa? + B6* + Cy? +Efy+Fyat Gap) cos’ 225 Do. 
Since the average value of cos* an, in an indefinitely ex-’ 
tended space is 4, we have for the statical energy in a unit of 
volume 
S=}(Aa’?+BA’+Cy?+Efy+Fya+Gaf). (2) 
