462. J. W. Gibbs—Double Refraction and Circular 
In estimating the statical energy for any considerable space 
by the integral 
/ ode, 
it will be allowable to substitute for the seventy-eight coéfli- 
cients contained implicitly in o their average values through- 
out the medium. at is, if we write s for a quadratic func- 
tion of &, 7, C, and diff. coeff. i in which the seventy-eight coéfti- 
cients are the space-averages of those in a, the statical energy 
of any considerable space may be estimated by the integral 
J sd. 
(This will appear most distinctly if we suppose the integration 
to be first effected for a thin slice of the medium d 
two wave-planes.) The seventy-eight coéfficients of this func- 
tion s are panei i Re 2 by the nature of the medium and 
the period of oscillat 
may divide s ante three parts, of which the first (s,) con- 
tains the a ee products of €, 7, , the second (s,,) co 
tains the products of &, 7, € with the differential coéfficients, 
and the third (s,,,) pe ins the squares and products of the 
differential coéfficients. It is evident that the average statical 
energy of the hoe medium per unit of volume is the space- 
average of s, and that it will consist of three parts, which are 
the space-averages of s,, s,, and s,, respectively. These parts 
we may call S,, S_, S,, Only the first of these was con- 
sidered in the preceding paper. 
Now the considerations which justify us in neglecting, for 
n approxi tate estimate, the terms of s which contain the dif- 
fore, to carry the approximation one step beyond that of the 
preceding paper, it “ only be necessary to take account of 
s, and s eae ye S, a : 
1. set 
ry Se ay +Gé&n, (5) 
| where, for a given medium and light of a given period, A, B, 
©, E, F, G are constant. 
