Polarization in perfectly transparent Media. 463 
Since the average values of 
sin’ on, cos” 2a, sin 2no cos on 
are respectively 4, 4, and 0, and since at the time to be 
considered 
t 
cos® a 1; 
it will appear from inspection of equations (1) that 
S,=4(Aa’+ BA" +Cy’+Ef,y,4+Fy.a,+ Ga,f,) 
+3(Aa’+Bf"+Cy?+Ef,y.+Fy.a,.+Ga.f,). (6) 
This is the first part of the statical energy of the whole medium 
per unit - volum 
second part of the statical energy of the whole medium 
per ‘unit “of volume is the space-average of s,,, which is a 
linear function of the twenty- -seven products of &, 7, € with their 
arpa: coéfficients with respect to the codrdinates. Now 
ce 
~45__ a(S") Bh PA ek 
Ge * de? “te 7 &? 
etc., 
the space-average of such products will be pie ae they will 
epetiipale nothing to the value of 8. Ther 1 be nine of 
hese products, in which the same component AE pete saeh 
hipeare twice. The remaining eighteen products may be 
divided into pairs according to the letters which they contain, as 
dé sis 
">. and on, 
A linear function of the eighteen mets may also be rezarded 
as a linear function “e the sums and differences of the products 
in such pairs. But si 
ne fe Palle cine) 
the terms of 8), containing such sums will contribute nothing to 
the value of S,. We have left a linear function of the nine 
differences 
ne dn ae de 
dé 
ae es ae ga ae fae! ete., 4 
Sy unwritten expressions being obtained by substituting in 
he denominators dy and dz for dx,) which constitutes the part 
