Polarization in perfectly transparent Media. 471 
By multiplication we obtain 
; Vv? (VU) (V*—U;)=9 2 (30) 
Since g is a very small quantity, it is evident from inspection 
: ag equation that it will admit three values of V®, of sty 
will be a very little greater than the grea ter of the 
we have to do are those which differ ree little from U,? and 
Us. 
‘For the numerical StS po of Y, n U,, U,, an vw 
are known numerically, we may divide ee ate ae = 
and then solve it as if the aac member were known. This 
will give 
vu ci Jan) gee ea Seo (31) 
By substituting U,U, . V* in the hots member, we may 
approximation to the two values of V2. Each 
of the values obtained may be improved by substitution of that 
value for V* in the second member of the equation 
For either value of V*, we may easily find the ratio of p, to 
fx, that is, the ratio of the axes of the ep accent nee 
from one of equations (29), or from the equatio 
be et bs 
Pal ores y*-U* (32) 
obtained by combining ee 
In equations (29), we are to read + the second 
members, according as the ray is right- anit or left- beak 
(See $16.) It follows that if the value of ¢ is positive, the 
: : : the 
the ae is tha ¢ case. Ex xcept when g = 0, and the polari ri- 
zation 1s linear, there will be one right-handed and one left- 
handed ray for any given wave-normal and period. 
18, When U, = U;, equations (29) give 
Pi = Ps, V =U +, 
* We should not stagione yg Lon significance to the third value of V2, 
For this value would imply a e-length very small in comparison with the 
length of ordinary waves of light, and with respect to which our fundamental 
- assumpiion that the wave-length is it in comparisou with the distances of 
gth is very 
ee molecules would be entirely false. Our analysis, therefore, tira! 
a that any such velocities are possible for the propagation 
Giesttical Maeavba 
Am. Jour. Sct. teas Serres, Vou. XXIII, No. 138.—Jung, 1882 
32 4 sf 
