Polarization in perfectly transparent Media. 473 
Without any ol) ha error, we may substitute U‘ for 
~V,’ Vz’, which will giv 
; =78. (37) 
19, Since these acs involve unknown functions of the 
‘period, they will not serve for an exact determination of the 
relation between @ and the period. For a rough approxima- 
tion, however, we may assume that the manner in which the 
_generai displacement in any small part of the medium dis- 
tributes itself among the molecules and intermolecular “isp 
is independent of the period, being determined entirely by th 
values of &, %, C, and bes differential coéfficients with nna 
to the coérdinates.t For a fixed direction of the wave-normal, 
@’ will then be soaieant Now equations (15) and (36) 
us p 272° @' 
“wp VeVe pave 2 
To express this result in terms of the quantities directly ob- 
served, we may use the equations 
A k 
eae Vas V.=—, Tae 
where & denotes the velocity of light in vacuo, 2 the wave- 
‘length im vacuo of the eit employed, Np, ry the absolute indi- 
-ces of refraction of the two rays, and n the index for the optic 
axis as eit from the ellipsoid (24) by Fresnel’s law. We 
thus obta 
_ GOnz*n,’ 270° O'ng’ ny" 
ee 9) 
In the case of uniaxial crystals, the direction of the optic axis 
is fixed. We may therefore wri 
“Vd. Wag © 
0=n,*m, (5. : (40) 
‘regarding K and K’ as constants. If we had used ae 
(37), we should have had the factor n‘ instead of np’n 
* The degree of accuracy of this substitution may be shown as follows. By 
es Vs (Va?—U)=Vi (U?—Vi 9), 
*whence 
VnF+Vi PF =(Ve + Vi )U*, 
Vz2—Va Ng 4+-Vi ied 3 is 
—(Ve aaa 
Vali: Vi). 
+ Compare § 12 of the former paper, on page 270 of this volume. 
