496 SEEBECK ON THE POLARIZATION OF LIGHT. 
he starts are these:—I1st, he supposes that the vibrations are 
parallel to the plane of polarization, but modifies Cauchy’s equa- 
tions so that the known third system of waves is dispensed 
with, thus the refraction at once accurately comes to the same 
as in Fresnel’s theory; 2nd, the resultant of the incident and 
reflected vibrations in reference to their direction and length is 
equal to that of the refracted; 3rd, the perpendicular pressure 
on the plane of incidence is equal to that on the surface of sepa- 
ration in both media. Now if we suppose a sphere to be de- 
scribed at the point of incidence, and that 1Z be the weight of 
incidence, I P the axis of the crystal, the great circle Z O E the 
plane of incidence, IO the ordinary ray produced backwards, 
and IE the normal of the extraordinary wave, let ZO=¢4, 
ZE=97',PO0=y, PE=V,<ZOP=0, <ZEP=@’; let? 
be the angle of incidence, 6 and a the reciprocals of the ordinary 
and extraordinary index of refraction. Each of the two refracted 
rays may be made to disappear by polarizing the incident ray 
in a certain direction. When the extraordinary ray disappears, 
the plane of polarization of the reflected light forms with the 
plane of incidence the angle , in which 
tan 6=cos(t+ ¢)tan@+ 2(a?—b?) sin Osin pcos vanq—ay (2.) 
When the ordinary ray disappears, the plane of polarization of 
the reflected light with the plane of incidence forms the angle 
B’, for which 
—tan 6’ = cos (t + 9’) cot 6! 
5 py CO sl » sin?4 
+(a?—b dies @r sin! cos f me st 
When 6 and si eins equal, the plane of polarization of the 
reflected ray becomes independent of that of the incident, and 
the angle of incidence, at — this occurs, is the angle of po- 
larization. Hence 
(3.) 
f : ; sin? 
cos(i+ >) £gO+2 (a?—4*) sin® sin f cos p in G=3) 
+ cos (i + $') cot ©! =0 (4.) 
Luge cos 20! : , Sin? 2 
+ (a? — 6?) Neem) sin! cosy! —— aa eS 9) J 
is the general conditional equation for the angle of porerizaiaens 
Since i+ ¢ is very nearly a right angle, if we make i+ ¢=90°+, 
3 will be a very small magnitude. If we now make P R perpen: 
