SEEBECK ON THE POLARIZATION OF LIGHT. 495 
Consequently the auxiliary hypothesis 2 for a ray polarized in a 
plane parallel to that of incidence, is 
(1+) cosi = ucos?, 
for one polarized at right angles, 
1l+v=4; 
— i!) 
hence for the former v= seal point 
sin (t+ i) 
tan (t — 7‘) 
for the latter ~ tan (i+ 7) 
consequently the same formule as above, but with reversed 
signs*. 
A similar alteration must be made in the calculation which I 
made on calcareous spar, whereby the formula there given may 
be carried out with somewhat more strict limits, whilst the in- 
convenience resulting from the supposition of a uniform elasticity 
of the ether vanishes. For if we assume the density in both me- 
dia to be equal, cos «: P cos y (the same signs being used as be- 
fore) is the proportion of the magnitude of the wave of a ray in- 
cident in the plane of the principal section, to that of the extraor- 
dinary ray ; hence, when the incident light is polarized in a plane 
perpendicular to that of incidence, according to the law of active 
forces, 
cos 2 (1 — v*) = Pcosy. u?, 
and according to the auxiliary hypothesis 2, 
l+v=4, 
__ cosa— P cos ”, 
7hus ~ cosa + Pcosy’ 
this is likewise the original formula with opposite signs. Hence, 
as before, 
cos « = Pcosy 
is the equation, which gives the angle of polarization a when the 
plane of reflexion is parallel to the principal section. 
Mr. MacCullagh+ has treated this subject and rendered the 
formule more universally applicable. The premises with which 
* Be the sign what it may, the formule in each case show that in external 
reflexion it is opposite to that in internal, as Young supposed in explaining the 
phenomenon that Newton’s coloured rings in refracted light are complementary 
to those in reflected light, a phenomenon which is otherwise explained in a 
much more artificial method, by the so-called loss of half a wave. Vide Herschel, 
‘Light,’ § 674. 
+ London and Edinburgh Philosophical Magazine, Feb. 1836. 
