od 
SEEBECK ON THE POLARIZATION OF LIGHT. 497 
dicular to ZO E and ZR =p, PR = q, we obtain more nearly 
and without reference to the reflexion in passing from air into 
calcareous spar*, 
ie ade 
2 b(1— 8?) (5-) 
When the axis lies in the plane of incidence, from the equation 
(4.) we can deduce 
1 — a*® sin? A — 4? cos? 
1 — a? 6? 
The latter equation is that at which I arrived by my calcula- 
tion, and which agrees very well with my observations. The 
angles of polarization calculated for other azimuths of the plane 
of incidence agree accurately with my measurementst, whilst 
the differences on the natural surface of fracture do not amount 
to more than three minutes, and in the case of the upper surfaces 
are not greater than might be expected considering the difficulty 
previously mentioned, that of procuring polished surfaces of cal- 
careous spar with a perfectly uninjured condition of the surface. 
Brewster’s measurements, to which Mr. MacCullagh refers for 
the confirmation of his theory, agree for the natural surfaces to 
within about one-fourth of a degree of those obtained by calcula- 
tion, the difference amounts to three-fourths of a degree for a 
surface inclined 5° towards the axis. 
Although Mr. MacCullagh’s calculations agree well with my 
measurements in regard to the angle of polarization of calca- 
reous spar, the same does not hold good in the case of the value 
of Band’. I have previously mentioned, that, when a ray is 
polarized by the reflexion produced at the surface between the 
air and the calcareous spar, the plane of polarization does not 
in general correspond with that of incidence, but forms an angle 
with it. This angle must be that which Mr. MacCullagh expresses 
by 6 and @'; but the values calculated according to the equations 
(2.) aud (3.) do not agree with the measurements which I made, 
but, for instance, for a surface parallel to the axis, in which each 
angle, according to observation, may amount to 4°, 6 and #! con- 
stantly or nearly so, are = 0, and do not differ less from experi- 
_ ment in the case of the natural surface of fracture. I shall take 
8= K cos’ g (cos* ¢ — cos*p), in which K = 
*, a being = ZP. 
sin? 7 = 
* Mr. MacCullagh distinctly alludes to the rhomboids of calcareous spar 
only ; however, what follows, shows that the equation (5.) agrees with obser- 
vation in the case of other surfaces of calcareous spar. 
+ Poggendorff’s Annalen, vol. xevii. p. 309. 
VOL. IV. PART XV. 2N 
