Prof. Potter on the Principle of Nicol’s Rhomb. 453 
adhe; andtaking the principal section ag bf, the angle af will 
be found to be about aright angle. Let ag df, fig. 2, represent 
the same section as in fig.1, Let S & be aray of light entering 
the rhomb at k, and separated by the double refraction into an 
ordinary ray /o, and an extraordinary one ke; and if theray Sk 
is incident nearly perpendicularly upon the surface } f, the ordi- 
nary ray ko will have very little deviation in direction; but the 
extraordmary ray, as Huygens found, will have the angle eko 
about 6° 40'; an inclination which is towards the obtuse summit 
of therhomb. Now the film of Canada balsam being represented 
by 4a, the angle of incidence of the ordinary ray ko may be so 
great that the ray cannot pass into the Canada balsam, but will 
be totally reflected according to the rules of geometrical optics, 
because Canada balsam has less refractive power than cale-spar for 
the ordinary ray, although it has more refractive power than calc- 
spar for the extraordinary ray when it passes in certain directions ; 
and the extraordinary ray may pass through the film and upper 
prism, as before stated, when ad has the proper direction wh 
regard to the optic axis of the crystal. Now Canada balsam has 
been found to vary in its refractive index from 1°528 to 1°549, 
therefore putting ,=1°538 for an average refractive index; also 
for cale-spar from M. Malus’s measures, let 4)>=1°6543 be the 
constant refractive index for the ordinary ray, and let pu, be the 
refractive index for the extraordinary ray, which varies from 
16543 at its maximum value to 1:4833 at its minimum value. 
The luminiferous surfaces for light radiating around a luminous 
point within the crystal, take the forms of a sphere and an ob- 
late spheroid, with their common axis the optic axis of the cry- 
stal, and the ray velocity is inversely proportional to the refract- 
ive index ; so that if a and d are respectively the major and minor 
axes of the ellipse which generates the spheroid by its revolution 
round the axis, 0 the angle which an extraordinary ray makes 
with the major axis, and p the corresponding radius vector, we 
have from the equation of the ellipse to the centre, 
b 
Nae V1—€ cos? @’ 
and Me 5 
Fo p 
ve Hbe=o WV 1—e? cos? 0; 
putting @=0, we have p=a, and 
_ (1.4833) 
16543 
We Me= 16543 V 119605 cos? S 
=] 
='19605, 
