156 Mr. Luoyp on Conical Refraction. 
pearance from two luminous points to a perfect luminous ring, contributed not a little 
to enhance the interest. 
The emergent light, in this experiment, being too faint to be reflected from a screen, 
I repeated the experiment with the sun’s light, and received the emergent cylinder 
upon a small piece of silver-paper. I could detect no sensible difference in the mag- 
nitude of the circular sections at different distances from the crystal. 
When the adjustment was perfect, the light of the entire annulus was white, and 
of equal intensity throughout. But when there was a very slight deviation from the 
exact position, two opposite quadrants of the circle appeared more faint than the other 
two, and the two pairs were of complementary colours.* The light of the circle was 
polarized, according to the law which I had before observed in the other case of 
conical refraction. In this instance, however, the law was anticipated from theory 
by Professor Hammron. 
I measured the angle of incidence by a method similar to that already employed 
for the emergent ray in the former case ; and found it to be 15° 40’. ‘This determi- 
nation is, for many reasons, capable of much greater accuracy than the other ; and 
was probably, in this instance, very near the truth. 
In order to compare it with the result of theory, it is to be observed that the optic 
axis isa normal to the wave-surface, and therefore the corresponding incident ray 
will be given by the ordinary law of the sines, the index of refraction being the 
mean index of the crystal. Now the angle which the normal to the circular 
section of the surface of elasticity, or the optic axis, makes with the axis of x, or the 
2 Hz 
perpendicular to the surface, is equal to feo ya j ; andits numerical value 
a 
in the case of Arragonite, is 9° 1’. We have then 
sin. c = 1.6863, sin. (9° 1’) ; 
from which we finds = 15° 19’. The difference between this and the observed angle 
SI 
In order to measure the angle of the cone, I was compelled to employ a method 
somewhat indirect, but (I think) susceptible of considerable accuracy. As the 
aperture on the first surface of the crystal must have some physical magnitude, it is 
obvious that instead of a cone of mathematical rays within the crystal, there will be 
in all cases a cone of cylindrical pencils, overlapping one another near the point of 
divergence ; and that the diameter of these pencils will be equal to the diameter of 
the aperture. Now I tried a number of apertures, until I found one with which 
these cylindrical pencils just separated at the second surface of the crystal. It is evi- 
dent that, in this case, the interval between the axes of the cylinders at the surface of 
* This part of the phenomenon appears to be explained by the non-coincidence of the optic axes for 
the rays of different colours. 
