152 Mr. Luioyp on Conical Refraction. 
to the line bisecting the optic axes, p = 16° 55' 27", and ep” = 13° 54/49". Ac- 
cordingly, the difference of these angles, p —¢’, which is the extreme angle of the 
emergent cone, is in the former case 2° 56 51",* and in the latter 3° 0' 38". Also, 
half the sum of these angles, which is the angle of emergence corresponding to the 
axis of the cone, is 15° 25' 8”. 
Comparing these with the results of observation, it will be seen that they agree 
nearly with respect to the mean angle of emergence, the difference amounting only to 
33' ; whereas the angle of the cone determined by experiment is about double of that 
furnished by calculation. 
Talso measured the angle of the cone by tracing the outline of its section on a 
screen of roughened glass, when the sun’s light was employed instead of that of a 
lamp. The mean diameter of this section being then accurately ascertained, and the 
distance of the screen from the aperture measured, the angle was given by the tables. 
Measurements taken in this manner gave for the value of the angle, 6° 24’, 5° 56', 
6° 22', respectively ; and the mean of these is 6° 14’, which, like the former mea- 
surement, differs very little from the double of the calculated angle. 
The results of observation thus appeared to be at variance with those of theory in 
two important particulars. In the first place, the emergent rays appeared to form a 
solid cone, instead of a conical surface ; and in the next, the magnitude of this cone 
was about double of the expected magnitude. Conceiving that these discrepancies 
might probably be owing to the rays which are inclined to the cusp-ray at small 
angles, aud which pass by the edge of the aperture, I determined to ascertain the 
fact by trying the effects of apertures of various sizes. 
I found accordingly that when the aperture was at all considerable, such as that 
formed by a large-sized pin, two concentric circles were seen to surround the axis, the 
interior of which had about double the brightness of the exterior annulus. And it 
was remarkable that the light of the interior circle was unpolarized, while that of the 
surrounding annulus was polarized according to the law already explained. When 
smaller apertures were used, the inner circle contracted, the breadth of the exterior 
annulus remaining nearly the same; until the former was finally reduced to a point 
in the centre of a fainter circle. When the aperture was still further diminished, a 
dark space sprung up in the centre, enlarging as the aperture decreased ; until finally, 
with a very minute aperture, the breadth of this central space increased to about 
3ths of the entire diameter. ; 
The phenomena exhibited in these cases assumed the forms represented in figures 
* It is easily shown that the sine of the angle of the cone, in this case, is generally expressed by the 
Va_h? VRP 
abe 
formula 
. 
