Mr. Luioyp on Conical Refraction. 153 
(f) and (g). (Fig. i) represents the appearance of the section when the line con- 
necting the aperture with the luminous point on the first surface was slightly inclined 
to the cusp-ray. 
It is easy to render an account of these various appearances. When the aperture 
mn, (fig. 3.) is at all considerable, the rays cm, cn, proceeding to its circumference 
from a point on the first surface, will be sensibly inclined to the cusp-ray, which 
we shall suppose to be the line ¢ 0, connecting the point on the first surface with the 
centre of the aperture. Consequently the interior refracted rays, mq, m7, as well as 
the exterior, mp, 2s, will be inclined outwards ; and it is obvious that there will be 
a central bright space, limited by the lines mq, 27, each point of which will be illu- 
minated by one interior and one exterior ray. The light in this space, therefore, will 
have double the intensity of that of the surrounding space ; and as the rays which 
combine to form it are polarized in planes at right-angles to one another, the result- 
ing light will be unpolarized. When the aperture is diminished, the inclination of 
the rays mq, n7, to one another is lessened, until finally they are reduced to 
parallelism, and the central bright space contracts to a point. ‘This is represented in 
(fig. 4.) When the aperture is still further diminished, the rays m q, nr, become in- 
clined inwards, and cross (fig. 5.) It is obvious that beyond the point of intersection 
there will be a dark space illumined by no ray whatever; and as in the surrounding 
annulus there is no meeting of rays oppositely polarized, the whole of the light will 
be polarized, and according to the law already explaimed. With a yet diminished 
aperture, the rays mq, 2 1r, approach to parallelism with the exterior rays, ” s, im p ; 
and the central dark space enlarges, and approaches to equality with the outer and 
limiting cone. Thus the annulus of light in any section is diminished indefinitely in 
breadth, and the cone approaches to a mathematical surface. 
Now if we assume that the divergence of the two refracted rays in this plane, cor- 
responding severally to the rays ¢ m, ¢ 0, ¢n, is the same, as must be nearly the case, 
it will follow that the angle of the true cone, which would arise from the single ray 
co, is half the sum of the angles of the exterior and interior surfaces of the conical 
annulus ; and that when a bright circle appears in the centre, as is the case with a 
considerable aperture, the dark space must be considered as negative, and the true 
angle is half the difference of the observed angles. 
From this it follows that when the central bright space is reduced to a point, the 
true angle is just half the observed. Now this was very nearly the case in the expe- 
riments from which the measures were taken ; consequently the corrected angle, de- 
duced from these measures, coincides very nearly with that assigned by theory. 
Two other measurements, taken since with a more direct reference to this correc- 
tion, were as follows :— 
VOL, XVII. 2Q 
