Mr. Luioyp on Conical Refraction. 155 
cases, the form of the conchoid, whose pole was the projection of the axis of the 
emergent cone, and asymptot the line on the first surface—(figs. /, m.) It is easy to 
show that these results are in accordance with theory. 
The second kind of conical refraction, whose existence has been anticipated by 
Professor Hamitron, depends (it will be remembered) on the mathematical fact, that 
the wave-surface is touched in an infinite number of points, constituting a small 
circle of contact, by a single plane parallel to one of the circular sections of the surface 
of elasticity. It takes place when a single external ray falls upon a biaxal crystal in 
such a manner, that one refracted ray may coincide with an optic axis. When this is 
the case, there will be a cone of rays within the crystal, determined by lines con- 
necting the centre of the wave with the points of the periphery of the circle of con- 
tact. The angle of this cone is equal to 
tang. —1 Van Ne as 5 
bz 
and its numerical value in the case of Arragonite is 1° 55’, assuming the values of the 
three indices as determined for the ray 7 by Professor RupBeEre ; (see page 151.) 
As the rays constituting this cone will be refracted at emergence in a direction 
parallel to the incident ray, they will form a small cylinder of rays in air. This 
cylinder, it will be seen, is in all cases extremely small; for the diameter of its section 
made by the surface of emergence: subtends an angle of 1° 55’ only, at a distance 
equal to the thickness of the crystal. Hence the experiments required to detect its 
existence and measure its magnitude, demand more care and precision than those 
already described. The incident light was that of a lamp placed at some distance ; 
and in order to reduce as much as possible the breadth of the incident beam, it was 
constrained to pass through two small apertures, the first of which was in a screen 
placed near the flame, and the second perforated in a thin metallic plate adjoining to 
the first surface of the crystal. Under ordinary circumstances, it is obvious, the inci- 
dent ray will be divided into two within the crystal, and these will emerge parallel 
from the second surface. I was able to distinguish these two rays by the aid of a 
lens ; and turning the crystal slowly, so as to vary the incidence gradually, I at length 
observed that there was a position in which the two rays changed their relative places 
rapidly, on any slight change of incidence, and appeared at times to revolve round 
one another, as the incidence was altered. Being convinced that the ray was now 
near the critical incidence, I changed the position of the crystal, with respect to the 
incident ray, very slowly ; and after much care in the adjustment, I at last saw the 
two rays spread into a continuous circle, whose diameter was apparently equal to 
their former interval. 
This phenomenon was exceedingly striking. It looked like a small ring of gold 
viewed upon a dark ground ; and the sudden and almost magical change of the ap- 
