Mr. Luioyp on Conical Refraction. 149 
and as the inclination of the internal ray to the cusp-ray was further increased, these 
two luminous portions merged gradually into the two pencils, into which a single ray 
is divided in the other parts of the crystal. ‘This change is represented in (fig. e.) 
Similar observations were made without the lens, by bringing the flame of the lamp 
near the first surface of the crystal, and forming the converging cone by covering that 
surface also with a thin metallic plate, perforated with a minute aperture. In this case 
the line connecting the two minute apertures was adjusted as before, and the pheno- 
mena were the same as in the former instance, the rays which passed along this line 
within the crystal forming a diverging cone at emergence. 
In all these experiments the emergent rays were received directly by the eye placed 
close to the aperture on the second surface. It was obviously desirable, however, to 
receive them on a screen, and thus to observe the section of the cone at different 
distances from its summit. After some trials, I effected this with the sun’s light, the 
light of a lamp being too weak for the purpose. The emergent cone being made to 
fall on a screen of roughened glass, I was enabled to observe its sections at various 
distances, and therefore with all the advantages of enlargement. ‘The light was suffi- 
ciently bright, and the appearance distinct, when the diameter of the section was 
between one and two inches. 
On examining the emergent cone with a tourmaline plate, I was surprised to observe 
that one radius only of the circular section* vanished in a given position of the axis of 
the tourmaline, and that the ray which disappeared ranged through 360° as the tour- 
maline plate was turned through 180°. Thus it appeared that all the rays of the cone 
are polarized in different planes. 
On examining this curious phenomenon more attentively, I discovered the remark- 
able law, “that the angle between the planes of polarization of any two rays of the 
cone is half the angle between the planes containing the rays themselves and the 
axis.” 
Having assured myself of the near truth of this law by experiment, I was naturally 
led to inquire how far it was in accordance with theory ; and on examining Fresnet’s 
theory with this view, I was gratified to find that it led to the very same result. 
According to the known rule, the plane of polarization of any one ray of the 
emergent cone must bisect the angle contained by the planes passing through the cor- 
responding normal to the front of the wave and the two optic axes. Now, it can be 
easily shown that the normals to the wave, at the cusp, surround one of the optic 
axes, and are inclined to it all round at small angles. For the tangent of the angle 
* These sections are not mathematically circular, the line being, in fact, one of the fourth 
order. 
