CONICAL REFRACTION. 7 



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 sufficiently 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 

 tourmaline 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 remarkable 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 experi- 

 ment, I was naturally led to inquire how far it was in accordance 

 with theory ; and on examining Fresnel'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 tho corresponding 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 which the normals to the circle and 

 ellipse in the plane of xz make with one another is 



ac 



* These sections are not mathematically circular, the line being, in fact, one of the 



fourth order. 



