210 FRESNEL'S THEORY OF DOUBLE REFRACTION. 



animation has been to prove the existence of both species of 

 conical refraction. 



The first case of conical refraction is that called by Sir 

 William Hamilton external conical refraction, and was ex- 

 pected to take place, as we have seen, when a single ray 

 passes within the crystal in the direction of either of the lines 

 of single ray-Telocity . These lines coincide nearly, but not 

 exactly, with the optic axes of the crystal ; and, in the case 

 of arragonite (the crystal submitted to experiment), contain 

 an angle of nearly 20. The plate of arragonite employed had 

 its faces perpendicular to the line bisecting the optic axes ; con- 

 sequently, the lines above mentioned were inclined to the per- 

 pendicular at an angle of about 10 on 

 either side. Let these lines be repre- 

 sented by OM and ON, equally in- 

 clined to the perpendicular OP. A 

 ray of common light traversing the 

 crystal in the direction OM or MO, 

 should emerge in a cone of rays, as 

 represented in the figure ; the angle 

 of this cone depending on the relative 



magnitude of the three elasticities of the crystal, a z , b z , c*. In 

 the case of arragonite this angle is considerable, and amounts 

 to 3 very nearly. 



A thin metallic plate, perforated with a very minute 

 aperture, was placed on each face of the crystal; and these 

 plates were so adjusted, that the line connecting the two aper- 

 tures should coincide with the line MO, or any parallel line 

 within the crystal. The flame of a lamp was then brought 

 near one of the apertures, and in such a position that the 

 central part of the beam converging from its several points 

 to the aperture should have an incidence of 15 or 16. When 

 the adjustment was completed, a brilliant annulus of light 



