212 FRESNEL'S THEORY OF DOUBLE REFRACTION. 



covered by observation. On reference to Fresnel's theory, it 

 was found to yield the same result. 



(222) A remarkable variation of the phenomenon took 

 place, on substituting a narrow linear aperture for the small 

 circular one, in the plate next the lamp, in the first-mentioned 

 mode of performing the experiment, the line being so ad- 

 justed, that the plane passing through it and the aperture on 

 the second surface should coincide with the plane of the optic 

 axes. In this case, according to the hitherto received views, 

 all the rays transmitted through the second aperture should be 

 refracted doubly in the plane of the optic axes, so that no part 

 of the line should appear enlarged in breadth, on looking 

 through this aperture ; while, according to Sir "William Ha- 

 milton, the ray which proceeds in the direction OM should 

 be refracted in every plane. The latter was found to be the 

 case : in the neighbourhood of each of the optic axes, the lu- 

 minous line was bent, on either side of the plane of the axes, 

 into an oval curve. This curve, it is easy to show, is the con- 

 choid of Nicomcdes, whose asymptot is the line on the first 

 surface. 



(223) The other case of conical refraction called internal 

 conical refraction by Sir William Hamilton was expected to 

 take place when a single ray has been incident externally upon 

 a biaxal crystal, in such a manner that one of the refracted 

 rays may coincide with an optic axis. The incident ray in 

 this case should be divided into a cone of rays within the 

 crystal, the angle of which, in the case 



of arragonite, is equal to l a 55'. The 

 rays composing this cone will be re- 

 fracted at the second surface of the crys- 

 tal, in directions parallel to the ray inci- 

 dent on the first, so as to form a small 

 cylinder of rays in air, whose base is the 



