16 CONICAL REFRACTION. 



The second kind of conical refraction, whose existence has been 

 anticipated by Professor Hamilton, 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 coin- 

 cide with an optic axis. When this is the case, there will be a cone 

 of rays within the crystal, determined by lines connecting the 

 centre of the wave with the points of the periphery of the circle of 

 contact. The angle of this cone is equal to 



tang 



and its numerical value in the case of arragonite is 1 55', assum- 

 ing the values of the three indices as determined for the ray E by 

 Professor Eudberg (see page 10). 



As the rays constituting this cone will be refracted at emer- 

 gence 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 dis- 

 tance 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 inci- 

 dent 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 rays 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 rela- 

 tive 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 



