4 CONICAL REFRACTION. 



Professor Hamilton has shown that the four planes of which 

 we have spoken touch the wave-surface, not in two points only, 

 but in an infinite number of points, constituting each a small 

 circle of contact, whose plane is parallel to one of the two circular 

 sections of the surface of elasticity ; and that, consequently, a 

 single ray of common light, incident externally in the above- 

 mentioned direction, should be divided within the crystal into an 

 infinite number of refracted rays, constituting a conical surface. 



Here, then, are two singular and unexpected consequences of 

 the undulatory theory, not only unsupported by any facts hitherto 

 observed, but even opposed to all the analogies derived from ex- 

 perience. If confirmed by experiment, they would furnish new 

 and almost convincing proofs of the truth of that theory ; and if 

 disproved, on the other hand, it is evident that the theory must be 

 abandoned or modified. 



Being naturally anxious to submit the undulatory hypothesis 

 to this delicate test, and to establish or disprove these new results 

 of theory, Professor Hamilton requested me to institute a series of 

 experiments with that view. I accordingly applied myself to this 

 interesting research with all the attention which the subject so 

 well merited, and have fortunately succeeded in verifying both 

 cases of conical refraction. The substance I employed in these 

 experiments was arragonite, which is well known to be a biaxal 

 crystal, whose axes are inclined at an angle of nearly 20. I 

 selected it partly on account of the magnitude of its biaxal energy, 

 and partly also because the optical elements 6f this mineral have 

 been determined, apparently with great care, by Professor Rudberg ; 

 and therefore the results of theory could be applied to it at once 

 without further examination. The specimen I used was one of 

 considerable size and purity, procured for me by Mr. Dollond, 

 and cut with its parallel faces perpendicular to the line bisecting 

 the optic axes. 



The first-mentioned species of conical refraction, it has been 

 observed, takes place in air, when a ray of common light is trans- 

 mitted within the crystal in the direction of the line joining two 

 opposite cusps of the wave. If we suppose such a ray to pass in 

 both directions out of the crystal, it is evident that it must emerge 

 similarly at both surfaces ; consequently, the rays which are trans- 

 mitted along this line within the crystal, and form a diverging 

 cone at emergence at the second surface, must be incident in a 



