36S - THIRD REPOUT — 1833. 



Fresnel's principles respecting biaxal crystals, he arrived at the 

 curious resvilt that the surface of components, in such a crystal, 

 has not at every point a determined tangent plane, but that at 

 each oi four cusps, opposite, two by two, it is touched by an 

 infinite number of such planes, or by a tangent cone; and 

 hence he immediately concluded, by his general method, that 

 if a ray in air fall so upon a biaxal crystal as to make the point 

 upon the air-sphere correspond (by the rule already explained) 

 to one of those cusps on the surface of components of normal 

 slowness in the crystal, his construction would give no unique 

 refracted ray, nor even a pair or other finite number of such 

 rays within the crystal, but an infinite number of refracted 

 rays, namely, all the perpendiculars which can be let fall from 

 the point of incidence on the tangent cone at the cusp. The 

 author saw also that these rays must terminate in some curve 

 of plane contact on FresneVs double wave, in the whole extent 

 of which curve the wave must be touched by one plane, and 

 that there must be four such curves, which he afterwards found 

 to be circles ; a curious property of this wave, which Fresnel 

 himself had not noticed. But the most remarkable part of this 

 result was, the new and delicate experimental test which it 

 offered for Fresnel's principles, since the internal conical 

 REFRACTION which it indicated, for certain cases of incidence 

 on a biaxal crystal, had not only not been hitherto observed, 

 but seemed contrary to all former analogies of observation ; so 

 that if this theoretical consequence of Fresnel's principles, 

 which he had not himself perceived, should be verified by 

 subsequent experiment, the principles would receive a new 

 and striking confirmation ; and if, on the contrary, after all 

 due care employed in experiments directed expressly to the 

 question, the small but finite conical dispersion in biaxal 

 crystals, which the author had thus theoretically concluded, 

 should not be found in fact to take place, the principles them- 

 selves would require to be abandoned or modified. Professor 

 Lloyd was applied to by the author to undertake this expe- 

 rimental inquiry. After some unsuccessful trials with crystals 

 of insufficient size and purity, he obtained a fine piece of arra- 

 gonite from Mr. Dollond, and at length completely succeeded in 

 exhibiting the phaenomenon which Mr. Hamilton had expected. 

 The rays of the internal cone emerged, as they ought, in a cy- 

 linder from the second face of the crystal ; and the size of this 

 nearly circular cylinder, though small, was decidedly perceptible, 

 so that with solar light it threw on silver paper a little luminous 

 ring, which seemed to remain the same at different distances 

 ^f the paper from the arragonite. Professor Lloyd describes 



