IN CRYSTALLIZED MEDIA. 359 



and by substitution we obtain, difFerence of retardation 



T I „ „, M" sin ?«' sin w' 



_ Z'(a" - c") sin a sin /3 

 2w6 ■ 



7. This formula for the retardation on which depends the expla- 

 nation of the coloured lemniscates, is true it would appear even if 

 the angle between the optic axes Avere considerable. I do not know 

 whether this be true experimentally or not. 



I forbear from proceeding further in the development of the lemnis- 

 cates, as that has been already eifected with a formula coincident with 

 my own, or nearly so. As to the experimental verification of formula 

 such as these, they involve so much of calculation that there is con- 

 siderable difficulty in being able to form a correct judgment on their 

 coincidence; as far as I am aware. Sir J. Herschel and Sir D. Brewster 

 calculate the angles between the optic axes (see Phil. Trans. 1820.) 

 from assuming the law of refraction to be the Snellian law; this is 

 evidently not treating of rays but of waves; and consequently any 

 law of velocity which would be by this means established, would be 

 one relating to the velocity of a wave; and in the same manner, the 

 directions within the crystal can be no other than the normals. 



So that M. Biot's law when translated into the language of the 

 undulatory theory, is precisely that which I have enunciated above. 

 Indeed as far as I can collect. Sir J. Herschel appears to state it so 

 in one place. {Ency. Met. 1812.) 



Many writers make M. Fresnel's beautiful law of the reciprocals 

 of the squares of the velocities of the rays, to be the same thing as 

 this of Biot and Brewster. The cause appears to lie in the confusion 

 of language which naturally has been fallen into by different writers, 

 the one denoting by ray what the other denotes by wave, and so on. 



