IN CRYSTALLIZED MEDIA. 351 



axes. The expression which I have given above is remarkably elegant, 

 and is evidently the one on which the differences of the refractions of 

 the different rays depends, whilst M. Fresnel's formula is not susceptible, 

 as far as I know, of any application, except in those numerous instances 

 where, being incorrectly adopted, it stiU gives a result nearly correct. 

 This arises from the difference of the reciprocals of the squares of the 

 velocities of the rmjs varying as the difference of the squares of the 

 velocities of the vibrations parallel to their fronts. 



27. To apply the formula to the particular case in question : 



Let T be the thickness of a plate of a biaxal crystal cut perpen- 

 dicularly to the greatest or least axis of elasticity ; 



V the velocity in air ; 



V, v' those of the vibrations perpendicular to their front, the inci- 

 dence being nearly perpendicular ; 



0, cp' the angles which the perpendiculars to the fronts of our 

 waves before and after incidence make with the normal ; 



Then the retardation of this wave may be easily shewn (Airy's 

 Tracts, p. 376.) to equal 



^^ j- - cos <^ cos </, - sm </> sm .^'J 



= ^^' 17 - '^^''^ V 1- ^sm>' - sin^0'-} 



cos 0(1; ^ V '^ j 



= tI— cos 0' - i ^/v^ - F' sin' <p'\ 



= Tl—cos(p'- 1> nearly. 



