IN CRYSTALLIZED MEDIA. 357 



in the direction of one of them, omitting consequently tlie variation 

 of velocity of one wave due to difference of its velocity from that 

 of the other, or in other words, omitting the variation of the differ- 

 ence of the velocities, compared with that difference itself whicli is 

 perfectly allowable. 



Let m', n' be the angles made by the direction, which we consider 

 common to the two, with the optic axes. 



a, /3 the angles made in air by the incident ray, with rays, which, 

 when they enter the crystal, move in rays; the normals to which are 

 the axes. 



Then retardation = Tv i~ - ~\ 



^Tv""-'' 



= Tv 



V Vi 



v'- — v," 



v'Vi (»' + V 



™ («^ — c°) sin 7)1 sin u , 

 And v' + V, = — , /u being the mean index of refraction ; 



f^ 





SO that sin ^ = M sin 0' as a factor of small terms. 

 Pz = (p', (see note at end) 

 Qz = <!>, 

 JSz = m, 



sin Sz = ^ sin Rx = ysmm = n sin m, 



Tz = Sz, PzO = e, 

 O and R the optic axes. 



zzs 



