64 PROFESSOR KELLAND ON THE POLARIZATION OF LIGHT 



To find the value of the deviation, we have recourse to equation (A). 

 By substituting for m, mf, &c. their values in the first side of this equation, 

 and omitting quantities of the second order, this is reduced to 



2 cos 6 sin & , 



cot a . Y.-rr sin (d>, d> ') cos (<b. + </>,) 

 sm <p, sin <p 



By the same substitution, and by virtue of equation (13), the second side is re- 

 duced to 



2 cos 6 cos & sin ($, <jf>') cos (9, + 9') 

 sin 9, sin 9' cos (9 + 9') 



By equating these we have 



tana= cos (0 + 0') tan 0" . . . (16) 

 On this result it is unnecessary to offer any remark. 



. SECTION V. BIAXAL CRYSTALS. 



We shall be very brief in our exposition of the method of proceeding which 

 must be applied to Biaxal Crystals. In fact, we have little else to do than to 

 repeat our previous formulae, making the slight difference in them which consists 

 in supposing a quantity s for each ray in both cases different from unity. Thus 

 for the one ray, we shall have 



. a T, . sin 3 d>. cos 6 tan e 

 tan a = cos (9 + 9,) cot 6 - =-' A . // ,, --* 



T sin (< 9,) sm 



and for the other, 



A, T' sin 3 *' sin & tan V 

 tan a = cos (< + 9') tan & ^ A - *- -- --- w 



1 sin (9 <p) cos u 



TT -r L a T sin d>. sin 2 d> cos <9sin ''w - aO sin i-J/( 2 c 2 ) r 2 

 and .-. cos0 + 4>,cot0- ^A E ... '. ., 9 y 



sin (< 0,) sm 2 



i. XT , a, T.' . sin d)' sin 2 (b sin 6' sin (a + w.) sin i \L (a 2 c 2 ) r. 2 

 = cos0 + ^'tan0'-- 7i f A- -_ ^^ - ^-^ 



sm 9 9 cos D 



See M'CULLAGH (Note to p. 37). 



It is to be noticed that a, a, are the angles Avhich the direction of transmission 

 of one (and therefore approximately of both) of the waves makes with the optic 

 axes, and 4/ the angle between the plane passing through these directions and the 

 optic axes. The same kind of proceeding may be applied to the other method. 

 We do not think it necessary to work out the equations for biaxal crystals at full 

 length. Should experiments be made on this branch of optics, requiring a refe- 

 rence to their results, a very little additional labour will enable us to reduce our 

 iormulse to a shape fitted for numerical computation. A c the present time, to 



