of Light produced by Quartz. 173 



axis ; and conceive a ray of light, polarized in a given plane, 

 to fall on the crystal in the direction of x ; causing a vibra- 

 tion of the molecules situated in the surface of the crystal, 

 which may be represented by 



>j = a sin . — — V t : (24-.) 



A 



where A and v are the length and velocity of the waves in the 

 incident ray. 



Suppose the origin of x to be at the surface of the crystal 

 on which the light falls : then, when x is zero, the expressions 

 (23.) must coincide with (24<.), which they will do if we make, 



a,^a,= -, ^=^=_. (25.) 



Let e = v/ (V^ + ?-)j then e is the actual displacement of a 

 molecule within the crystal ; and if we denote by « the angle 

 which £ makes with y\, then 



tan a — -^ ; 



therefore, since c^ = flg, the expressions (23.) give 



tan a = 



COS. — [Vc^t—x) — cos . (u, t—x) 



h \ 



27r , ^ , . 27r , 

 sm . - — - {v^t~x)+ sm . [v t — x) 



All Ai 



= tan . 2 TT a; ( — ) ; 



and hence ^ , I 1 \ 



Now the equations (21.) give us 





B. ^ , (26.) 



nearly : therefore, since — ^ = — ^ , we find 

 Ai B, ^ ^ A*, B, TT . 



A^ A*, A*; A, A*, A/' 



. 1 1 Bo / 1 1 X 



hence =_„_^( +__] 



\ A2 Ai, ^ \^i Ao- / 



" ~ A* A^' ne-'^riy; 



