Double Refraction of Quartz. 89 



c.sin — (vt-x). sin (a + <{>) parallel to AC. The former of these 



A 



furnishes the ordinary ray, the latter the extraordinary. Now 

 after they have passed through the crystal, we may still keep 

 the expression for the vibration of the ordinary ray, provided we 

 make the proper alteration in the value of x : but (by what has 

 gone before) we must then suppose the path of the extraordinary 

 ray shorter by e. Consequently after passing through the cry- 

 stal, the vibration produced by the ordinary ray is 



. 2w 



c.sin —{vt-x).cos a + <f> perpendicular to AC, 



and that produced by the extraordinary ray is 



2tt 



c.sin —-(vt— # + 9). sin a + cp parallel to AC. 



A 



When these are received on the analyzing plate, those parts only 

 are transmitted to the eye or to the screen, which are perpen- 

 dicular to AP 2 . They are 



2 



c . sin — - (vt - x) . COS a + <p . COS <j>, 



and c . sin — (vt— x + 9) . sin a + <p . sin <j> : 



and the sum of these represents the magnitude of the vibration 

 which comes to the eye, or falls on the screen. It may be put 

 under this form 



sin — (vt— x) {c.cos a + 0.cos + c.cos —^ 9. sin a + 0.sin <f>\ 



7T 



+ cos — (vt - x) . c . sin — - 9 . sin a + <£ . sin (p. 



A A. 



Vol. IV. Part I. M 



