74 On the Laws of the Double Refraction of Quartz. 



from (20) ; which showed that D = - C, since the values of s, 

 corresponding to the same circular vibration, ought to be equal. 

 The transition from this simple case to that of a ray inclined at 

 a given angle to the axis was easily made, by taking into ac- 

 count the doubly refracting structure of the crystal. This was 

 done by supposing and j parallel to the principal directions in 

 the plane of the wave, and by changing #*, in equation (20), into 

 a"" - (<r 2 - i 2 ) sin 2 ; and thus the fundamental equations (1) and 

 (2) were obtained. 



