Double Refraction of Quartz. 109 



Comparing the coefficients of sin f and of cos £, 



a c 



7* 



kx ~ i =- ~^ cos a + 9 



c . 



w + y = —j= sin a + A 

 x/2 Y 



c 



X + S = —j= COS a + (p. 



Obtaining the values of w, x, y, %, and substituting in the expres- 

 sions for the vibrations, we find (omitting the common factor 



c - ) 



(1+^)72/' 



In Oo, (1 - k) . cos £- (a + <p). 



In o^., k(l—k). sin ^-(a + cp). 



In #e, * (1 + k) . cos %-( a + <p). 



la e t e„ - (1 + A) . sin £_( a + 0)- 

 After emerging from the crystal, f in the two latter expressions 

 must be increased by . 



Taking the resolved parts of the vibration perpendicular to 

 AP t , we find for the efficient vibration, 



(1 -k) . cos £- («+0) . cos + k (1 -A) . sin f - ( a + 0) . sin 



A 



The coefficient of sin £-( a + 0) is 



* (1 -k) . sin <j>-k (1 + 4) .cos <p. sin ~ -(1 +4) .sin 0. cos 



2tt0 „ , ,. . , 2-TrB 



