Double Refraction of Quartz. 



113 



In Oo, , cos a + <p . sin £ + k . sin a + <p . cos £. 

 In o^o t , k~ sin a + <p. sin £ — £.cos a + <f>. cos £. 



In -E<? 15 * s cosa + 0.sin £ + _^Z _ £. s i n a + rf>.cos£ + 



2tt9 



In e,e,, sin a + <p . sin £ + — ?— + & cos a + $ . cos £ + 



27T0 



We have now to resolve these into the elliptical vibrations in 

 a plate of left-handed quartz of the same thickness, with its 

 principal plane in the same position. It will be observed, that 

 the difference of right-handed and left-handed quartz consists only 

 in the difference of the sign of k. 



Taking first the vibrations in Oo x and o^, and using those 

 letters to express the vibrations in those directions, 



Oo l = vibration in Oo\ + that in E'e\ 



= w sin J + x cos £+ y sin £ + z cos £ 



o,o„ = vibration in o>'„ + that in e\e\ 



= -kx sin £ + kw cos f + j sin £ — f cos P. 



it k 



Comparing the coefficients of sin £ and cos f, 



\-V 



COS a + (p = w +y, 

 k sin a + <f> = x + z, 



k" sin a + ^>= -kx + - 

 -It COS 7+0 = /{-m; -|, 

 ra. IV. /W I. 



whence * 



■IV = _^ cc .Sa + 0, 



A(l-iP) . 



X = ,„ sin a + 0. 



2F 



y = I+ ^ cos n + 9' 



2k 



rr sin a + 0. 



I +k r 



