Double Refraction of Quartz. 95 



The intensity, or the sum of the squares of these coefficients, is 

 (after reduction) 



c 



- {1+ cos 2/3. cos 20. cos 2./3+a + 



2tt 



+ cos — 0. cos 2/3. sin 20. sin 2./3 + a + — sin — .sin 2/3 . sin 20j. 



A A 



Now if /3 = 45°, cos 2/3 = 0; sin 2/3 = 1; 



and the intensity = — < 1 — sin — e . sin 2 i . 



1 st . Since a has disappeared from this expression, the figure will be 

 the same whatever be the value of a, that is, whatever be the position 

 of the analyzing plate. 



2 nd . When = 0, =90°, = 180°, = 270°, the expression becomes °- 



which shews that there is a faint cross parallel and perpendicular to the 

 plane of reflexion at the analyzing plate. 



3 Id . When is >0<90°, or > 180° < 270°, the intensity is greatest 



if -t-©=-^-, — , &c. and least if — = — , — , &c. When is 



A a 2 A 2 2 



>90°<180°, or >270°<360°, the intensity is least if ~Q= — , — , & c . 



A 2 2 



and greatest if — = - , — - , &c. 



4 th . If /3=135°, the expression becomes 



— < 1 + sin — - . sin 2 <h\ : 

 2 ( a ) 



from which it is easily seen that the bright parts of the quadrantal rings 

 in this case correspond to the faint ones when /3 = 45°: and vice versa. 



III. If in the last experiment the rhomb be placed in posi- 

 tion 0, we must make /3 = 0, which gives for the intensity 



C ( 2tt . . ) 



— <l + cos 20. cos 2 .a + cp+ cos — 0. sm 2 0. sin 2. a + (/>>, 



exactly as in the general case of experiment I. 



