Double Refraction of Quartz. 91 



intensity of light on all the different parts of the screen. It 

 will be remarked that 6 is very nearly proportional to the radius 

 vector of the corresponding point on the screen, and the angle 

 measured from the lower part towards the right. 



If the eye be placed to receive the light coming from dif- 

 ferent parts of the analyzing plate, the appearance will be re- 

 versed with regard to right and left, and here the angle must 

 be measured from the lower point towards the left. 



1 st . Let the plates be crossed, or a = 90°: 



cos 2. a + = —cos 20: sin 2 .a + <p= — sin 20: 

 and the intensity is 



— . sin 2 20.snr — — : 

 2 Y \ 



or putting for its value, the intensity is 



TV a--¥ 



-.sm-20.sin-(— .-&-*). 



This is 0, or there is darkness, if = 0, or = 90", or =180", or = 270", 

 whatever be the value of 8. This shews that there is a black cross 

 through the center, parallel and perpendicular to the plane of reflection 

 Also there is darkness whatever be the value of 0, if 



TV a'-b"- ^ 



or lf e=0 > = gv-ay = TW^)' &c - 



This shews that there is a dark spot at the center, and a succession 

 of dark rings, of which the difference between the radii diminishes con- 

 tinually. Caeteris paribus, the squares of the diameters of these rings are 



inversely as — ^ — , or are least in the crystal where the double refrac- 



m2 



