96 Professor Airy on the 



If the rhomb be in position 90°, the expression is exactly 

 the same. 



If the analyzing and polarising plates be crossed, we must 

 make a = 90°, and the general expression becomes 



e 



{1 —cos 2/3. cos 20. cos 2 . /3 + 



m 

 2tT 27T 



— cos—- G. cos 2/3. sin 20. sin 2./3 + — sin —©.sin 2/3. sin 20} . 



A A 



Here if = 0, =90°, =180°, =270°, the intensity is -sin 2 2/3, 



which shews that there is a faint cross parallel and perpendi- 

 cular to the plane of reflection. For other values of the only 

 variable part is comprehended in the two last terms or 



- - sin 20. {sin 2/3. sin -~9+ cos 2/3 . sin 2 . /3 + <j> . cos-r^ Q\. 



'2_7T. 



\ 

 where 



tan 2/3 



This may be put under the form ^4 cos (-^0-2?), 



A--— sin 20 x/shr 2/3 + cos" 2/3. sin" 2./3 + 0, and tan 2?= — 



2 r- ■ ■ -r sin 2 . /3 + 



The equation to the dark rings will be found by making 



~Q-J3 = 0, or = 2tt, or = 4ir, &c; 



A 



, ^ \B \B \B . 



hence = — - , or = X + tt— 5 or = 2\ + -— , &c. 



27T 27T 27T 



Now when /3 is small, sin 2./3 + being positive, tan 2/3 is small, 

 and tan B is small: except sin2./3 + is small, when B sud- 



