100 Professor Airy on the 



Now when the light is received on the analyzing plate, the 

 only parts sensible are those perpendicular to its plane of re- 

 flexion. They are, (putting £ as before for -^-(vt-x)), 



A 



From Oo„ cosa + 0.cos0.sin£+£.sina + 0.cos<£.eos£. 



From o^,, #\sina + 0.sin0.sin£ — £ . cos a + <£ . sin <£ . cos £. 



2tt9 ,. • — — i __. r , 2x0 



From Ee„ k". cos a + <p . cos <p . sin jf h — ^— . — k . sin a + <f> . cos (/> . cos £ + 



X X 



2irO , 7 . — — -. ■ . y , 2tt9 



From e r e s , sin a + <p . sin (p . sin £ + + A . cos a + <p . sin $ . cos £ + 



X X 



Taking the sum, the coefficient of sin £ is 



2?rQ 



cos a + cp . cos <p + /r. sin a + <£ . sin <p + k 1 . cos a + . cos <p . cos — — 



X 



, . . 2ir9 . . , 2tt9 



+ k . sin a . sin — \- sin a + <£ . sin <p . cos - 



The coefficient of cos £ is 



SttG 7 . 2x9 . . . , . 2x9 



k sin a + A", cos a + <p . cos . sin — k sin a . cos — — \- sin a + . sin (f> . sin 



The sum of the squares of the coefficients is (after all re- 

 ductions) 



. ir9V 

 + '2 k . sin a . 

 X V X 



(1 - k°y. cos 4 a + 2<p . sin 2 ^— + U + k\ cos a . cos^— + 2 A . sin a . sin ~ J 



And restoring the multiplier , , we have for the brightness 



,/1-ifcV , — . „T0 ,/ xG 2Ar , 7r9\- 



ci- — ™j .cos .a + 2$.sin — + cl COS a. cos— + ■— -jo sin a . sin — I . 



