Interference Methods to Astronomical Measurements. 11 



l = Q + iQAcos ^(#— 7 &)+iQAcos^(#'-7& + 2#0 



or 



I = Q + QA(cos y [P s + ^ "^ cos X ^ ) ; 

 whence for the visibility 



(13) 



or finally 



V= T i T ^=Acos —/3s. 



ll + J.2 A. 



V = A COS 7T — . 



«0 



(14) 



1st. When the sources are two equal uniformly illuminated 

 slits of height 2h, 



f{w) = h, and Q = Mi. 



Hence 



-£ 



27T/3 



cos -r 1 w aw = 



A. Z7T 



. 27T. 



sin — jo?' 



A, 



. . . . (15) 



T* 



Putting — -/3? j = 7r— , and substituting for A in equation (14), 

 A, a 



S1U7T 



V 



7T 



COS 7T 



(16) 



«o 



2nd. For the case of two equal uniformly illuminated 

 circular apertures of radius r, 



Hence 



f (w)= \/r 2 —w 2 , and Q = tjt 2 

 2tt 



4 /**■ 



A =— 1 y/r*- 



w 2 cos -^-fiwdw. 



Putting — =£, this reduces to the form already given for 

 Airy's integral, and the expression for the visibility of the 



V = A 1 C0S7T- (17) 



fringes i 



