Interference Methods to Astronomical Measurements. 3 



when the disappearance depends on the existence of well- 

 marked minima of distinctness ; and, as will appear below, it is 

 possible to measure, with accuracy, by the observation of these 

 minima the width of a source of light, which in a telescope 

 can with difficulty be ascertained to have an appreciable size. 



The theory of these successive appearances and disappear- 

 ances is as follows: — 



Returning to fig. 1, let x be the distance of any element of 

 the source from the axis of the telescope, dx the width of the 

 element, and y = (f>(x) the length. 



Then the difference in the two paths #S and ^SjP terminating 

 at the wave-front P, which makes an angle 7 with the plane 

 perpendicular to the axis of the telescope, will be fix — 76, and 

 the resulting intensity in the direction 7 for the whole source 

 will therefore be 



I=$cl>(x)[l + cos '^(f3v-yb)]dx. . . . (1) 



f 



Case I. — Uniformly Illuminated Slit. 



If the source be a slit whose centre is in the axis, and whose 

 length is parallel to the slits SS l5 and whose width is a, then 



T \ . 7J-/3 27T7 7 /aN 



l=a-| — 5 sm— acos ^— -0 (2) 



7Tp A, A, 



If I x be the intensity at the centre of a bright fringe, and I 2 

 that at the centre of a dark fringe, then the visibility of the 

 fringes may be expressed by 



v =Aw (3) 



X . 7T/3 



h = a-\ ^sm — a, 



7Tp A, 



T A. . tt£ 

 l 2 = a -5 sin —-a; 



7TJ3 \ 



. 7T/3 



sm — a 



But 



7T/3 



B2 



