456 Mr. L. N. Gr. Filon on certain Diffraction Fringes 

 all over the range of integration, whence 

 29A2P7.2 



b 2 X- 

 32A 2 M 



b 2 \ 2 



/~ X.iraq f ±-nav 7 . krraq ( . 47r<2w . \ 



where fl = total area of the image, 



R cos c£ = 1 u cos — yr- - rfw, Rsin ^> = tw sin . dv, 



the integrals being taken all over the image. The visibility 

 = R/fl and therefore vanishes when R vanishes. 

 In the case of a circular source we find 



<£ = 0, R = (some non-vanishing factor), J } I— — V 



where Ji is the Bessel's function of order unity and r is the 

 radius of the image, so that rjb is the angular radius of the 

 source. The dark fringes are given by 



q being measured from the centre of the source. The fringes 

 are parallel to the slits and disappear whenever 



This result agrees with the one given by Michelson for 

 any circular source. We see that it only holds provided 

 the dimensions of the source do not exceed a certain 

 limit. 



In the case of an elliptic source </> = also, and R is not 

 altered by any sliding of the image parallel to the direction 

 of the slits. Hence we may replace the oblique ellipse by 

 one having its principal axis parallel and perpendicular to the 

 slits, the values of the semi-axes being d and txr, where d — 

 length of semi-diameter of original image parallel to the slits, 

 tff = length of perpendicular from the centre upon the parallel 

 tangent. We find without difficulty : 



