120 Prof. S. Bauerji on the Radiation of Light 



from an actual experiment. The data were : 



U = -94 mm., / = 272 mm., H x = 1'72 mm., 

 P 2 = 2-61 mm., X = '00045 mm. 



We thus obtain for this case 

 I = ^[{^^67(l-|)- S i80-84(l-|)} 



-{Ci 122-67 (l + |)-0i 80-84(l + |)} 



t\( ) + &C.] • 



The values of this expression for different values of fity 

 are shown in Table II., in which the calculated and the 

 •observed values of the ratio fy'jty at which the illumination 

 is a maximum or a minimum are given for comparison. It 

 will be seen from the table that <s/l changes sign at the 

 minima, and these are therefore absolute zeros. The values 

 for I shown in Table II. have been plotted in fig. 2. It will 

 be seen from Tables I. and II. that ^/l changes sign as 

 it passes through its values at the boundary </>'/^=l, 

 showing that the radiations from the edge on the two sides 

 of the boundary differ in phase by ir. 



The investigation given above may be modified to suit the 

 case in which we have one or more slits (instead of an 

 annulus) in the focal plane by suitably altering the limits of 

 integration in the expression (5) given above. The writer 

 hopes to give the detailed numerical calculations in a later 

 paper. It is possible, however, to understand in a general 

 way the reason for the peculiar configuration of the fringes 

 shown in PI. III. figs. 6, 12, & 15. If instead of a 

 slit we have in the focal plane a small aperture at (V, 6') 

 through which the boundary is viewed, the luminosity of 

 the latter appears confined to certain regions lying in the 

 neighbourhood of the two points r = R, 6 = 6 r , and — 7r-\-0', 

 and which are more or less well-defined according to the 

 size and the position of the aperture. The further the 

 aperture is from the centre of the focal plane, the feebler is 

 the luminosity observed through it. Accordingly, if we 

 regard the horizontal slit placed in the focal plane as 

 consisting of a number of elements along its length, the 

 vanishing of the luminosity of the boundary at the ends of a 

 horizontal diameter is seen to follow as a consequence. At 



