122 Prof. S. Banerji on the Radiation of Light 



and near these points also the radial width of the luminosity 

 should obviously be the least, as the latter is, roughly 

 speaking, in inverse proportion to the corresponding radial 

 width of the aperture in the focal plane. This gives us 

 a qualitative explanation of the lunette-shaped form of the 

 fringes in these cases. Figs. 5, 8, 11, & 14 in PL III. 

 illustrate the remarks made above regarding the localization 

 of the luminosity of the boundary observed in certain cases. 

 Fig. 5 represents the effect observed when there were two 

 small circular apertures in the focal plane not lying on the 

 same radius vector. Accordingly we have on the boundary 

 four separate regions of luminosityc Fig. 8 represents a 

 photograph obtained when a ring of six circular holes was 

 placed symmetrically in the focal plane. Each of the six 

 spots seen along the boundary is crossed by very fine 

 fringes, due to the interference of the effects produced 

 by the pair of apertures at the end of each diameter. 

 Fig. 11 was obtained when the ring of holes was slightly 

 displaced in the focal plane. Twelve spots appear on the 

 boundary. Fig. 11 represents the effect observed when 

 the screen in the focal plane was so placed that two out 

 of the three pairs of apertures fell on lines passing through 

 the centre of the field. Accordingly only eight spots arc 

 seen, the four larger ones being crossed by fine interference 

 fringes. 



3. Case of the Rectangular Boundary. 



It has been shown by Lord Hayleigh* that when an 

 optical surface bounded by parallel straight edges and 

 illuminated by a linear source of light is examined by 

 the " knife-edge " test, the intensity of the field as viewed 

 in the direction <f> is given by 



I= [si{^OH-*)&}-5i{^(0 + *)£ l } 



+ Si{^(0-<^ -Si (^ (£-,£)£ jj 



+ [ Ci { T ( ^ )?2 } _Ci {? (*"*)&} 



where 6 is the angular semi-aperture of the lens, fi denotes 



* Log. cit. 



