with special reference to Coronce and Iridescent Clouds. 277 



line and the diffracting aperture a parallel slit, for the blurring 

 is of the same nature as that involved in the transition from 

 (2) to (5). 



Diagonals of Square Aperture. 



Before giving the accurate expression for the illumination 

 when the diffracting aperture is circular, it will be instructive 

 to examine a case which presents 

 the same peculiarities in an exag- 

 gerated form. The main difference 

 between a circle and a square, as 

 regards diffraction in directions 

 parallel to the sides of the square, 

 is that in the former the outlying 

 portions, where the phase-differ- 

 ence is greatest, are relatively 

 small. This feature is still more 

 marked in diffraction by a square 

 parallel to its diagonals (see fig. 2), 

 and this is a case we have inci- 

 dentally solved. 



Let c be the diagonal of the square, and £ the distance of 

 the point on the screen from the centre of the figure in a direc- 

 tion parallel to the diagonal. Then, putting 7=73-/2 in (2), 

 we obtain 



4f 2 X 2 



1 = 



(8) 



The dark points are given by c$=2mf\, where m is any 

 integer other than zero ; and in general corresponding points 

 are twice as far out as in directions parallel to the sides of a 

 square of side c. As we have already seen, the diminution of 

 brightness is much more rapid, and the colours, when sunlight 

 is used, are purer. 



Circular Aperture. 

 The expression corresponding to (2) for a circular aperture 



18 TT^R 2 4^(2) * 



A 2 / 2 £ 2 



1= 



(9) 



where z=2ir-Rr/f\; 



R. is the radius of the aperture, and r the distance on the 

 screen from the centre of the diffraction-figure. The dark 



* 'Wave Theory/ p. 432. 



