ON LINES OF EQUAL INTENSITY. ]_ ]_ 



. . sin a x , sin By , -, , . r 



Assuming' ^ = , */> = — ' , the lines ot zero 



ty 



intensity are given by 



?M TT n TT 



ß 



where m, n are integers. 



The curves of equal intensity are hyperbolas — 



£ f) = ± &• m w. 



The semi-axes of the hyperbolas are proportional to */mn. The 

 curve of equal intensity consequently recedes from the line of zero 

 intensity, when either m or n is increased, and at a still greater rate 

 as m and n are simultaneously increased. Thus the bright part 

 mostly extends along the sides of the rectangle, but very little along 

 the diagonals. 



Two circular apertures. — The intensity of the diffracted ray is 

 given by 



J l {ar) 



I = \ar) C08 /9 ' 



where /' = V x 2 + y 2 , when the axis of x is taken parallel to the line 

 joining the centres. 



We have here to put 



w = , ti = cos 3 x . 



T a r 



Making" use of the relation 



J2(ar)= —J x {ar)-J*{ar), 

 a r 



