324 H - NAGAOKA; DIFFRACTION PHENOMENA 



If the luminous source be an infinitely large plane, 



since J" (0)=1, J\(0)=0, J (*)=0, ,T 1 (cc)=0. 



We shall henceforth assume the intensity for an infinite plane 

 to be unity, as is done by other writers ; thus 



and 



I= iffmn drdl) (i) 



Denoting the limits of integration with respect to r by r and r 15 

 which are generally functions of 0, we obtain 



I ^/WrJ + JM-JoKrJ-JAr^dd _ (II) 



At the centre of a circular image, of radius r, the above expression 

 reduces to 



I = l-Jo\r)-Jft) , (II.) 



and at the vertex of a circular sector including angle a to 



I = ~\l-J^r)-JAr)\ _ (II.) 



§ 2. Curve y=J*(x)+J?{x) 

 Before entérine- into further discussion it will be worth while to 



o 



examine the term J 2 (r) + J*(r) which enters into the expression for 

 the intensity of the diffracted light. 



Although the values of J -(r) and j;\r) are in themselves oscil- 

 lating, the sum of these two functions presents a remarkable aspect, as 

 will be easily seen by representing it as a curve 

 y=J \x)+J l \x) . 

 In the first place, y cannot be negative, so that the curve is confined 

 to the positive part of the ordinate ; in the second place the relation 

 J a {x)+2J l \z)+2J a \x) + 2J % \x)+ =1 



