by Apertures with Curvilinear Boundaries. 295 



is in the XY plane, and the projection of SP (S being the 

 source and P the point at which the effect is sought) on 

 the plane of the aperture is the X axis, the origin lying 

 on SP and in the plane of the screen. 



-Fiar. 2. 



Let p Y and p be the distances of S and P from the origin, 

 (x, y) the coordinates of an elementary portion of the strip 

 (which is taken parallel to the x axis), i\ and r the distances 

 ot Sand P respectively from (x,y), and x\y' the coordinates 

 of n l . The effect S at P due to the whole strip may be 

 written 



Q A ' f cos (nr) — cos(W.) . ' (t r-\-r x \, 



ko = ^r \ sin 2tt rT , -— )da, 



2?vjv rr Y \1 X / 



where A is the amplitude of light disturbance at unit 

 distance from S, (nr) and (nri) are the angles which the 

 normal at (#, y) makes with r and o\ respectively. In this 

 equation we can take the quantities r i^ as constant when- 

 ever they are not divided by X, because a limited region of 

 integration near )i 1 is determinative of the intensity at P, 



