ivith special reference to Coronce and Iridescent Clouds. 273 



cides with that of the aperture. The side a is at right angles 



to the incident light. In fig. 1 



only a quarter of the aperture Fig. 1. 



is represented. * 



is the origin of coordi- 

 nates ; the axis of z is drawn 

 towards the source of light, 

 while the axis of x is parallel 

 to the side a of the aperture. 



F(xyz) is a point in the 

 aperture. 



M(f 7] JJ) a point on the sphe- 

 rical screen. 



The source of light is small 

 and very distant. 



Let the vibration at be 

 represented by cos xvt, where 

 t is the time, v the velocity, 

 and k = 2it/\. The intensity 

 is then unity. The vibration 

 at P is cos k (vt + z). 



We now break up the primary wave into its secondary 

 components over the plane of the aperture, which is not a 

 wave-front. The disturbance at M due to the element dx dy 



at Pis 



dxdy . . .„ 



(I) 



where p = MP. 



Now 



?=(m-t? + {8-if +[?-%?> and P + *" + P-/** 



xyz are small compared with f^f; so, neglecting their 

 squares, we have 



P *=f-2x%-2y V -2z$. 



In the last term we can put £= — /, and obtain 



p=*+/(i-£+®). 



/• 



In the denominator of (1) we may write p=f- So the vibra- 

 tion at M is 



- i JJsin « (* -/ + 5I+2S) dx dy, 



the limits of x and ?/ being ± - and + — 5— - respectively. 



* Encyc. Brit, art. " Wave Theory of Light," p. 429. 



