106 PROFESSOR AIRY ON THE CALCULATION OF 



the point p, q, of the aperture. For the effect of the wave spreading 

 from the small rectangle whose sides are ip, ^q, we must multiply by 

 ^p, Sq. Hence we find that the quantity to be integrated is 



where, after integrating with respect to q, the limits of q must be ex- 

 pressed in terms of p before the next integration. 



Puttmg A' + a' + b'+ ^ ^ = B', this expression becomes 



The first integral is 



27r 



sm 



-COS - {..-2? - ^— (p _ _^) J /^ sm {2 .-^r^ (? - ^) } 

 /tt 2(«'+ft')/ «y^'l , TT / ./2{a'+b') ,^/ 2m:' y 



which between the limits q = r}-irnp, q — Q-^np, is proportional to 



^1 ^ «7yx ^ ^ i' («' + *') x^ «'*'x J 



The quantity proportional to .4 sin j^.i^lt*} L _ 4^) | will be ex- 

 pressed in the same manner, putting >// in the place of 0. 



The whole displacement of ether at the point x', y', will therefore 

 be found to be 



