320 PROFESSOR KELLAND ON THE THEORETICAL INVESTIGATION OF 



r> , 7 - , ,. /ON /"" COS X d X IT . ,. 2/ V 1 



Put a = J-ly,q=Im(2).: _ , - (J-ly + I)e 



* 00 x sin x d x IT 

 Put = V-l^=l 



so that we get 



4a a c a A a 6 8 sinacosa/' c J f 1 1 . 2 !T +ta 



w = - = - / dy \ fr- , + - sin y + <717i lv y+ l; cos y 



TrD 2 ,/-! / I 2y 3 2>* "f 



_ 2 a 2 c 2 \ 2 d? sin a cos a r<*> r cos 2 y 1 1 



- -5- sin y (cos y - J~^T sin y ) j- 



^ 



_ 2 a 2 c 2 X 2 ft 2 sin a cos a /"* f J. _ siny cosy"! 

 From (1), by putting y=0, a=0, we gety o ^= ^, =0 . y o -f = ~ 



r x sin y cosy dy 1 f sin 2 y , P* sin x , 



Also / = o / ~dy=2 I r rf, 



o/ y 3 2^/0 y 3 J o x* 



/OO 0t 



L- ^ ^ rf^r= ^ - from (3.), q being equal to 1, 



and a to 0. 



TJ /^ /^y ^^ siny cosy\ 7T/1 e a \ tr . n 



Hence / I a- -*- - =:prl = since a = 0. 



/ VJr y 3 / 2 \ a a / 2 



a 2 c 2 \ 2 6 2 sin a cos a X 2 6 s 

 .. M = - =rg - = ^2- x a 15 x r sm a cos a 



X 2 & 

 = p2 x a 2 x area of aperture. 



Now it ought to be a 2 x area of aperture 



.-. D = \b. 

 Remark. The intensity at the point p, q is expressed by 



( sin * " ~y sin 



But this is not the problem as it is most frequently presented to us. We must 

 therefore solve another case. 



