:;34 



H. XAGAOKA; DIFFRACTION PHENOMENA 



71 'a ./o ... 



■dr cW 



= 2 f* a j; 2 {r) _ _ i 

 [ntegrating by parts, 



~ 2 7T / V 4rt 3 — r' J 



= / "^ V ; -c^rc cos-j — . $/• 



JT ,/ (?•) 2a 



J= J L / ** JM + Jflr) ^ 



The above integral shows that the intensity at the rim ap- 

 proaches -p- as the radius of the disc is indefinitely increased. 



We have already seen how J" 2 (r) + J"f(r) can be expanded in 

 ascending powers of r as well as in a semi-convergent series. For 

 values of r smaller than x n we can not use the last mentioned 

 series, while for values of r somewhat greater than .*-,, it is dis- 

 advantageous to use the former series. We shall therefore have 

 to divide the integral into two parts : namely, one extending from to 

 x v for which the expansion in ascending powers of? 1 should be used ; 

 and the other from x x to 2«, for which the semi-convergent series 

 should be employed. 



It is to be noticed that the variation of J' 2 (r)+J' 1 3 (r) is very small 

 in the neighbourhood of r=x v so that it would be advantageous to 

 assume the limit of integration at r=x v in order to diminish the error 

 in integration. 



Thus, 



~./o \ / \/4 a r 



2 7Z 2a /o «,/éa-- r n I t \ / ^/W—r 



