332 



H. NAGAOKA ; DIFFRACTION PHENOMENA 



limiting angles of the zones, instead of taking some other proper value 

 of « n , which will exactly give the illumination due to the zone con- 

 sidered. 



The correction is calculated in the following way. Let r x = A 

 and r., = B represent the radii of the circles bounding a zone; 

 consider the outer edge AB of the zone to be straight, and that 

 we have for the effect of the zone the expression -^{Jô 2 (>'•_<) + J r 2 0'i)} 

 where & is the angle subtended at the 

 given point by a circular arc described 



with radius l =r , and înclnd- 



A 



ed between the edges of the zone. 

 The correction to be applied in 

 the above expression is evidently the 

 difference in the illumination due to 

 AEM and BDM. Writing this 1\ and 

 J'., , we have 



nJ a Jr -° r 

 d = r tg a . d- , 



f f 



r oß= " t , tg a. 



Fig. I. 



where 



'•-4-/T 



ß/r +S J2(r) 



dr dd- 



Similary 

 whence we obtain 



I\ ~ I\ = ^f fc(r + o) + Jî 2 (r + 3) + JJ{r-d) + J? (r ü -5)-2.7 s (r i )-2«/- 1 s (r ) | dd 

 = ^/\ _.+y, -%>•„ Ida 



£~'o » (>o+o) (ro-ô) i 



Expanding the expression within the parenthesis, we obtain 

 where b=r tga. 



