2 H. NAGAOKA. 



the coordinates of homologous points by ,i l} b , a, 6„ , a n _, &„_„ the 



expression for the intensity becomes 



(A) r=r?S •'*"■*'" Y- 



*- o -' 



where 



which, integrated over any owe of the openings, has always the same 

 absolute value. 



Introducing polar coordinates r m &. m , we can write 



fi ci m +vb m =r r m cos (#,„ - d) , 

 provided 



T=V/r+S , tgd= —. 

 The expression (A) is thus transformed into 



(B) i=r ¥ %e i >"~°°'i>"- s) y 



*— o ~ ' 



In (A) and (£>), the expression under the sign of summation 

 depends on the relative position of the openings only, while (<p) will 

 be known when the form and size of the opening is given. 



I shall here treat of a special case of summation, whereby 



r m = const., & m —ma and na = 2~. 

 Writing yr at = c, Ave easily find by expansion 



1) g* e lccos{ma ~ ô) = n J°(c)-i n . 2n(cos()id)J n (c) + cos(2nd)J? n (c)+ J 



o 



when n is even ; 



