H. XAGAOKA. 



following distribution of equal, similar, and similarly situated openings 

 can be reduced to the form 



(C) r=«s(j»y (iff, 



when the above mentioned conditions are satisfied. 



In the following three cases, we can bring the expression for the 

 intensity of diffracted light into form (C). 



I. Suppose the homologous points of n openings are arranged in 

 a straight line such that their coordinates are given by 



a m = a cos (m a — ß) , b m = o. 



with the condition na = 2~. Such distribution is well illustrated by 

 the usual diagrams of the condensation and rarefaction wave, but it is 

 to be remarked that in the condensed part the neighbouring openings 

 must not overlap each other. The intensity of the diffracted light is 

 evidently given by (A) and (C) 



Vi i/«cos(wa-j5)"l 



If ß=o and n be an even number, every two of the openings 

 overlap each other with the exception of the o-tli and the -^-th; if n 

 be an odd number, with the exception of the o-tli, the expression must 

 be slightly changed. 



The diffraction-figure will consist of straight lines perpendicular 

 to the line joining the homologous points. 



II. The openings are distributed on the periphery of a circle of 

 radius a at equal angular intervals, so that 



a m = a cos (m a — ß) , b m = a sin {m a — ß). 



