042 H. NAGA0KA; DIFFRACTION PHENOMENA 



Writing the integral in the form given by the above process of 



reduction, we obtain 



o(2a — d) \ dz 



-I," nearly. 



~ 2«s/a(a—d) 

 where 





V-v-r-ô- 



When the point is external to the circle 



_/,=^ JL— + I* 



s - 2</a(ar—d) s 

 Gauss's method of mechanical quadrature seems specially suited for 

 calculating the two integrals 1/ and I". Assuming n=3 in the usual 

 formula, the error of approximation will in the present case scarcely 

 affect the fourth decimal place. The course of // and /," is shown in 

 Fig's 3 and 4 (Plate XYI & XVII). If greater accuracy be desired, 

 we must assume the values of n greater than 3 ; to facilitate the calcu- 

 lation, I have calculated a table* (see Appendix) of Jô\x) + J 1 -(x) for 

 values of x ranging from to 3.83. The table gives, as was already 

 noticed, the intensity at the centre of a circular image, whose radius is 

 x, if the number given in the table be subtracted from 1. 



* For the construction of the table, I am indebted to Mr. S. Miyazaki ; the following errors 

 were noticed in Meissel's 'Tafel der Bessel'schen Functionen.' 



A;=0.62 J (k) = 0.9061843 instead of 0.9051813 



%»- 1.71 7 (Ä) = 0.3922044 „ „ 3932044 



Ä=1.89 J (Ä;) = 0.2876313 „ „ 0.2866313 



The value of e7" (1.7l) was corrected by Meissel, as reprinted in Gray-Matthew's 

 ' Treatise on Bessel Functions.' 



