18 ART. .1. ATCIII AND TANAKADATP: : THEORY OF 



larger and the pei-iû(l_of sin^ ä -z^^/zö) is prolonged; in the limit- 

 ing case 0=0, ^I^Ht^J^ IiJL) becomes equal to ~ .-, as ex- 

 pected. Also for smaller values of x, i.e. of r, the same reason- 

 ing will hold true. Thus for large values of '!> and r, the differ- 

 ence of the two cases becomes manifest. 

 From this approximate expression, 



F=- 



3 



,siir2r(^Y'sif,(-,/3-x<D-,/^) 



it follows that F does not increase at maxima to 2 x (mean term), 

 but only to (mean ^erm + v^-^^^^^J ; and at minima it does not 



diminish to zero, but only to (mean term — .^ .^^^^^^ j ; moreover, 

 for values of ll for which ^'i^'{^''ïî^x'^^/xö)<0, the maxima of 

 sin2^-^p changes to minima and the minima to maxima. 

 Finally, the expression for the intensity being 



9" 



r(^)=ci)n.st.( -^-j /-(//^) for point source, 



I(/9,<I>)=con8t.f -^^j F(x,^,y.d) for circular source; 



it follows, first, that for larger values of ^i), the difference of i(d) 

 and I(^, <I^) becomes larger; secondly, that for larger values of r, 

 the difference of maximum and minimum values of i{6) becomes 

 larger in virtue of r:5, but for I(/^, (I>) at the same time it is 

 diminished by the presence of F. 



7. Case of the cylinder and slit. 



We shall now treat the case which has often been tested 

 by experiment with the glass rod, and straight slit as the source 

 of light. In this case, if we neglect the breadth of the slit, 



