266 Prof. G. F. FitzGerald on the 



light. I will take the simple case of a slit bounded by obstacles 

 which completely stop all action. Although such do not 

 exist, very close approximations to them do exist. 



If we take the slit as parallel to z, and make this axis the 

 centre of the slit, and assume the phase the same all over the 

 slit, we have for the vector potential at a point z , y , 0, due 

 to any line of the slit at a distance y. from its centre, 



Jo T 



where 



r 2 = t i' 2 + 2/o-j/ 2 H-^. 



integrating this for the width of the slit, i. e. from + b to 

 — b, we get for the complete value of the vector potential 



H = 2H f +6 [ m 2™J*EEdzto. 



J~bJo r 



When we are dealing with the case of b being a small 

 quantity we may take 



y° spt - qr dy=m-y) 



and we have 



+ b 



I 



cos pt — or 7 . ,. 7N 



,, dy =j(y + b) -/(z/o - &) 



But 



-2b( df \ 1 2b * ( d *A + 



and when y = is put in 



fdf\ __ cos (pt — gr) _ 

 \dyJo ~ r 



t 



— v 2 j_ », 2 I ~2 J2 j_ ^2 



If we now integrate with respect to z we get 



Now \ udz is a function of p only, and is a Bessel func- 

 Jfl 



