320 H. NAGAOKA. 



C= —j^lcos {^T xy- d (\/ ? x), S = lain (^T x)- d {^T x). 



The second iuteural is intei'TaljIe : thus, 



= j' + i a. 



Introducing the expressions ( 3 ) (4) (5) (0) in ( 1' ), we lind inr 

 the intensity, 



/ = Mod- a (C + i S) {K +i L) + i2 a '/ : {y +i^)\ [K + i L) - f / '+ 1 2') [ . 



In hndin,u" Mod.'-, we can neglect tlie terms in\<)Iving />"'. 

 J'husj we get for the expression of the intensity 



(7) I ^ir^[C- + S-}{K'+ L-) + iafl^\C[Pr-Qr7) + S{(Jy + Pn)l'l^. 



where 



r - A' 1' - L 1 \ 



(J = K [K - /') + 7. (L - 2'). 



Tlie expression f<jr the intensity of light dittVacted hv a A\l on a 

 circular cylinder ditfers from that for the ])lane slit hy the intro(hiction 

 of the fictor K- + L-, and a small athlitional term multiplied Ijy ''K 

 lîoth K and L remain constant proyided the distances of the slit from 

 the source of hght and the point at Avhich the intensity is recpiired do 

 not change. If we observe the fringes in a plane parallel to the axis 

 of the cylinder, /v and L will remain scnsihly constant. Aeglecting 

 the term multiplied hy '''', the positions of maxima and minima wiJl 

 be the same :is those pnxbiccd l)y ])lane slit of the same l)readth. 



If the observer approaches or recedes from tlie sht, the intensity 

 of light at u point directly opposite the slit will differ from that of 

 the plane slit, for the intensity is affected Ijy the fictor K- + L'\ wliich 

 is ijo lonu'er constant. 



