92 Lord Rayleigh on Pin-hole Photography. 



he finds in the first place 



C = ^ 2 (^ siniy 1 . m ^ 



where 



B -^{*fi«u l -i?i«u i } l . . . (id 



u 1 =!j 1 (^)-^j 3 ( 2 )+^j 5 w-..., . . (12) 



2 N a" 



,4 



u,= £j,M- J •»*(*) + (13) 



These series are convenient when y is less than z. 

 The second set of expressions are 



9 f2 . z 2 , sini?/ TT cos4y TT "1 ,., J% 



ly 2y J# iy J ' 



2 f2 z 2 cos-|y Tr sin^?y Tr \ ,• . 



= 7rrH -cos-> ^^o r^ V i k . . (15) 



where 



Vo=JoW-Jj^) + pJ^)--., • • (16) 



Vi-JJi(«)-pJ/*) + 07) 



These series are suitable when z/y is small. 



When the primary wave is complete, r = co , and we have 

 at once from the second set of expressions 



n 2tt . Z 2 Q 2tt Z 2 



so that 



j 2 = Cl+S a L_ ( 



a 2 b 2 \ 2 (a + b)*' ' ' • ' ^ iJ; 



as we know it should be. 



At the central point of the image where z = 0, V = 1, Vj = 0, 



and 



~ 9 smiy 2 j2 cosjyl 



