264 Mr Mayall, On the Diffraction Pattern [Feb. 22, 



and the intensity of light at points of the image close to the 

 geometrical boundary is given by 



={ i -^( i - p -4 + { 1 4^( p -< 



-M*) 



(1 — P — Q)\ cos/jz— - — — (P — Q) sin /xz 



4 v ' k ) 4 sj k 



This may be still further simplified, for (1 + /c)/4 sJk differs from ^ 

 by y 1 ^ (1 — ' k)- when k is nearly equal to unity, and the error in 

 h 2 M 2 produced by putting k = I in the squared terms is 



^(1-«)*(2P* + 2Q*-1) 



or about ^ (1 — k) 2 at the greatest, while the error in the Jo (z) 



i t i p i 1 (1 — k;) 2 

 term would be ot order —= . - — ., „ . 

 \lz 16 



We have then M 2 = M? + e, 



where h 2 M 2 = H(l + P + Q) 2 + (P - Qf] 



and S 2 e = — \ J (z) [(1 + P + Q) cos yu,2 — (P — Q) sin /xz]. 



It appears from this that the variation in the intensity of illumi- 

 nation consists of two parts, one of which M^ represents all the 

 main features in the variation, the other being a small correction 

 of irregular form to be applied to it. 



For points outside the geometrical boundary, M 2 takes a 

 different form. Here k > 1 and 



z . 



1 f 77 . /cos ay cos 2&) \ , 



= - e «cos» _ _ + -—+... )dt 



7rJo \ K K- J 



If 77 . K COS ft) — 1 



QlZ COS fc> 



TV J o 1 — 2/£ COS ft) + « 2 



(- 



glZCOSfc) ^ + 



27r J o V 1 — 2/e cos to + k 2 . 



1 r , , r-1 f f .... d&> 



2 " 27r ./ o 1 — 2/c cos &) + « 2 ' 



