104 



PROFESSOR AIRY ON THE CALCULATION OF 



The whole displacement at the point w will therefore be 



sm — 



{yi-A-a)x{ (p(iB\/^-w\/^]-<p(a\/%-w\/-^]] 

 ' I ^V aX aXJ ^\ aX aXl j 



2ir f / 



+ cos —— (yt — A — a) X < - \l/ [j3 



aX 



— w 



aXJ ^ \ aX aXl ] 



Suppose now this displacement to be the origin of a small wave 

 which diverges from it as a center. The distance of the point w of 

 the slit from the point x of the screen is 



^{¥ + {w-xY]=h^^{w-x)\ 



and this distance must be added to ^ + a in the expressions 



sin -^{yt-A-a) and cos ~ {vt— A-a), 

 X X 



in order to find an expression proportional to the displacement produced 

 by it on the screen at the point x. The expression must also be mul- 

 tiplied by Sw, the breadth of the small space from which the wave 

 proceeds. Thus we find for the whole displacement at the point x of 

 the screen. 



sin 



-.)..{ ^(/5V^-«,v'|;)-?.(«\/|;-».V|;)}' 



COS J— {w 

 ■{vt-A-a-b)y. { — — 



+COS -:^{vt- A -a-b)x j ■■ 



si„i(„-.)..{-*(^ v^-. V„4).«(<.v/|;-. V|)}j 



.co.i (.-.)'x{-V.(/3 V|;-» Vi) .+(« V|;-«- X/|) Y 



