230 
MR. AIRY ON THE THEORETICAL EXPLANATION OF 
+ cos ^ (vt -/) {s (\/^ ■ h - v) + s (v/^-S + ~) } 
+ sin^V-/).cosR{c (s/^-A + ^)-c(\/ ; + 
+ sin ~ (vt -/) . sinR { S (\/ ~ • k + - S (s/ ^ ■ g + ~) } 
+ cos^(i.<-/).cosR|s( v /|iL.A + ^) -s(y/ ~-g+ ~) } 
2- 
COS 
«n R { C (y/g; .h + f)-c{y/Jl. g + f)}. 
The expression in this general form is rather troublesome. If, however, we suppose 
a not to be exceedingly small, so that.y / ' ’ h is equal to several units, and if we 
remark that the values of C ( s ) and S (s) approach rapidly to the limit it will be seen 
that (for all values of g which are not very nearly equal to h) we shall commit no sen- 
sible error in putting ~ for h + ~), S (y/ ■ h - 
c (JJL .h^ ) c ( a/I± ■ h T5) . 
\V A ,ce «/’ VV A ,ce a) 
Making this substitution, our integral may be put into this form : 
sin X [i + C (\/ ^“<? + ^) + cosR +t)} 
+ sinR{-i-s( V /j^.g + ^)}] 
+ cos^(«f-/)X [|-+S (y/^- .g + C -±) 
+ cosR (i-S^l^.g + ^j-sinR { 4— C (v/ + 
The intensity of light being estimated, as is usual in the theory of undulations, by 
• 2tt 2 7T 
the sum of the squares of the coefficients of sin-^(?;£ — f) and cos-^- (vt —f), we 
find the following expression for the intensity of light on the point of the retina : 
+ COSRX [l-2 {c( A /|i.g + ^)j 2 -2{s( V /^.g + ^)} 2 ] 
+ sin R X 
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