OBJECT-GLASS WITH A TRIANGULAR APERTURE. 435 



The intensity of the light at the point 31, as is well known, is 

 equal to the sum of the squares of the coefficients of sin V and cos F, 

 and therefore calling it Z, we find 



Z 



cos {2ni sin(a + G)} 1 - cos j2»^ sin {a ~ 0)\ 



sin' (a + 6) sin- (a - G) 



_ r/'sin'a fl 

 8?;/' s'm°G ' \ 



_ 1 - cos { 2m sin (a +6)\ - eos{2m sin (a -6)\+ eos{2m . 2 cos a sin G) ] 



sin (a + G) . sin (a - G) "^ ~f 



_ a' sin^g f sin' \ni sin (a + G)\ sin' {»« sin (a - G)\ 

 ~ 4»«' sin'fJ ■ \ sin' (« + 0) ^ sin" (a + 0) 



_ sin' {/« sin (a + g) j + sin' \m sin (g - g) | — sin^ (2?« cos a sin tf ) j 

 sin {a + 6). sin (a - 0) ' j 



a SUV a . cos u 



2 »»' sin G . sin (a + 0) . sin (a - G) 



^ | sin'(2»<cosasine) _ sin' { ?« sin (a + g) } sin' { m sin (« - 6) H 

 \ 2 cos a sin G sin (a + 6) "*" iin (« - 0) [• 



ar-TT 



If in this expression we write -y— for its equal m, we have the 

 brightness at any point of the screen expressed in terms of its polar co- 



ordinates r and 0. 



When the triangle is equilateral a = 60", and the equation for the 

 brightness assumes the very symmetrical form 



Z= ^'' 



I6tn' sin G . sin (60" + 0) . sin (60" - G) 



^ pin' (m sin G) _ sin' {m sin(60° + g)} sin' {»? sin (60° - G)\ ) 

 I sin G sin (60° + 6) '*' sin (60» -6) / ' 



or more simply 

 3 a" 



Z = 



4/«' sin B0 



pin' (m sin 0) _ sm " {m sin (60" + 0)\ sin' {w sin (60" - 0)\) 



I sine ^ sin (60' -I- 0) "^ sin (00" - 0) | ^'^• 



X 



Vol. VI. Paut III. 3 K 



