Mr. J. Bridge on the Diffraction of Light. 32f 



/rt . „ Traa sin (30 + ^) „ . o7raasin(30 — ^)\ 

 /„ / 2 sin^ -i 2 sm^ e \ 



A= 



■ + 



STT^a^cos (9 \ asiu(30 + ^) a sin (30-6') 



\^\/3 

 87r^«^cos^ 



(. 27r«asin(30+^) . 27raasin (30-^)\ 

 X ^^^ X ) 



asin(30 + ^) «sin(30-^) /" 



If we take in the plane of the image supposed formed by a 

 lens of focal length f, axes perpendicular to two sides of the tri- 

 angle, we must put 



«cos^=i^±|^,«sin(30 + ^) = ^^«sin(30-^)=^-^^ 



and then 



(, 7ra\/3 - iraVS \ 





'67r2a(a; + 2/) \ ^ 



y 



A2 I T>2_ ^/ 



— i^ — + p 



=^ X COS (c^ + ?/) 



For a square in any direction. Taking origin at centre, B = 

 by (6), and A is twice the difference of the results from two trian- 

 gles whose heights are «(cos ^ + sin^), ;(cos 6— sin 6) ; and bases 



a~~= — n> 'n~- — s- Therefore 



cos asmO cos 6 sm 6 



A= 



\^ / 27r«A 2Truh'> 



— 2-5 a~- — 3 ■ cos r COS -— — , 



TT^'ar cos 6/ sm y v. X X J 



. 2'iroi.a cos 6 . 2'jTua sin d" 

 X^ «^n— ^^— sm ^ 



Tr'^a^ sin 6 . cos ^ ' 



or if X, y be coordinates in the plane of the image, 

 . 27ra,r . 2'iruy 



TT^ xy 



