ON CERTAIN DTPFEACTION PHENOMENA. 807 



AR + AR = ^ (;. .r + fUJ + i^zy-- {X'-+ j/ + ..2)^^_L_ ^ _I_\ 



Introdncino- fin's v.-iliic in (TT), we o'et for the iutensity of h'oht ;it D 

 ( 11') / = MocP. fda .^^[(^^' ^ "'-^ + ''^^' - (^' -^ y^ + ■^^)](-zr + -7p)^ 



where the inteo-rntion extends over the whole npertnre. 



Thus the pro1)leiii of the ditiVnctioii of lio-ht produced hy nn 

 n]ierture on n curved suriace is reduced to the inte^Tntion of expres- 

 sions (I') nnd (TT') for Fraunhoter's and Fresnel's diffraction phenomena 

 respectively. 



Fraunhofer's Diffraclion Phenomena produced by a narrow 

 Slit on a cylindrical Surface. 



Let us now discuss Fraunhofer's diffraction phenomena produced 

 hy a narrow slit cut on a right circular cylinder and perpendicular to 

 the generating line of the cylinder. 



Tn order to calculate the intensity of liglit for different positions 

 of the telescope, dro]i a perpendicular on the axis of the cylinder 

 from the centre of the slit. Assume the centre as the orio-in of 

 co-ordinate axes. Fet the x axis he parallel to the axis of the cylinder, 

 and the z axis perpendicular thereto, hoth drawn through the centre 

 of the slit. 



The axes heing thus fixed, we have, 1)y ( T'), to find the integral 



/• 



^^^^i(U + viy + nz) 



where the integration extends over the whole ajierture, and /, vi, 

 n are determined ])y tlie (hrections of the incident light and of the 

 <)T)servirig telesco])e referred to the rectangular axes ahove specified, 



