ox CERTAIN DIFFRACTION TUEXOMEXA. 309 



riicii a {in sill 'V — n cos â) = ç cos [r) + I'J') = ç cos c, 



where ç stands i'or ij + />'. 



Thus fdn e'"^'" "'" ^ - " ''' ^' ^ fdif e' ' '"' '^• 



'J'lie Jiiiiit.s of integral ion with respect to (f are fljiind ir«Mu ij' and 

 the known limils witli respect to ü. 



The dithcuJl y of the })ro1j]eni hes simply in fin<linu- the inteu-ral 



I shall hencef(.)i-th put J ~-= K + iL, where 



K — I cos (-f COS (f) d(f, 



L =- /sill (ç cos (f) dç. 



Evaluation of the Integral '^ = fif c ^ ''' f^ 



There are various ways of evaluating tlie ahove integral. The 

 siin}»lest way would l)e lo lind a differential e(jualion which is satisfied 

 hy J, and hy this means to expand it in a scries proceedinuf accordin"' 

 to ascending powci*« of ^. 



îSincc every integral of tlie form fdire^'""^ hctween known 

 limits can be decomposed into a smn of two separate integrals of the 



/•a ■ .- , , 



form id(r c ^ "'" '^ , I sliall (jnly consider 



•/o 



*ultinu' 



cos ç — U, cos (J. — c, 

 J = - / 4zz=rr- du. 



■h ^\ - i(^ 



