418 On Gratings in Theory and Practice. 



• • buan -vr 



When n is very large, writing —^-=pn = 7rJSn + q 9 we 



have 



Whence, writing 



c = bdi^—KO?), 



c" = b{/m 3l + ih(jia 1 —Ka'yj > 



c"< = &c. 



the summation is 

 f 



«*» -i 





dq 2 



d?_ 

 dq 3 



dq* 



sin q 



+ z 



+ &c. ) 



d sin q _ q cos q— sin ^ 

 dq q q 2 ' 



d 2 sin ^ _ — 2g cos ^ 4- (2 — <? 2 ) sin q 

 dtf~q~~ q* ""* 



d 3 sin q __ q(& — q 2 ) cosq— (6— 3q 2 ) sin^ 



£^ 3 ? 



Ac. 



? 4 



&c. 



These equations serve to calculate the distribution of light 

 intensity in a grating with any error of line distribution 

 suitable to this method of expansion and at any focal length. 

 For this purpose the above summation must be multiplied by 

 itself with +i in place of —i. 



The result is for the light intensity 



