AGGREGATE EFFECT OF INTERFERENCE. 167 



we obtain, calling this arc 9 for the sake of brevity, 



Imcos = fJ£pD + jvcos = *»<* -/) + 4p/l s . n 



+ {i^sin^^y^-iv-sin^^-^+^cosg; 



so that the intensity at the point is represented by 



M 2 + A ra + 2 MN cos — Pte+f) § 



X o 



We must next integrate this expression between the limits — oo and 

 + oo for p. 



now/:^^/^^^^; ^-/)^^) .^-/) 



- ** >. I 1 " C ° S X * ft J (j, -/)' 



= — — — 1 1 — e~ \ b I , a being equal to zero, 

 c*X 2 ft 2 «* g+f 



Similarly, f° N*dp = c 2 Xft(# +/). 



•/-co 



Hence we find that the whole effect of each mirror is proportional to its 

 aperture : which result is strongly confirmatory of the general character 

 of our calculations. 



Lastly, MNcob^P^D 

 =V (i , 2 _ /2 sin x ft sm x ft cos x ft ' 



ft* 2tt 



g>-(f -r> \ ^ — ; — °"t r-/™""x 



