AGGREGATE EFFECT OF INTERFERENCE. 155 



The notation is as follows : 



e is the breadth of one of the openings between the wires ; 



g the breadth of a wire ; 



p, q the co-ordinates of the point, measured along the screen from the 

 focus of the lens, 



p being perpendicular to the wires ; 



m the number of openings and of wires. 



To obtain the whole quantity of light, then, we must multiply this 

 expression by 4:dpdq, and integrate between the limits and oo . 



Let the result of the integration for q give 



■He* r»i /sin aV/ 01 " V e) 



sin 1 1 + - 1 mx\ 



w r*p (nr) . / V\ ) b y writin s * for w 



\ sin 1 + - ) x I 



Then dp = — dx, so that the expression becomes 



ire 



He Cdx (*™-Z)' ( ^rmx y f _ g 

 J \ x J \ sin rx I e 



1. Now first, we must integrate this expression on the hypothesis that 

 the aperture is uninterrupted, or that m — 1. I shall make use of the well 

 known formula of Laplace : viz. 



/ 



» a cos qx .dx _ir _ aq 



a? + x* 2 



the particular value of a being 0. 



Thus r^-f 



Jo x i 2a 



- ~e- a 



2a 



£■ 



2a 



2a " 



&c. 



