AGGREGATE EFFECT OF INTERFERENCE. 157 



But e = - E ; since the original aperture is divided into four equal parts, 

 two of which are appropriated to the openings, and two to the wires. 



.-. The intensity = ^ HE 



= - the result found for the intensity when there are 

 no wires. 



3. Thirdly, let us retain the hypothesis, that the breadths of the 

 wires are the same as the openings between them, but suppose the number 

 of wires and of openings to be any number whatever, (m). 



Write — , for sin x: 



2v/- 1 



then the expression (sin xf r 1 ? |~ j is put under the form, 



1 (0 fl-«Y ( ** - *"" V 



" 1 \ e + e- 1 ) ' 



or 



Let (^ — ^-J = oofl 4 — •+ «!0 4m - 4 + &c. 



+ a4 m - 2 0- (4m - rt ; 



.-. 4 " 1 - 2 + 0" 4m = O 4 "' + a 1 , "-* + 0,0*—*+ ... + a4 m -20- (4m_4) 



+ 20 o 4 "" 2 + 2« 1 4 '"- 4 + ... + 2a 4m . 2 0- u '"- 2) 

 + OO0 4 — 4 + ... + a tm -z0- im ; 

 from which we obtain by equating coefficients, 



1 = 00, 



= 0,+ 20 o> 



= 2 + 20*1 + 0o, 

 = 03 + 20 2 + 0„ 



