AGGREGATE EFFECT OF INTERFERENCE. 159 



Hence the expression becomes 



- Hem: 

 2 



that is, - H x space left uncovered. 



Or, which is the same thing, since m . 2e = E, 

 the expression is - . - HE, 

 or, one half the quantity of light which would fall were there no grating. 



4. To give one more particular case, we will take that in which 

 g = 2e, or the breadth of the wire is double that of the opening between the 

 wires. 



Our expression then becomes He f ( ) (— = ) dx, 



Jo \ x I \ sin 3x J 



and - 4 (sin *)■ ( *? *"* )' = (0 - <H)' fl ~ £") ' = ( g ~ '"" X 



y J V sm 3x I y } \ e 3 - o- 3 I ye* + i + e-J 



Assume this expression to be expanded in the form 



a,^"- 4 + « 2 6m - 6 + 



+ a 2 0- (6m - 6) + «,0- <8m - 4) : 



the terms from the beginning and end of the series having obviously equal 

 coefficients, 



. 0S. _ 2 + e - 6m = (04 + 29 2 + 3 + 20- 2 + 6-*) 



x \a l 6 6 "'- i + ch& m -« + + a 2 0- (6m - 6) + a 1 0- (6ra - 4, } 



= a,& m + a 2 &'"-* + OvO 6 "-* + « 4 6m - 6 + a^'"-^... 



+ 2a l e 6 "'- 2 + 2a#'"- 4 + 2a 3 & m - e + 2a t 6 6m - b +... 



+ Sflifi 8 " -4 + 3(h& m -' i +- 3a 3 d 6m - s +... 



+ 2a 1 6 6m - 6 + 2ck& m - 8 +... 



