NEWTON'S EXPERIMENTS ON DIFFRACTION. 



107 



cos 



\ a'h' V a' + b'J I ^\ ^ a'b'X ^ ^ b'la' + b')\ 



sm~(yt-B')x f ^ 

 jp 





+ sin; 



27r, . 

 f-COS— (v^ 

 A 



-B')x\ < 



Jp 



. TT a'+b' f a'x'Y r f . . /2 (a' + b') ,./ 2a' i 



+ COS; 



TT a'+b' 1^ a'x' Y r , L./2(«' + 6') ,./ 2^^ 



where the integrals are to be taken between the limits p = €, p = ^. 

 The brightness at the point x', i/, of the screen will then be propor- 

 tional to the sum of the squares of the coefficients of sin — (v#— ^') 



A 



and cos -— {v t - B'). 



A 



We have now to shew that, for a constant value of y', and a vari- 

 able value of x', these expressions may be made similar to those ob- 

 tained in the first case. For this purpose it will be necessary, first, to 

 make the coefficients of the expressions under the integral sign equal: 

 secondly, to make the limits of integration the same. 



