324 Mr. J. Bridge on the Diffraction of Light. 



The same thing may be seen by the formulae. For, by (7), 

 instead of A and B must be put 



A(l+C, + C2+ ...)+B(Si+S2+...) 

 B(l+Ci+C2+...)-A(Si + S2+...), 



c,, 5,, C2, s^, &c. being the cosines and sines of certain angles. 

 And in the case of the points for A and B we have 



1+C,+C2+... 



and 



Sl+S2+--- 



The sum of the squares of the first pair is equal to those of the 

 second pair multiplied by A^ + B^. 



(9) For determining the expressions for intensity arising from 

 any apertures bounded by straight lines, we only need integra- 

 tion in the cases of a triangle and of a parallelogram whose bases 

 are in the axis of y. The remainder of the process is svipplied 

 by means of the preceding observations, which also afford a 

 simple means of determining the figures produced by apertures 

 bounded by conic sections. 



For a parallelogram of height h, base b, the base being in the 

 axis of y, the law of variation in the direction perpendicular to 

 the base is obtained from 



. bX . 27rxh „ —bX/^ 2'Troch\ 



A=p: — Sin— r — ; B=— — il — cos ' 



0-, 



^sm-^; ii=^_^i_cos-^; 



Intensity = . „ „ • sm-^ -— — 



For a triangle of height h, base b, the base being in the axis 

 of y, 



X% . 2iTcth Xb 



Intensity = -^-^,(^1- _sm-^ + ^2^2^^^^;. 



(10) As an application of these results, I will take the case of 

 an equilateral triangle. We may divide it into two triangles having 



their bases in the axis of y; bases, ^ ^; heights,«sin(3O + 



and a sin (30— 6). Whence 



