OBJECT-GLASS WITH A TRIANGULAR APERTURE. iSS 



Let p, q be co-ordinates of any point M in the screen : tlien the dis- 

 turbance caused at M by the element Sa;.Si/ of the wave surface may 

 be represented by 



-p^ .sm~{vt - PM). 



But as p^^ refers only to the intensity of the light, wliich emanates 



from P, when it reaches 31, it will not vary sensibly with the variation 

 of PM in the problem under consideration, since both the triangle and 

 its image are small. No appreciable error, therefore, will be committed if 

 for the purpose of simplifying our calculations we suppose PM constant 

 in this term, and assume the disturbance at M due to the element 

 Ix . ly to be 



Ix.hjmv ^{vi - PM). 



Now Pdl- = {x - pY + (y - qf + s:- 



= x" + y^ + s;- — Qxp — 2yq -f p- + q' 

 = b' + p' -V q- — 2px — 2qy ; 



...Pi,/=, + ?^^_^_^ nearly 



- 7? _ ^' _ £y 

 h b ■ 



Hence the disturbance at M due to the element ^x . Sy is represented by 

 Sx.Sysm^{vt-B+J^+fy 



The whole disturbance at 31 will be found by integrating this ex- 

 pression, first with regard to y, between the limits y = - (2c - .r) cot«, 

 and y = (2c - x) cot a ; and then with regard to x between the limits 

 X = — c and x = 2c. 



The integral with regard to y is 



5 b\ Stt / . „ px qy\ 



