THE ABSOLUTE INTENSITY OF INTERFERING LIGHT. 317 



g = x ' =y ' '' dp ~~ dx ' &C ' 



64 a 2 e 2 / 2 l> 2 A 2 J 



-- dx - 



st^acosmxdx TT ma 

 N W> Jo ~ 



/ 



"I l-cos2ar 



. , 2a 



= [ - J ; a being equal to 0. 



7T 2 + &C. / n \ 



= - I = 1 



4 V / 



7T 



4 



total quantity of light = 



= area of parallelogram x ^ 

 Now, it ought to be, area of parallelogram x a 2 ; 



PROB. II. A series of equal parallelograms are placed before a lens, to find the whole 

 quantity of light received on a screen placed perpendicular to the axis of the lens 

 at its focus. 



Let e, 2/be the breadth and length of one of the openings, g the breadth of 

 one of the opaque sides of one of the parallelograms ; p, q the co-ordinates of a 

 point on the screen, measured from the focus of the lens, q being parallel to the 

 sides of the parallelograms, b the focal length of the lens, or the perpendicular 

 distance between the screen and the lens ; m the number of openings. 



The intensity of the light at the point p, q is given by AIKY (Tracts, p. 328) as 



4a 2 e 2 / 2 / X6 . 2-7ry/\ 2 / \b . -rr p e\ 

 D 2 \2 TT qf S1 X b ) \irp e S ' \ 6 ) 



m 



\ A 6 / 



~ being introduced as the coefficient of vibration, and the divisor which we seek 



to determine respectively. 



The whole quantity of light received on the screen is the integral of this 

 pression with respect to p and q, each between the limits of + oo and - oo . i 



ex- 

 oo. Call 



