230        ON THE TOTAL  INTENSITY  OF  INTERFERING  LIGHT.
A similar formula holds good for q, whence D^2I= limit of
Let now
2?r (#' — x)
-----1_------i. = q._u)
whence
^ ,           _7
dx = -=-— du,
A7T
and the limits of u are ultimately — oo aud + °o , since a ultimately vanishes.    Hence
..    . f
imit Of J
du
A similar formula holds good for y, and we have, therefore,
if A be the whole area of the aperture or apertures. Now / ought to be equal to A, and, therefore,
D = b\.
case II.    Aperture in front of a screen.
The formula for the illumination is given   iu  Airy's Tract, Art. 73.    We have as before,
= limit of jjjjjj*****^1 cos j^"^- [^ - & + 2/"^J - f]
~ ^y>^dx ^dy ^dx'^dy'