0, viz. at the geometrical
image of the radiant point. It is traversed by dark lines whose
equations are

[xi] = mf[lambda]/a, [eta] = mf[lambda]/b.

Within the rectangle formed by pairs of consecutive dark lines, and
not far from its centre, the brightness rises to a maximum; but these
subsequent maxima are in all cases much inferior to the brightness at
the centre of the entire pattern ([xi] = 0, [eta] = 0).

By the principle of energy the illumination over the entire focal
plane must be equal to that over the diffracting area; and thus, in
accordance with the suppositions by which (3) was obtained, its value
when integrated from [xi] = [oo] to [xi] = +[oo], and from [eta] =
-[oo] to [eta] = +[oo] should be equal to ab. This integration,
employed originally by P. Kelland (_Edin. Trans._ 15, p. 315) to
determine the absolute intensity of a secondary wave, may be at once
effected by means of the known formula

_+[oo] _+[oo]
/ sin^2u / sin u
| ----- du = | ----- du = [pi].
_/ u^2 _/ u
-[oo] -[oo]

It will be observed that, while the total intensity is proportional to
ab, the intensity at the focal point is proportional to a^2b^2. If the
aperture be increased, not only is the total brightness over the focal
plane increased with it, but there is also a concentration of the
diffraction pattern. The form of (3) shows immediately that, if a and
b be altered, the co-ordinates of any characteristic point in the
pattern vary as a^-1 and b^-1.

The contraction of the diffraction pattern with increase of aperture
is of fundamental importance in connexion with the resolving power of
optical instruments. According to common optics, where images are
absolute, the diffraction pattern is supposed to be infinitely small,
and two radiant points, however near together, form separated images.
This is tantamount to an assumption that [lambda] is infinitely small.
The actual finiteness of [lambda] imposes a limit upon the separating
or resolving power of an optical instrument.

This indefiniteness of images is sometimes said to be due to
diffraction by the edge of the aperture, and proposals have even been
made for curing it by causing the transition between the interrupted
and transmitted parts of the primary wave to be less abrupt. Such a
view of the matter is altogether misleading. What requires explanat