n to Fresnel's theory that it
required at the centre of a circular shadow a point as bright as if no
obstacle were intervening. If we conceive the primary wave to be
broken up at the plane of the disk, a system of Fresnel's zones can be
constructed which begin from the circumference; and the first zone
external to the disk plays the part ordinarily taken by the centre of
the entire system. The whole effect is the half of that of the first
existing zone, and this is sensibly the same as if there were no
obstruction.

When light passes through a small circular or annular aperture, the
illumination at any point along the axis depends upon the precise
relation between the aperture and the distance from it at which the
point is taken. If, as in the last paragraph, we imagine a system of
zones to be drawn commencing from the inner circular boundary of the
aperture, the question turns upon the manner in which the series
terminates at the outer boundary. If the aperture be such as to fit
exactly an integral number of zones, the aggregate effect may be
regarded as the half of those due to the first and last zones. If the
number of zones be even, the action of the first and last zones are
antagonistic, and there is complete darkness at the point. If on the
other hand the number of zones be odd, the effects conspire; and the
illumination (proportional to the square of the amplitude) is four
times as great as if there were no obstruction at all.

The process of augmenting the resultant illumination at a particular
point by stopping some of the secondary rays may be carried much
further (Soret, _Pogg. Ann._, 1875, 156, p. 99). By the aid of
photography it is easy to prepare a plate, transparent where the zones
of odd order fall, and opaque where those of even order fall. Such a
plate has the power of a condensing lens, and gives an illumination
out of all proportion to what could be obtained without it. An even
greater effect (fourfold) can be attained by providing that the
stoppage of the light from the alternate zones is replaced by a
phase-reversal without loss of amplitude. R. W. Wood (_Phil. Mag._,
1898, 45, p 513) has succeeded in constructing zone plates upon this
principle.

In such experiments the narrowness of the zones renders necessary a
pretty close approximation to the geometrical conditions. Thus in the
case of the circular disk, equidistant