-undulations in the marginal waves, we have a luminous band, but
one of considerably less intensity than the undiffracted central band.

With a marginal difference of path of four semi-undulations we have a
second extinction of the entire beam, because here the beam can be
divided into four equal parts, every two of which quench each other.
A second space of absolute darkness will therefore correspond to the
obliquity producing this difference. In this way we might proceed
further, the general result being that, whenever the direction of
wave-motion is such as to produce a marginal difference of path of an
_even_ number of semi-undulations, we have complete extinction; while,
when the marginal difference is an _odd_ number of semi-undulations,
we have only partial extinction, a portion of the beam remaining as a
luminous band.

A moment's reflection will make it plain that the wider the slit the
less will be the obliquity of direction needed to produce the
necessary difference of path. With a wide slit, therefore, the bands,
as observed, will be closer together than with a narrow one. It is
also plain that the shorter the wave, the less will be the obliquity
required to produce the necessary retardation. The maxima and minima
of violet light must therefore fall nearer to the centre than the
maxima and minima of red light. The maxima and minima of the other
colours fall between these extremes. In this simple way the undulatory
theory completely accounts for the extraordinary appearance above
referred to.

When a slit and telescope are used, instead of the slit and naked eye,
the effects are magnified and rendered more brilliant. Looking,
moreover, through a properly adjusted telescope with a small circular
aperture in front of it, at a distant point of light, the point is
seen encircled by a series of coloured bands. If monochromatic light
be used, these bands are simply bright and dark, but with white light
the circles display iris-colours. If a slit be shortened so as to form
a square aperture, we have two series of spectra at right angles to
each other. The effects, indeed, are capable of endless variation by
varying the size, shape, and number of the apertures through which the
point of light is observed. Through two square apertures, with their
corners touching each other as at A, Schwerd observed the appearance
shown in fig. 20. Adding two others to them, as at B, he observed the
appearance represented in fig. 2