ght
occurs in unusual directions. If the source be a point or a line, and
a collimating lens be used, the incident waves may be regarded as
plane. If, further, on leaving the grating the light be received by a
focusing lens, e.g. the object-glass of a telescope, the Fresnel's
zones are reduced to parallel and equidistant straight strips, which
at certain angles coincide with the ruling. The directions of the
lateral spectra are such that the passage from one element of the
grating to the corresponding point of the next implies a retardation
of an integral number of wave-lengths. If the grating be composed of
alternate transparent and opaque parts, the question may be treated by
means of the general integrals (S 3) by merely limiting the
integration to the transparent parts of the aperture. For an
investigation upon these lines the reader is referred to Airy's
_Tracts_, to Verdet's _Lecons_, or to R. W. Wood's _Physical Optics_.
If, however, we assume the theory of a simple rectangular aperture (S
3); the results of the ruling can be inferred by elementary methods,
which are perhaps more instructive.

Apart from the ruling, we know that the image of a mathematical line
will be a series of narrow bands, of which the central one is by far
the brightest. At the middle of this band there is complete agreement
of phase among the secondary waves. The dark lines which separate the
bands are the places at which the phases of the secondary wave range
over an integral number of periods. If now we suppose the aperture AB
to be covered by a great number of opaque strips or bars of width d,
separated by transparent intervals of width a, the condition of things
in the directions just spoken of is not materially changed. At the
central point there is still complete agreement of phase; but the
amplitude is diminished in the ratio of a : a + d. In another
direction, making a small angle with the last, such that the
projection of AB upon it amounts to a few wave-lengths, it is easy to
see that the mode of interference is the same as if there were no
ruling. For example, when the direction is such that the projection of
AB upon it amounts to one wave-length, the elementary components
neutralize one another, because their phases are distributed
symmetrically, though discontinuously, round the entire period. The
only effect of the ruling is to diminish the amplitude in t