ull discussion would call for the formal
application of Fourier's theorem, but some conclusions of importance
are almost obvious.

Previously to the introduction of the plate we have an effect
corresponding to wave-lengths closely grouped around the principal
wave-length, viz. [sigma] sin [phi], where [sigma] is the
grating-interval and [phi] the obliquity, the closeness of the
grouping increasing with the number of intervals. In addition to these
wave-lengths there are other groups centred round the wave-lengths
which are submultiples of the principal one--the overlapping spectra
of the second and higher orders. Suppose now that the plate is
introduced so as to cover naif the aperture and that it retards those
pulses which would otherwise arrive first. The consequences must
depend upon the amount of the retardation. As this increases from
zero, the two processions which correspond to the two halves of the
aperture begin to overlap, and the overlapping gradually increases
until there is almost complete superposition. The stage upon which we
will fix our attention is that where the one procession bisects the
intervals between the other, so that a new simple procession is
constituted, containing the same number of members as before the
insertion of the plate, but now spaced at intervals only half as
great. It is evident that the effect at the focal point is the
obliteration of the first and other spectra of odd order, so that as
regards the spectrum of the first order we may consider that the two
beams _interfere_. The formation of black bands is thus explained, and
it requires that the plate be introduced upon one particular side, and
that the amount of the retardation be adjusted to a particular value.
If the retardation be too little, the overlapping of the processions
is incomplete, so that besides the procession of half period there are
residues of the original processions of full period. The same thing
occurs if the retardation be too great. If it exceed the double of the
value necessary for black bands, there is again no overlapping and
consequently no interference. If the plate be introduced upon the
other side, so as to retard the procession originally in arrear, there
is no overlapping, whatever may be the amount of retardation. In this
way the principal features of the phenomenon are accounted for, and
Schuster has shown further how to exte