th respect to g1 it may be proved that

w = 0 from g1 = -[oo] to g1 = -2h1,
w = 1/2[pi](2h1 + g1) from g1 = -2h1 to g1 = 0,
w = 1/2[pi](2h1 - g1) from g1 = 0 to g1 = 2h1,
w = 0 from g1 = 2h1 to g1 = [oo].

The integrated intensity, I', or

2[pi]h1 + 2 cos[rho]w,

is thus

I' = 2[pi]h1 (11),

when g1 numerically exceeds 2h1; and, when g1 lies between [+-]2h1,

I = [pi]2h1 + (2h1 - [sqrt] g1^2) cos[rho]' (12).

It appears therefore that there are no bands at all unless [omega]
lies between 0 and +4h1, and that within these limits the best bands
are formed at the middle of the range when [omega] = 2h1. The
formation of bands thus requires that the retarding plate be held upon
the side already specified, so that [omega] be positive; and that the
thickness of the plate (to which [omega] is proportional) do not
exceed a certain limit, which we may call 2T0. At the best thickness
T0 the bands are black, and not otherwise.

The linear width of the band (e) is the increment of [xi] which alters
[rho] by 2[pi], so that

e = 2[pi]/[=omega] (13).

With the best thickness

[=omega] = 2[pi]h/[lambda]f (14),

so that in this case

e = [lambda]f/h (15).

The bands are thus of the same width as those due to two infinitely
narrow apertures coincident with the central lines of the retarded and
unretarded streams, the subject of examination being itself a fine
luminous line.

If it be desired to see a given number of bands in the whole or in any
part of the spectrum, the thickness of the retarding plate is thereby
determined, independently of all other considerations. But in order
that the bands may be really visible, and still more in order that
they may be black, another condition must be satisfied. It is
necessary that the aperture of the pupil be accommodated to the
angular extent of the spectrum, or reciprocally. Black bands will be
too fine to be well seen unless the aperture (2h) of the pupil be
somewhat contracted. One-twentieth to one-fiftieth of an inch is
suitable. The aperture and the number of bands being both fixed, the
condition of blackness determines the angular magnitude of a band and
of the spectrum. The use of a grating is very convenient, for not only
are there