When V = 0, viz. at the edge of the shadow, I^2 = 1/2; when V = [oo],
I^2 = 2, on the scale adopted. The latter is the intensity due to the
uninterrupted wave. The quadrupling of the intensity in passing
outwards from the edge of the shadow is, however, accompanied by
fluctuations giving rise to bright and dark bands. The position of
these bands determined by (23) may be very simply expressed when V is
large, for then sensibly G = 0, and

1/2[pi]V^2 = 3/4[pi] + n[pi] (24),

n being an integer. In terms of [delta], we have from (2)

[delta] = (3/8 + 1/2n)[lambda] (25).

The first maximum in fact occurs when [delta] = 3/8[lambda]
-.0046[lambda], and the first minimum when [delta] = 7/8[lambda]
-.0016[lambda], the corrections being readily obtainable from a table
of G by substitution of the approximate value of V.

The position of Q corresponding to a given value of V, that is, to a
band of given order, is by (19)

a + b / / b[lambda](a + b) \
BQ = ----- AD = V / ( ----------------- ) (26).
a \/ \ 2a /

By means of this expression we may trace the locus of a band of given
order as b varies. With sufficient approximation we may regard BQ and
b as rectangular co-ordinates of Q. Denoting them by x, y, so that AB
is axis of y and a perpendicular through A the axis of x, and
rationalizing (26), we have

2ax^2 - V^2[lambda]y^2 - V^2a[lambda]y = 0,

which represents a hyperbola with vertices at O and A.

From (24), (26) we see that the width of the bands is of the order
[sqrt] {b[lambda](a + b)/a}. From this we may infer the limitation
upon the width of the source of light, in order that the bands may be
properly formed. If [omega] be the apparent magnitude of the source
seen from A, [omega]b should be much smaller than the above quantity,
or

[omega] < [sqrt] {[lambda](a + b)/ab} (27).

If a be very great in relation to b, the condition becomes

[omega] < [sqrt] ([lambda]/b) (28).

so that if b is to be moderately great (1 metre), the apparent
magnitude of the sun must be greatly reduced before it can be used as
a source. The values of V for the maxima and minima of intensity, and
the magnitudes of the latter, were calculated by Fresnel. An extract
from his results is given in t