ness this idea is
appropriate only when the source is a luminous line, emitting
cylindrical waves, such as might be obtained from a luminous point
with the aid of a cylindrical lens. When, in order to apply Huygens's
principle, the wave is supposed to be broken up, the phase is the same
at every element of the surface of resolution which lies upon a line
perpendicular to the plane of reference, and thus the effect of the
whole line, or rather infinitesimal strip, is related in a constant
manner to that of the element which lies in the plane of reference,
and may be considered to be represented thereby. The same method of
representation is applicable to spherical waves, issuing from a
_point_, if the radius of curvature be large; for, although there is
variation of phase along the length of the infinitesimal strip, the
whole effect depends practically upon that of the central parts where
the phase is sensibly constant.[10]

[Illustration: FIG. 17.]

In fig. 17 APQ is the arc of the circle representative of the
wave-front of resolution, the centre being at O, and the radius QA
being equal to a. B is the point at which the effect is required,
distant a + b from O, so that AB = b, AP = s, PQ = ds.

Taking as the standard phase that of the secondary wave from A, we may
represent the effect of PQ by

/t [delta] \
cos 2[pi] ( - - -------- ).ds,
\r [lambda]/

where [delta] = BP - AP is the retardation at B of the wave from P
relatively to that from A.

Now

[delta] = (a + b) s^2/2ab (1),

so that, if we write

2[pi][delta] = [pi](a + b)s^2 [pi]v^2
------------ --------------- = ------ (2),
[lambda] ab[lambda] 2

the effect at B is
_ _
/ab[lambda]\1/2 / 2[pi]t / 2[pi]t / \
( ---------- ) ( cos ------ | cos 1/2[pi]v^2.dv + sin ------ | sin 1/2[pi]v^2.dv ) (3),
\2(a + b) / \ [tau] _/ [tau] _/ /

the limits of integration depending upon the disposition of the
diffracting edges. When a, b, [lambda] are regarded as constant, the
first factor may be omitted,--as indeed should be done for
consistency's sake, inasmuch as other factors of the same nature have
been omitted already.

The int