of the slit. It is easy to see
that the length of the chord (which passes in all cases through O)
increases to a maximum near the place where the phase-retardation is
3/8 of a period, then diminishes to a minimum when the retardation is
about 7/8 of a period, and so on.

If the slit is of constant width and we require the illumination at
various points on the screen behind it, we must regard the arc of the
curve as of _constant length_. The intensity is then, as always,
represented by the square of the length of the chord. If the slit be
narrow, so that the arc is short, the intensity is constant over a
wide range, and does not fall off to an important extent until the
discrepancy of the extreme phases reaches about a quarter of a period.

We have hitherto supposed that the shadow of a diffracting obstacle is
received upon a diffusing screen, or, which comes to nearly the same
thing, is observed with an eye-piece. If the eye, provided if
necessary with a perforated plate in order to reduce the aperture, be
situated inside the shadow at a place where the illumination is still
sensible, and be focused upon the diffracting edge, the light which it
receives will appear to come from the neighbourhood of the edge, and
will present the effect of a silver lining. This is doubtless the
explanation of a "pretty optical phenomenon, seen in Switzerland, when
the sun rises from behind distant trees standing on the summit of a
mountain."[11]

II. _Dynamical Theory of Diffraction._--The explanation of diffraction
phenomena given by Fresnel and his followers is independent of special
views as to the nature of the aether, at least in its main features; for
in the absence of a more complete foundation it is impossible to treat
rigorously the mode of action of a solid obstacle such as a screen. But,
without entering upon matters of this kind, we may inquire in what
manner a primary wave may be resolved into elementary secondary waves,
and in particular as to the law of intensity and polarization in a
secondary wave as dependent upon its direction of propagation, and upon
the character as regards polarization of the primary wave. This question
was treated by Stokes in his "Dynamical Theory of Diffraction" (_Camb.
Phil. Trans._, 1849) on the basis of the elastic solid theory.

Let x, y, z be the co-ordinates of any particle of the medium in its
natural state, and [chi], [eta], [zeta] the d