of
slightly shorter wave-length is refracted upward and illuminates the
top of the slit. Fig. 4 represents the inverted image seen in the
telescope. The light corresponding to the D lines and the space
between them is absorbed, as evidenced by the dark interval. If the
sodium is only gently heated, so as to produce a comparatively
rarefied vapour, and a grating spectroscope employed, the spectrum
obtained is like that shown in fig. 5, which was the effect noticed by
Becquerel with the sodium flame. Here the light corresponding to the
space between the D lines is transmitted, being strongly refracted
upward near D1, and downward near D2.

[Illustration: FIG. 5.]

The theory of anomalous dispersion has been applied in a very
interesting way by W. H. Julius to explain the "flash spectrum" seen
during a solar eclipse at the moment at which totality occurs. The
conditions of this phenomenon have been imitated in the laboratory by
Wood, and the corresponding effect obtained.

_Theories of Dispersion._--The first attempt at a mathematical theory
of dispersion was made by A. Cauchy and published in 1835. This was
based on the assumption that the medium in which the light is
propagated is discontinuous and molecular in character, the molecules
being subject to a mutual attraction. Thus, if one molecule is
disturbed from its mean position, it communicates the disturbance to
its neighbours, and so a wave is propagated. The formula arrived at by
Cauchy was

B C
n = A + --------- + --------- + ....
[lambda]2 [lambda]4

n being the refractive index, [lambda] the wave-length, and A, B, C,
&c., constants depending on the material, which diminish so rapidly
that only the first three as here written need be taken into account.
If suitable values are chosen for these constants, the formula can be
made to represent the dispersion of ordinary transparent media within
the visible spectrum very well, but when extended to the infra-red
region it often departs considerably from the truth, and it fails
altogether in cases of anomalous dispersion. There are also grave
theoretical objections to Cauchy's formula.

The modern theory of dispersion, the foundation of which was laid by
W. Sellmeier, is based upon the assumption that an interaction takes
place between ether and matter. Sellmeier adopted the elastic-solid
theory