The constitution and evolution of the stars

90 Recent Advances in Stellar Astronomy

attracted four times more strongly. The whole com-
pressive force will, therefore, be four times as great as
at first; but the area over which this force is distributed
will have shrunk to one-fourth of its former amount.
Hence the pressure per unit of area will increase sixteen-
fold, as against an eight-fold increase of density. Applying
the familiar laws of gases, we find that the temperature
of the gas, after contraction, must be twice its original
value in order that equilibrium shall still exist when the
star has shrunk to half its former size. More generally,
during the whole process of contraction, the temperatures
at corresponding points will be inversely proportional to
the star’s radius—so long, indeed, as the star continues to
be built on the same model, and the simple gas laws hold
good. This proportion was first proved by Lane of
Washington, in 1870, and is known as Lane’s Law.

It appears at first sight paradoxical that a star may
grow hotter by losing heat; but the difficulty disappears
when it is realized that the heat produced by the contrac-
tion exceeds the amount which is required to raise the
temperature of the mass to the extent demanded by Lane’s
Law. The remainder is available for radiation, and it is
only as it is gradually lost into space that the process
of contraction can take place. The manner in which the
surface temperature of a star, which determines its color
and spectral type, will vary as it contracts is somewhat
different. As has already been shown, the light from the
far interior of a star stands no chance of getting out to
the surface, but practically all of it will be scattered away
by the gases through which it passes, and remain inside the
star. Light can only reach us directly from a relatively
shallow layer close to the surface, and it is a certain sort
of average of the temperatures throughout this layer that

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