The constitution and evolution of the stars



Constitution and Evolution of the Stars 91
gives the effective surface temperature. As the density of
the star varies, the depth of this layer will alter, and in
such a way that it always contains the same number of tons
of material per square foot, since it is upon this quantity
that the amount of scattering of light passing through the
layer depends. As the star contracts, the total quantity of
matter in this superficial radiating layer will therefore
diminish proportionally to the surface area; that is, the
radiating layer will form an ever decreasing part of the
whole mass of the star, and its depth will be a smaller
fraction of the star’s radius. If the depth were a fixed
fraction of the radius, we could apply the law of cor-
responding points and say that the temperature would vary
inversely as the radius; but, in fact, after contraction the
new radiating layer will form only the upper portion of
the layer which “corresponds” to the old radiating layer,
and its average temperature will be lower than that of the
“corresponding” layer. On any reasonable assumptions
regarding the way in which the temperature varies in the
outer part of the star, it is found that the effective temper-
ature of the surface will increase as it contracts, but much
more slowly than the central temperature.

All these conclusions are based upon the fundamental
assumption that the simple gas laws hold good throughout
the star. This may safely be assumed if the density is
low—say not more than twenty times that of air—but
when the density begins to approach that of water, it will
certainly be very far from the truth. As the density in-
creases, the compressibility diminishes, so that, at the same
temperature, it takes a greater increase of pressure to
produce a further increase of density than would be neces-
sary in a perfect gas. In other words, the material is better
able than a perfect gas to stand up under pressure. Hence,



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