The constitution and evolution of the stars

98 Recent Advances in Stellar Astronomy
atoms and electrons, huge as the latter is. Following this
lead, and working out the laws of flow of energy outward
down the temperature gradient, he showed that certain
simple and probable assumptions about the opacity of the
medium led to the conclusion that, all through the star,
the gravitational pressure would be proportional to the
fourth power of the temperature, and that the shares of
this pressure which were sustained by the gas-pressure and
the radiation pressure would be everywhere in the same
ratio. These conditions, combined with the law of gravita-
tion and the gas laws, suffice to determine completely the
model upon which the star is built, and to tell us practically
all that we need to know about it.

For the case where the simple gas laws hold, the ma-
thematical work had already been done by Emden, who
found that the outer regions of the star were of very low
density, while there was a rapid concentration toward the
centre, where the density reaches fifty-four times the mean
density. The central temperature of such a star obeys
Lane’s Law, while the surface brightness varies inversely
in the square root of the radius. This means that the
whole amount of energy radiated from the star’s surface
will be independent of its size—the increase in surface
brightness and decrease in area, as it contracts, balancing
one another exactly. The amount of the star’s radiation
depends upon the opacity of its material—diminishing as
this increases—and is also proportional to the ratio which
the radiation pressure bears to the total pressure at any
part inside the star. This ratio increases rapidly with
the star’s mass, and the brightness should do the same.

These conclusions form a theory of giant stars. To
extend it to dwarf stars Eddington repeated his calcula-
tions, taking into account the manner in which the com-

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