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SOLUTION OF THE EQUATIONS
121
in k 0 for the series of stars from M to A, and therefore to an equal range
of L. This is equivalent to a range of 1-4 bolometric magnitudes. No idea
was formed as to which direction of variation was the more likely.
Having found that k 0 is tolerably constant throughout a 12 -fold range
of temperature it would seem natural to conclude that at stellar tempera
tures it tends to a constant value independent of physical conditions
altogether. The opacity would then be the same for all stars whatever
their masses. This conclusion, which was accepted in the writer’s earlier
papers, turns out to be fallacious. We are now convinced that k does
indeed vary rapidly with the temperature, but it also varies with the
density. The major part of the variation is proportional to pjT z which is
a constant for stars of the same mass (and also within any one star).
Thus the main variation conceals itself in our first study of the observational
data, and it springs a surprise on us when we begin to compare stars of
different masses.
88 . The approximate constancy of k 0 from star to star in the giant
series which we have found must be distinguished from the approximate
constancy of k (and more strictly of rjk) within a single star which we have
assumed. A little consideration will show that there has been no vicious
circle. If rjk is variable within a star we may still expect that some kind
of average value of it will be determined by (83-4); then comparison with
observation gives us the unexpected result that nearly the same average
value holds in other stars in spite of great differences of physical condition.
But having now found that the absorption changes very little from
star to star notwithstanding great differences of temperature, it seems so
much the more likely that we were right in assuming that its variations
within a single star could be neglected. A tenfold range of temperature
covers all the interior of a star with which it is necessary for us to deal,
and we have verified the approximate constancy over a tenfold range of
temperature from star to star. We have verified it for stars presumed to
be of the same mass and therefore subject to the limitation p/T s = con
stant; but that is just the condition satisfied by different parts of the same
star. Thus we have already evidence that our first wild shot is likely to
be a tolerable approximation. We now turn to some results which suggest
that it may be an especially good approximation.
The Approximation rjk = constant.
89. Anticipating the results of the theoretical investigation of absorp
tion in Chapter ix we accept as the law of absorption
kccp/jiT* (89-1),