The constitution and evolution of the stars

92 Recent Advances in Stellar Astronomy
referring to the argument by which Lane’s Law was
proved, we see that a smaller increase of temperature than
is demanded by this law will enable it to meet the changing
conditions resulting from contraction. Indeed, a point will
in time be reached, when no further rise of temperature
at all is needed, the decreased compressibility of the dense
gas taking the whole load. Beyond this the increased
pressure due to contraction acting alone will be insufficient
to produce the necessary increase in density, and a fall in
temperature must complete the adjustment.

We see, therefore, that a sphere of real gas, contracting
under its own gravitation, will follow Lane’s Law only
while its density is small. As it contracts further its tem-
perature will rise more slowly than this law indicates,
reach a maximum, and then gradually diminish. During
this long process, the model upon which the mass is built
will itself gradually change—the increase of density toward
the centre diminishing—but this will not alter the general
character of the phenomena. We may at least say with
confidence that the surface temperature, as well as that in
the interior, will reach a maximum and then diminish, un-
til at last the mass will shrink nearly to the greatest density
which it can possibly attain, and end by cooling off almost
like a solid body. During the early stages, while the
temperature is rising, the body will be of large diameter.
As it contracts its surface will diminish, but its surface
brightness will increase, so that the amount of light which
it gives out will not change much. It will, however, grow
whiter as it gets hotter, until it reaches its maximum attain-
able temperature. By this time it will be much smaller
in diameter than at the start, but only a little fainter. But
after it begins to fall in temperature, while still contract-
ing, the situation is different. There are now fewer square

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