n,
since the pressure of a gas decreases when the temperature falls, the
pressure beneath the superficial layer of the gas will decrease, while
the gravitation is unaltered. The consequence will inevitably be that
the gravitation will now conquer the pressure, and the globe of gas will
accordingly contract. There is, however, another way in which we can
look at the matter. We know that heat is equivalent to energy, so that
when the globe radiates forth heat, it must expend energy. A part of the
energy of the globe will be due to its temperature; but another, and in
some respects a more important, part is that due to the separation of
its particles. If we allow the particles to come closer together we
shall diminish the energy due to separation, and the energy thus set
free can take the form of heat. But this drawing in of the particles
necessarily involves a shrinking of the globe.

And now for the remarkable consequence, which seems to have a very
important application in astronomy. As the globe contracts, a part of
its energy of separation is changed into heat; that heat is partly
radiated away, but not so rapidly as it is produced by the contraction.
The consequence is, that although the globe is really losing heat and
really contracting, yet that its temperature is actually rising.[43] A
simple case will suffice to demonstrate this result, paradoxical as it
may at first seem. Let us suppose that by contraction of the sphere it
had diminished to one-half its diameter; and let us fix our attention on
a cubic inch of the gaseous matter in any point of the mass. After the
contraction has taken place each edge of the cube would be reduced to
half an inch, and the volume would therefore be reduced to one-eighth
part of its original amount. The law of gases tells us that if the
temperature be unaltered the pressure varies inversely as the volume,
and consequently the internal pressure in the cube would in that case be
increased eightfold. As, however, in the case before us, the distance
between every two particles is reduced to one-half, it will follow that
the gravitation between every two particles is increased fourfold, and
as the area is also reduced to one-fourth, it will follow that the
pressure inside the reduced cube is increased sixteenfold; but we have
already seen that with a constant temperature it only increases
eightfold, and hence the temperature cannot be constant, but must rise
with the contraction.

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