This may not seem obvious at first; it may be thought that a
disturbance which only affected a small area of gas would only produce
a condensation of small extent. Such an argument overlooks the way
in which the gravitational pull of a small body acts throughout
the universe. The moon raises tides on the distant earth, and also
tides, although incomparably less in amount, on the most distant of
stars. Each time the child throws its toy out of its baby-carriage,
it disturbs the motion of every star in the universe. So long as
gravitation acts, no disturbance can be confined to any area less than
the whole of space. The more violent the disturbance which creates
them, the more intense the condensations will be to begin with, but
even the smallest disturbance must set up condensations, although
these may be of extremely feeble intensity. And we have seen that the
fate of a condensation is not determined by its intensity but by its
size. No matter how feeble their original intensity may have been, the
big condensations go on growing, the small ones disappear. In time
nothing is left but a collection of big condensations. The mathematical
analysis already referred to shews that there is a definite minimum
weight such that all condensations below this weight merely dissipate
away into space. To a good enough approximation for our present
purpose, this minimum weight is such that if a tenth of this weight of
gas were isolated in space, and all the rest of the gas annihilated,
the molecules would just and only just fail to escape from its
surface[20].
[20] This is near enough, but not absolutely accurate. Exact
mathematical analysis shews that the weight of the minimum condensation
_M_ is given by
____ _C_³
_M_ = ³√⅓πκ ———————,
³√γ √ρ
where _C_, γ, ρ, κ are the molecular velocity, gravitation constant,
initial density, and ratio of specific heats, whereas the weight from
which molecules moving with velocity _C_ just fail to escape is given by
3 _C_³
_M_ = —— —————————.
4π ³√γ √ρ
With κ = 1⅔ the minimum weight of condensation is 9·7 times the weight
which is just adequate to retain the molecules.
We may say that the original uniformly distributed mass of gas was
“unstable” because any disturbance, however slight, causes it to change
its configuration entirely; it had the dynamical attributes of a stick
balanced on its point, or of a soap-bubble which is just ready to burst.
Public-domain text, read in full here on John Shaqi.
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