PHILOSOPHICAL TRANSACTIONS. 
I. The Stability of a Spherical Nebula . 
By J. H. Jeans, B.A ., Fellow of Trinity College, and Isaac Newton Student in the, 
University of Cambridge. 
Communicated by Professor G. H. Darwin, F.R.S. 
Received June 15,—Read June 20, 1901. Revised February 28, 1902. 
Introduction. 
§ 1. The object of the present paper can lie best explained by referring to a sentence 
which occurs in a paper by Professor G. H. Darwin. # This is as follows :— 
“ The principal question involved in the nebular hypothesis seems to be the 
stability of a rotating mass of gas; but, unfortunately, this has remained up to now 
an untouched field of mathematical research. We can only judge of probable results 
from the investigations which have been made concerning the stability of a rotating 
mass of liquid. ” 
In so far as the two cases are parallel, the argument by analogy will, of course, be 
valid enough, but the compressibility of a gas makes possible in the gaseous nebula a 
whole series of vibrations which have no counterpart in a liquid, and no inference as 
to the stability of these motions can be drawn from an examination of the behaviour 
of a liquid. Thus, although there will be unstable vibrations in a rotating mass of 
gas similar to those which are known to exist in a rotating liquid, it does not at all 
follow that a rotating gas will become unstable, in the first place, through vibrations 
which have a counterpart in a rotating liquid : it is at any rate conceivable that the 
vibrations through which the gas first becomes unstable are vibrations in which the 
compressibility of the gas plays so prominent a part, that no vibration of the kind 
can occur in a liquid. If this is so, the conditions of the formation of planetary 
systems will be widely different in the two cases. 
With a view to answering the questions suggested by this argument, the present 
paper attempts to examine in a direct manner the stability of a mass of gravitating 
gas, and it wall be found that, on the whole, the results are not such as could have 
been predicted by analogy from the results in the case of a gravitating liquid. The 
* “ On the Mechanical Conditions of a Swarm of Meteorites, and on Theories of Cosmogony,” ‘ Phil. 
Trans.,’ A, vol. 180, p. 1 (1888). 
VOL. CXCIX.—A 312. B 
31.7.02. 
