MR. J. H. JEANS ON THE STABILITY OF A SPHERICAL NEBULA. 
3 
which lends itself well to mathematical treatment. The principal difficulty lies in 
finding a system which shall satisfy the ordinarily assumed gas equations, and shall 
at the same time give an adequate representation of the primitive nebula of 
astronomy. 
If we begin by supposing a nebula to consist of a gas which satisfies at every 
point the ordinarily assumed gas equations, and to be free from the influence of all 
external forces, then the only configuration of equilibrium is one which extends to an 
infinite distance, and is such that the nebula contains an infinite mass of gas. The 
only alternative is to suppose the gas to be totally devoid of thermal conductivity, 
and in this case there is an equilibrium configuration which is of finite size and 
involves only a finite mass of gas. But the assumption that a gas may be treated as 
non-conducting finds no justification in nature. When we are dealing, as in the 
present case, with changes extending through the course of thousands of years, we 
cannot suppose the gas to be such a bad conductor of heat, that any configuration, 
other than one of thermal equilibrium, may be regarded as permanent. 
Professor Darwin has pointed out that a nebula which consists of a swarm of 
meteorites may, under certain limitations, be treated as a gas of which the meteorites 
are the “ molecules.”* In this quasi-gas the mean time of describing a free path must 
be measured in days, rather than (as in the case of an actual gas) in units of 
10~ 9 second. The process of equalisation of temperature will therefore be much 
slower than in the case of an actual gas, and it is possible that the conduction of heat 
may be so slow that it would be legitimate to regard adiabatic equilibrium as 
permanent, t 
Except for this the mathematical conditions are identical, whether we assume the 
gaseous or meteoritic hypothesis. The present paper deals primarily with a nebula in 
which the equilibrium is conductive, but it will be found possible from the results 
arrived at, to obtain some insight into the behaviour of a nebula in which the 
equilibrium is partially or wholly convective. 
§ 4. Whether we suppose the thermal equilibrium of the gas to be conductive or 
adiabatic, we are still met by the difficulty that the gas equations break down over 
the outermost part of the nebula, through the density not being sufficiently great to 
warrant the statistical methods of the kinetic theory. This difficulty could be avoided 
by supposing that the nebula is of finite size, and that equilibrium is maintained by 
a constant pressure applied to the outer surface of the nebula. If this pressure is so 
great that the density of gas at the outer surface of the nebula is sufficiently large to 
justify us in supposing that the gas equations are satisfied everywhere inside this 
surface, then the difficulty in question will have been removed. On the other hand, 
this pressure can only be produced in nature by the impact of matter, this matter 
* G. H. Darwin, lor. tit., ante. 
t Ibid., p. 64. 
