38 
MR. J. H. JEANS ON THE STABILITY OF A SPHERICAL NEBULA. 
Let us suppose the temperature of the nebula to be continually cooling, owing 
either to radiation of heat from its surface or to a process of quasi-evaporation such 
as is described in Professor Darwin’s paper (§13 or p. 66). Since the gas (or quasi¬ 
gas) is not a perfect conductor, the nebula will not at any time be in perfect thermal 
equilibrium. The changes in density of all parts, and in the temperature of the 
inner parts of the nebula will, so to speak, lag behind their equilibrium values as 
determined by the changes in the temperature of the outer part of the nebula. It 
is, therefore, clear that so long as the nebula is cooling, the ratio of the density to 
elasticity in the outermost layers of gas will be greater than that calculated upon 
the assumption of perfect equilibrium. This “lag” accordingly decreases the value 
of the stability-function, and so supplies a factor which tends to instability. 
Summary and Discussion of Pvesults. 
§ 34. Let us now examine to what extent we have found solutions of the two 
problems propounded in § 4. 
Firstly, as regards the stability of a spherical nebula of very great size, of which 
the outer surface is maintained at constant pressure. We have found that the 
stability-function for such a nebula (in the limiting case in which the outer radius is 
infinite) has a unit value when the nebula is in equilibrium and at rest. This value 
is increased by allowing for the “ lag’ in temperature caused by the cooling of the 
nebula. It is also increased by a rotation of the nebula, at any rate so long as this 
rotation is small. The nebula will become unstable as soon as the stability-function 
becomes greater than a certain value, which has not been calculated, but is known to 
be between 1 and 1|-. The investigation of § 23 leads us to expect that the critical 
value of the stability-function will increase as P x decreases, although this has only 
been strictly proved for a single case. 
It is therefore possible that, even when the nebula is non-rotating, the temperature- 
lag may be sufficient to make the nebula unstable. If sve disregard the temperature- 
lag, it seems probable that a small rotation will suffice to bring about instability. 
This latter question, however, deserves more detailed examination. 
§ 35. Let us suppose that the nebula starts from rest in a configuration of absolute 
equilibrium, and that the rotation is gradually increased. In this way we obtain a 
linear series of configurations of relative equilibrium. When the rotation is small, 
the configuration, instead of being strictly sjiherical is slightly spheroidal. The 
series we are considering is therefore the analogue of the series of Maclaurin 
spheroids of an incompressible fluid. So long as the rotation remains small, we may 
separate the two terms of the rotation-potential in the manner explained in § 31. 
We may, in fact, suppose our analysis still to apply as if the configuration remained 
spherical, and the only effect of the rotation is to increase the value of the stability- 
function. For larger values of or, all our results are subject to a correction of the 
