MR. J. H. JEANS ON THE STABILITY OF A SPHERICAL NEBULA. 
47 
from spherical symmetry becoming continually greater. It is therefore quite 
conceivable that the motion may become adiabatic at an early stage, and it is possible 
that it may be better imagined as a collapse or explosion, rather than as a gradual 
slipping from a spherical state of equilibrium into and through a series of 
unsynnnetrical states of equilibrium. 
But an examination of the physical character of the motion will show that in this 
extreme case, as also in any intermediate case, the motion must be, in its essentials, 
the same as that which has been found for the other extreme case, namely, that of 
infinitely slow cooling and perfect thermal equilibrium. In the spherical state, the 
outermost layers of gas may be regarded as stretched out in opposition to their 
gravitational attractions, being maintained in this state by the elasticity of the gas. 
The balance between these two agencies (which is, speaking loosely, measured by the 
stability function, u x ) must be supposed to be continually changing, and instability 
always results from the same cause, namely, that the elasticity of these outer layers 
becomes inadequate to resist the gravitational tendency to collapse. In every case 
the outer layers concentrate about a single radius of the nebula, the axis of harmonics 
(6 = 0 in equation (72)) and so increase the pressure along this radius, while 
decreasing that along the opposite radius (6 = tt). This pressure acting upon the 
inner layers of gas and the core sets them in motion, and in this way we have the 
tendency to separation into two nebulae. 
A Nebula in “ Isothermal-adiabatic ” Equilibrium. 
§ 44. A nebula which consists of an isothermal nucleus with a layer in convective 
equilibrium above it, is said to be in “ isothermal-adiabatic ” equilibrium. At the 
surface at which the law changes from the adiabatic to the isothermal, the quantities 
<77. T and p must all be continuous. 
The isothermal part is capable of executing a vibration of frequency p = 0 while 
remaining in isothermal equilibrium throughout, provided the forces acting upon it 
from the adiabatic part are the same as would act if the adiabatic part were replaced 
by an isothermal part in such a way that the whole made up an infinite isothermal 
nebula. If the nebula is rotating, the amplitude of vibration of the infinite nebula 
will vanish at infinity proportionally to some inverse power of r, this power increasing 
with the rotation. For sufficiently large rotations, the vibrations may be regarded 
as inappreciable except over the original isothermal nucleus, so that the vibration is 
approximately unaltered when the outer layers are again replaced by layers in 
convective equilibrium. 
We see, therefore, that an “ isothermal-adiabatic ” nebula may become unstable, for 
sufficiently large rotations, through a vibration of order n— I. No attempt is made 
to obtain any numerical results. We can, however, follow up the subsequent motion 
in the same way as in the case of an isothermal nebula. 
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