MR. J. H. JEANS ON THE STABILITY OF A SPHERICAL NEBULA. 
5 
9 
The Evolution o f Planetary Systems. 
§ 49. Let us now regard a single centre, together with the matter collected round 
it, as the spherical nebula which is the subject of discussion. On account of the 
way in which it has been formed, this nebula will, in general, be endowed with 
a certain amount of angular momentum. We have seen that a primitive nebula of 
this kind may be supposed, under certain conditions, to become unstable. We have 
also seen that the motion, when the nebula becomes unstable, is such as to strongly 
suggest the ejection of a satellite. 
As a nebula cools the rotation increases, owing to the contraction of the nebula, 
and fi also increases. Thus the quantity H 2 /3X 2 T 2 , which measures the rotational 
tendency to instability, has a double cause of increase; firstly owing to the increase 
in H, and secondly owing to the decrease in T. We can accordingly imagine the 
primitive nebula becoming unstable time after time, throwing off a satellite each time. 
In the usually accepted form of the nebular hypothesis, the rotation is supposed to 
be the sole cause of instability, so that the system resulting from a single nebula 
ought theoretically to be entirely symmetrical about an axis. On the view of the 
present paper, there is no reason for expecting this symmetry. For large rotations 
of the primitive nebula, the configuration of the resultant planetary system will 
approximate to perfect symmetry, but for small rotations, a slight irregularity 
occurring at the. critical moment, at a point out of the equatorial plane, may produce 
a satellite of which the orbit is far removed from the equatorial plane. 
In conclusion, two particular cases of “ irregularities” may he referred to. If the 
nebula is penetrated by a wandering meteorite, at a moment at which it is close to a 
state of instability, the presence of the meteorite will constitute an irregularity, and 
may easily result in the formation of a satellite. And if a quasi-tide is raised in the 
nebula by the presence of a distant mass, the same result may be produced. In the 
former case, the plane of the satellite would, if the rotation is sufficiently small, 
be largely determined by the path of the meteorite ; in the second case, by the 
position (or path) of the attracting mass. It would not, in either case, depend much 
upon the axis of rotation of the nebula. 
Conclusion. 
§ 50. To sum up, it appears that the behaviour of a gaseous nebula differs in 
at least two important respects from that of an incompressible liquid. In the first 
place, it differs as regards the amount of rotation which is required to produce 
instability, and, in the second place, it differs as regards the disposition of the orbits 
of the planets which will be formed out of the primitive nebula. It will be noticed 
that no definite numerical results have been obtained ; my aim has been to obtain 
qualitative rather than quantitative results, so as to show, if possible, that the 
