46 
MR. J. H. JEANS ON THE STABILITY OF A SPHERICAL NEBULA. 
central nucleus in the direction of the opposite radius. Whether or not actual 
separation takes place would probably depend on the amount of the angular velocity. 
It is of interest to compare the result just arrived at, with the corresponding 
result found by Poincare for the motion when an ellipsoid of Jacobi first becomes 
unstable. # This is described as follows :— 
“ La plus grande portion de la matiere semble se rapprocher de la forme spherique, 
tandis cpie la plus petite portion de cette merne matiere sort de l’ellipsoide par 
l’extremite du grand axe, comme si elle voulait se separer de la masse principale.” 
Thus, although the initial motions are, since they start from different configurations, 
necessarily different, yet it would seem as if the final result was very much the same 
in the two cases. In either case we have a diminution of matter in the equatorial 
regions, suggesting the ultimate division of the mass into two, and in each case these 
two masses are of unequal size, a result which could hardly have been foreseen 
without analysis. 
§ 43. If the rate of cooling of a nebula is appreciable, the motion will not be along 
a “series” of equilibrium configurations. The value of p, the frequency which is 
nearest to instability, will be changing at a finite rate, and may run to some distance 
beyond the zero value, before the deviation of the nebula from the spherical shape is 
sufficient to invalidate the analysis of our paper. In this case we can imagine the 
first unstable vibration, that for which p — 0? being overtaken by other unstable 
vibrations of greater and greater frequency, the corresponding velocity of divergence 
* ‘Acta Mathematica,’ vol. 7, p. 347. 
