The Stability of a Splmncal Nebula. 



455 



are satisfied at every point, = I. Hence the stability or insta- 

 bility of an actual nebula may be regarded as determined by the sign 

 of the algebraical sum of a number of corrections. The signs of these 

 corrections are as follows : — 



(i.) Kotation, however small, tends to instability. 



(ii.) If the nebula is in process of cooling, the configuration at any 

 instant will not be strictly an equilibrium configuration ; the values of 

 some quantities will lag behind their equilibrium values, and this 

 4 ' lag " tends to instability. 



(iii.) Viscosity does not influence the question of stability or in- 

 stability. 



(iv.) A correction is required by the fact that the assumed gas 

 equations cannot remain true for densities below a certain critical 

 value. This can be seen to supply a factor which tends towards 

 stability. 



We conclude that a nebula may become unstable for values of the 

 rotation, which are quite small in comparison with those required in 

 the case of a rotating fluid. 



The instability first enters through a vibration of frequency p = 0, 

 the configuration at this instant corresponding to what Poincare 

 describes as a " point of bifurcation." The subsequent motion consists 

 at first of a condensation of matter about one radius of the nebula, and 

 a rarefaction about the opposite radius. In the later stages there is 

 superimposed upon this a condensation about the axis formed by these 

 two radii, and a rarefaction in the neighbourhood of the corresponding 

 equator. This motion, it will be seen, strongly suggests the ultimate 

 separation of the nebula into two nebulae of unequal size, or, in other 

 words, the ejection of a satellite. 



The influence of rotation in effecting instability will increase as the 

 temperature decreases, and we can imagine the same nebula becoming 

 unstable time after time as it cools, stability being regained each time 

 after the ejection of a satellite. 



If the rotation of the primary is large, the planes of the orbits of 

 the satellites will be almost entirely determined by the direction of 

 the axis of rotation ; for smaller values of the rotation other factors 

 may come into play, so that there is theoretically no limit to the 

 obliquity of the planes of the satellites. For instance, if a slowly 

 rotating nebula, when near to the critical state of neutral equilibrium, 

 is penetrated by a meteorite of sufficient size, the result will be the 

 ejection of a satellite, of which the plane will almost entirely depend 

 on the path of the disturbing meteorite. The same effect may be 

 caused by the attraction of a distant mass, the plane of the satellite 

 depending mainly upon the position or path of this mass. 



