MR. J. H. JEANS ON THE STABILITY OF A SPHERICAL NEBULA. 
49 
These are equations similar to ( 122 ) and (123); the last term in (136) is different 
from the last term in (123), but both terms agree in being invariably positive. Hence 
it appears that the question of the sign of oq turns, as in § 37, upon the sign of the 
factor (6 — 2 u). We can no longer actually evaluate this factor, as in § 37, but it 
seems to be safe to infer from analogy that it will be positive at every point, and this 
in turn shows that oq must be positive at every point. Hence it appears probable 
that the motion will be that described in § 38. 
Rotating Nebula. 
§ 45. The equations of an unsymmetrical series starting from a symmetrical 
configuration in which there is a finite amount of rotation would be extremely 
complicated, and no attempt to handle them is made in this paper. The correction 
for a small rotation will clearly consist merely of an increase in the terms containing 
the second harmonic, so that the general shape of the curves will be similar to that 
of the last two curves of fig. 3. 
Little difficulty will be experienced in imagining the shape of curves appropriate 
to larger rotations. 
Problems of Cosmic Evolution. 
Infinite Space filled with Matter. 
§ 46. A limiting solution of the equations of equilibrium (corresponding to A = co , 
B = co in equation (114)) gives a nebula in which the density is constant every¬ 
where. This solution may be supposed to represent infinite space filled with matter 
distributed at random. If space has no boundary there is presumably no need to 
satisfy a boundary-equation at infinity, so that p may have any value; if, however, 
this equation must be satisfied the only solution is p = 0. 
Let us consider the former case. Space is filled with a medium of mean density p 
and of mean temperature T. Since the space under consideration is infinite, we may 
measure linear distances on any scale we please, and, by taking this scale sufficiently 
great, we can cause all irregularities in density and temperature to disappear. We 
may, therefore, suppose at once that the density and temperature have the constant 
values p and T. 
The equations of motion for small displacements referred to rectangular axes are, 
in the old notation (cfi. § 6), since V 0 and are constants, 
(137), 
or, operating with d/dx, d/dy, d/dz, and adding 
VOL. CXCIX.—A. H 
(fifi _ _ i/\' dm' 
dt 2 dx p 0 dx ’ 
