372 
The Galactic System of Stars [ch. xiv 
closed surfaces is quite small, then the stars inside it form an approximately 
permanent system, although there is a continual slow loss of stars across this 
surface. If however the density at the last closed surface, and so also at the 
first open surface, is not quite small, there will be a rapid loss across these 
surfaces, the stars streaming off in all directions in their efforts to establish 
the law of density (343‘4), and as the velocity of many of these is, by 
formula (343‘3), greater than the velocities of escape V(2F), a great part of 
the loss is permanent. 
The escaping stars are of high velocity and so take away more than their 
due share of angular momentum, so that in time the value of <w may become 
so small that the system assumes a nearly spherical shape with only slight 
escape of stars. It seems probable that the globular star clusters may be 
formations of this kind. 
The galactic system may possibly be going through a process of the kind 
just described, but if so it cannot be anywhere near its final state. 
The question naturally suggests itself as to whether the spiral nebulae 
admit of interpretation, in terms of the foregoing conceptions, as clouds of 
stars on their way to a steady state. The elliptical nebulae have, as we have 
seen, surfaces whose equations are of the form of (343‘5), so that to this 
extent they admit of interpretation as rotating clouds of stars. But the spiral 
nebulae do not, since such an interpretation fails to explain the concen 
tration of stars in the equatorial plane of the nebula. If the lenticular 
central part of a spiral nebula consists of stars, then by formula (3434) the 
star-density will be uniform over the whole surface of this lens, and since the 
velocities are also fairly uniform, stars will stream away in approximately 
equal numbers from all parts of the surface. The stars can in no way be 
restricted either to escaping only in the equatorial plane or to moving only 
in that plane after they have escaped. For this reason we cannot interpret 
the inner parts of the spiral nebulae as clouds of stars, and must fall back on 
the explanation already given in Chapter xm. As the spiral nebulae appear 
from all available evidence to be merely an extension of the series of elliptical 
nebulae, this indicates that the latter also must be interpreted as clouds of gas. 
The Dynamics of Moving Clusters. 
346. We have seen that the general gravitational field of the galactic 
system as a whole can adequately explain both the general random motion of 
the stars and their ordered motion of star-streaming. Apart from these motions, 
groups of stars, the “moving clusters,” are seen pursuing a steady motion 
through the random motion of the surrounding stars, all the stars of a cluster 
moving with approximately parallel and equal velocities so that the cluster 
retains its identity. This phenomenon of course admits of dynamical dis 
cussion.