SECTIONAL TRANSACTIONS .—A. 449 
theory must give way to a statistical theory in order to compute the proba- 
bility of the momentum responsible for the rotation of the nebula, and there- 
fore of its more or less elongated shape. The total mass of the nebula is also 
a matter of chance. Some mass might be more probable, and therefore 
more frequent, than another, but nebulze of any mass might exist, and it is 
no longer astonishing that we are living in a fairly large nebula. 
We have used so far in these considerations the two possible types of 
motions which must most probably occur—the ever-expanding type of 
motion for the universe at large, the collapsing type for the nebula itself. 
Between these two types of motion there is an intermediate type, in which 
the motion tends to the equilibrium radius without further contraction or 
expansion. Although this event must be comparatively less probable it 
must some time occur, and we have to investigate what would happen in 
this case. The region under investigation would finally form a part of an 
Einstein universe ; it would be in equilibrium, but in unstable equilibrium. 
As the time-scale is short and the time of disintegration is rather long, at 
least for such a region of large size, we might expect it to survive. We may 
hope that the equilibrium would remain in the mean, but not for every small 
part of the region, so that local condensations must occur and form ordinary 
nebulz by the mechanism we have just described, although the assembly of 
these nebulz would neither contract nor expand. The result will be 
a cluster of nebulz. 
It is possible to test this hypothesis on the origin of the clusters of nebulz. 
If it is true, all clusters must have the same density, and this density must be 
adjusted to the cosmical constant, as in an Einstein universe. The value of 
the theoretical density of a cluster can therefore be computed from Hubble’s 
ratio of the distance to the spectroscopic velocity of the nebule. ‘The data 
are not yet very numerous, but computation for eight clusters, according to 
Hubble’s data, gives concordant results in good agreement with previous 
estimates of the mass of a nebula computed from the spectroscopic rotation 
or the absolute luminosity. If this hypothesis can be definitely tested it 
would practically determine the value of the density of matter in the universe. 
The result is really not new; it simply confirms Hubble’s estimates, but 
although Hubble’s determination was thought to be subject to an uncer- 
tainty of perhaps a factor of one hundred, it would practically turn out to be 
exact. 
Prof. W. DE Sitrer.—A critical discussion of certain solutions. 
