SECTIONAL TRANSACTIONS.—A. 443 
principle here employed differs from the homogeneity principle of rela- 
tivistic cosmology in that it compares the world-wide experiences of observers 
with one another, whereas the homogeneity principle compares merely their 
local experiences. But the theory here outlined agrees in many quantitative 
respects with the general relativity theories. It avoids, however, such 
predictions as the possibility of closed light-circuits, or the prediction of the 
ultimate dissolution of the universe into causally disconnected systems. All 
roads lead to heaven, or, at worst, those which lead elsewhere are paved with 
good intentions. 
Dr. G. C. McVirr1e.—Condensations of matter in an expanding 
universe. 
In the expanding universe theory as originally developed by Lemaitre it 
was assumed that a fair approximation to the actual universe could be 
obtained by treating all the matter in the universe as if it were evenly spread 
out in space so as to form a cosmic cloud. Like a gas or fluid, this cosmic 
cloud is characterised by possessing a definite density and pressure at each 
point. But actually the matter in the universe is not evenly spread out in 
space : it occurs in the form of discrete masses, such as the spiral nebulz or 
the stars, separated by regions of comparatively empty space. The question 
therefore arises : Can the theory of the expanding universe be adjusted so 
as to take account of the discontinuous distribution of matter in the universe ? 
The answer to this question is found to be closely bound up with a number 
of problems left unsolved by the theory of Lemaitre. 
We have, then, to substitute for Lemaitre’s cosmic cloud a set of discrete 
massive ‘ particles,’ as I shall call them, or condensations of thecosmic cloud. 
Put mathematically, we have to find, by solving the equations of general 
relativity, the metric of a universe occupied by an arbitrary number of 
discrete particles. At the very outset it must be admitted that no one has 
yet succeeded in doing this. Even if we assume that there are only two 
particles in the universe, the problem proves intractable. So we try to 
dodge the difficulty in the following way : we concentrate our attention on 
one particle and smooth outall the others so that their material forms a cosmic 
cloud of the type imagined by Lemaitre. Thus our solitary particle, instead 
of being surrounded by empty space in which other particles occur here and 
there, is surrounded by a cosmic cloud which fills practically the whole 
universe. It turns out that the equations of general relativity are soluble 
for such a case. The solution is not, however, unique: various types of 
single particles surrounded by cosmic clouds are possible. One particle, 
for instance, is of constant mass ; another grows at the expense of the cosmic 
cloud. Moreover, the presence of the particle causes changes in the density, 
pressure and state of flow of the cosmic cloud in its immediate neighbour- 
hood, Further away, however, these disturbances become quite negligible, 
and the universe approximates closely to the completely smoothed-out 
universe of Lemaitre’s theory. 
Having obtained these solutions, we can now turn to the problems 
already mentioned which were left untouched by Lemaitre’s theory. The 
chief of these is, perhaps, the question of the disturbance of the equilibrium 
of the Einstein universe. It is probable that our own universe started to 
expand from a state of equilibrium in which the cosmic cloud had constant 
density everywhere and approximately zero pressure. Space was also 
spherical and closed. Such a state of affairs had been known long before 
Lemaitre’s theory was thought of, under the name of the Einstein universe. 
