444 SECTIONAL TRANSACTIONS.—A. 
Its equilibrium, it is easy to show, is unstable: an appropriate impulse 
will set it off either expanding or contracting. Now Lemaitre’s theory 
gave no indication as to why it should begin doing the one rather than the 
other. It was the inquiry whether the condensation of the cosmic cloud 
in the Einstein universe into particles would start it expanding, that first 
gave rise to the theory of condensations. 
Unfortunately, the effects produced by the formation of particles on the 
equilibrium of the Einstein universe turned out to be much more numerous 
and complex than appeared at first sight. ‘The reason is that the dis- 
turbance of the equilibrium is a second-order effect : to a firstapproximation 
the formation of the particles has no effect whatever on the equilibrium. 
This so complicates the problem mathematically that no really satisfactory 
method of solution has yet been evolved. Instead attempts have been made 
to decide on more or less a priori grounds which one of the many perturba- 
tions produced by the particle is the predominating one from the point of 
view of upsetting the equilibrium. Lemaitre, for example, has tried to show 
that the presence of the particle never has any direct effect on the equili- 
brium at all, on the ground that the neutral zone surrounding the particle 
must always remain in equilibrium. This neutral zone is the region where 
the gravitational effect of the particle is balanced by that of the cosmic 
cloud. He postulates instead that expansion is due to a diminution in the 
pressure of the cosmic cloud at this neutral zone. Unfortunately, it seems 
doubtful whether particles do actually possess these neutral zones; and, 
moreover, it cannot be proved that there must be a diminution in the pressure 
at the neutral zone, supposing the latter to exist. 
Another investigator, N. R. Sen, has put forward a theory that expansion 
is caused by the very effect Lemaitre disbelieves in, viz. the mere presence of 
particles. Sen neglects all possible counterbalancing effects such as 
changes in pressure in the cosmic cloud, and shows that, under these circum- 
stances, the formation of a particle in the Einstein universe is impossible 
unless expansion sets in. His theory certainly seems more convincing than 
Lemaitre’s, but in both cases you will see that the attempts to solve this 
problem suffer from over-simplification. ‘The most we can say to-day is 
that it is probable that the bubble of our universe began to burst the moment 
those particles we call spiral nebulz started to condense out of the primeval 
cosmic cloud. 
I now pass to another question on which the theory of condensations 
sheds a more certain light. It is the much-debated one of ‘ cosmic’ time. 
The introduction of ‘cosmic’ time into Lemaitre’s universe is directly 
attributable to the Einstein assumption which it satisfies: ‘ All points in 
the universe are equivalent.’ This means, amongst other things, that all 
observers in the universe can differ from one another only in position. It 
then becomes possible to define a sort of time common to all of them, which 
has been called ‘ cosmic’ time, since it allows of the reintroduction of the 
idea of simultaneity of events. Opponents of Lemaitre’s theory of the 
expanding universe, notably E. A. Milne, have spoken as if this ‘ cosmic’ 
time were a consequence, or a necessary ingredient, of the theory. ‘The 
truth is that ‘ cosmic ’ time is an a priori simplification introduced into the 
theory by investigators anxious to make the mathematics easier! 'The 
position becomes clearer if we allow the universe to contain a particle of the 
kind I have tried to describe. Consider an observer in the neighbourhood 
of this particle. His proximity to it marks him out as different from all 
other observers in the universe ; he also has atime peculiar to himself. Now 
it is easy to show that Lemaitre’s theory holds for this observer to a high 
degree of approximation everywhere except near the particle, with the 
