584 DISCUSSION ON THE 
the beginning of the evolution of the universe is to be measured in billions 
of years, or perhaps in thousands of billions. I do not propose to discuss 
the question whether there ever was a beginning. It suffices for my 
argument to define the ‘ beginning’ as that state of the universe and its 
A 
constituent parts which we are with our present knowledge and theories — 
content to use as a starting-point, beyond which we do not wish, or are 
not able, to extend our investigations. 
It is in accordance with this slowness of the evolution of the universe— 
or I should rather say of the constituent parts of the universe, galaxies and 
stars—that the universe was, until very recently, assumed to be practically 
in a state of equilibrium. Accordingly, a theory of the universe, in order 
to find popular favour, had to be static. Some may have felt inclined to 
disagree with this generally adopted attitude, but if they ventured to 
cecnfess their dissenting views at all, they did so rather diffidently. A 
static solution of the fundamental equations of the theory of relativity 
was what was asked for. 
The choice was between two possible statical solutions, which I have 
been in the habit of calling the solutions A and B, but which may be better 
distinguished by the names of the ‘ static’ and the ‘empty’ universe. 
Einstein’s solution, the ‘ static ’ universe, was a genuine statical solution. 
The other one was essentially non-static, but, as a consequence of its 
emptiness, it could parade in the garb of a static one. Both of these, 
however, failed to represent the observed facts in the actual universe, 
which is neither empty nor static, since it is full of galactic systems, 
which are all moving with large and systematic velocities. The way out 
of this dilemma has been shown by Prof. Lemaitre, whose brilliant dis- 
covery, the ‘ expanding universe,’ was discovered by the scientific world 
about a year and a half ago, three years after it had been published. 
It is not necessary to explain this theory in detail here. It has become 
widely known by technical and popular expositions in many periodicals. 
The principal point of it is that it shows the observed radial motions of 
the spiral nebulae to be in accordance with an isotropic, homogeneous, 
but non-static solution of the field equations of the general theory of 
relativity, or, we can say, to be a pure effect of the inertia of these bodies. 
The static solution, in which inertia leaves the relative distances of different 
material bodies (statistically) unchanged, is shown to be unstable. The 
actual universe must therefore be represented by one of the non-static 
solutions. In these, the change at a certain moment may be either an 
expansion or a contraction. Observation shows that at the present 
moment we are on an expanding branch. The solutions are arranged in 
families. In some, the universe contracts to a finite minimum radius 
and then starts to expand again; in others, this minimum is zero, in other 
solutions again the radius oscillates between zero and a finite maximum 
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value in a, rather short, period. These oscillating solutions, however, — 
require a density exceeding that which is indicated by our knowledge of 
the distribution of matter in our neighbourhood. 
I must lay stress on the fact that, in using the words ‘ universe,’ 
‘radius,’ “ expansion,’ etc., we are really speaking metaphorically, putting 
an interpretation on the equation of the theory, which is by no means 
imperative. There occurs in the equation a certain quantity, which may 
