EVOLUTION OF THE UNIVERSE. 587 
apparent contradictions are more satisfactorily hidden from view. But 
this does not affect the theory, which will retain its value independent of 
the interpretations put upon it. 
Prof. Sir ARTHUR Eppineton, F.R.S. 
Discussion of detailed theories of stellar evolution is overshadowed by 
the fact that the time-scale is once again in the melting-pot. I think it 
will be agreed that if Prof. de Sitter is right in the facts he has put before 
us indicating a rapid expansion of the universe or scattering apart of 
the galaxies, the very long time-scale of billions of years which has been 
fashionable of late becomes exceedingly incongruous ; we should have to 
accept an age of the order 10" years for the galaxies, and presumably 
also for the stars. But the theory of the expanding universe is in some 
respects so preposterous that we naturally hesitate before committing 
ourselves to it. It contains elements apparently so incredible that I feel 
almost an indignation that anyone should believe in it—except myself. 
I have had a ‘pecial reason for believing it which I have referred to from 
time to time; but it was not until last month that I was able to put it 
into definite shape. I believe that from pure physical theory we can 
not only predict that this phenomenon of expansion will occur, but also 
predict the actual rate of expansion; and the calculated result agrees 
with the observed recession of the nebulae. This result comes out of 
the wave equation for an electron—the fundamental equation of modern 
quantum theory. When I adapt the wave equation to take account of 
_ the curvature of space I find that it ought to contain a term y N/R, that 
is to say, the square roct of the number of electrons in the universe divided 
by the radius of the universe in its equilibrium state. 
I do not suppose that this is a new term to be inserted as a correction 
_ to the ordinary equation ; it is already in the equation in disguise. It is 
the term attributed to the mass of the electron and ordinarily written 
mele’. 1 think that the President of our section (Sir J. J. Thomson) was 
the first person to measure the mass of an electron. It is safe to say that 
he did not realise in 1897 that the thing he was after—the constant which 
was responsible for the effects in vacuum tubes attributed to mass—was 
the square root of the number of electrons in the universe divided by the 
radius of the universe. Really he was poaching on astronomical preserves. 
He was finding the rate of recession of the spiral nebulae, or at least a 
very little calculation will derive it from his measures. 
I take the value of N/R (or, as he mysteriously called it, mc*/e’) 
according to measurements by him and his successors, and combine it 
with well-known formulae of the relativity theory which Prof. de Sitter 
has been describing; then I can find at once the principal data about the 
size of the universe. For example, its original radius was 1,070 million 
light years before it started to expand. Also N=1:29X 10". And, what 
_ is of special interest, the rate of recession of distant objects can be caleu- 
lated ; the result in the usual units (km. per sec. per megaparsec) is 528. 
This is the whole expansion effect which will be reduced a little by the 
attraction of the galaxies on one another, but the reduction is not likely 
to be large. The value found from astronomical observation by various 
_ investigators ranges from 430 to 550. 
