SECTIONAL TRANSACTIONS.—A. | 435 
Thus observation tells us that the galaxies form an expanding system; 
and theory tells us that there is a force of cosmical repulsion which, if not 
counteracted, will produce just such an expansion. So far, so good. But 
there is still a doubt whether the theory has anything to do with the observa- 
tion, because the relativity theory omits to tell us how large the force of 
cosmical repulsion will be. So far as the current theory is concerned, it 
might be imperceptible in the system of the galaxies. ‘Therefore, having 
no idea of the size of the effect, it is rather a big jump to identify it with the 
first thing we come across that looks at all like it. I have tried to contribute 
to the settlement of this question by developing relativity theory (with the 
aid of wave mechanics) in a way which leads to a direct calculation of the 
amount of the cosmical repulsion. I have to begin at the other end of 
things and ask you to consider the mass of an electron. 
By the mass of the electron we mean the mass in C.G.S. units—i.e. in 
terms of the standard kilogram. Accordingly, in any experimental deter- 
mination of the mass of an electron, whatever auxiliary apparatus may be 
employed, there are two indispensables, viz. an electron and the lump of 
metal called the standard kilogram. ‘The experimenter cannot proceed 
without a theory: he reads certain deflections, angles, etc.; but he would 
not know what to do with these, unless a theorist gave him directions 
how to combine them and extract the numerical quantity m out of them. 
What is this theory—these equations which connect the behaviour of 
the two indispensables, the electron and the kilogram mass? ‘The 
experiment will consist of a number of links, and each link will have its 
corresponding theory; at the electron end we shall use microscopic, i.e. 
quantum theory ; at the kilogram end we shall use macroscopic theory, i.e. 
classical mechanics, or, for greater refinement, relativity theory. But there 
must be one link which unites a microscopic mass with a macroscopic mass, 
included neither in quantum theory nor in relativity theory but with one 
‘end in each. It is this link that my investigation supplies. It will be said 
that this link is already known; we know how to make the step from 
microscopic to macroscopic theory, e.g. as in Bohr’s Correspondence 
Principle. Quite so. We know how to do it; it only remains to do it— 
to find what formule result in this particular problem. I do not require 
any new hypothesis in my investigation: it is the mathematical working 
out of principles already accepted. ‘The result is that microscopic and 
macroscopic masses are linked through the equation 
1om® — 136mm + mo? = 
where m is the mass attributed to the single particle and mo is the mass of 
the reference frame to which it is implicitly referred. 
' In passing it may be mentioned that this equation gives two values of m, 
one 1847°6 times the other, which is as nearly as we can tell the ratio of the 
‘mass of the proton to that of the electron. But we are more concerned with 
Mo, which is connected with cosmical magnitudes. I will try to show, by 
‘a short cut, how the mass of the reference frame arises. "The argument will 
probably appear fishy—as short cuts generally are. But I have also found 
the same result by going the long way round. The short cut depends on 
the Uncertainty Principle. 
If we have a particle in space of radius of curvature R and know nothing 
at all about its location, we may express its uncertainty of position as + R; 
‘+ is here an abbreviation for ‘in an unknown direction.’ ‘The particle is 
“distant ’ R from the centre of curvature of space in an unknown direction. 
By the Uncertainty Principle the corresponding uncertainty of momentum is 
+h/2rR ; that is to say, it has a momentum //27R in an unknown direction 
