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THE QUANTUM [ X i. 2 
able of separate existence, as Lucretius held) is raised to a natural 
and necessary consequence of the new standpoint. We may 
even reverse the argument, and derive from the ascertained 
atomic constitution of matter a philosophical necessity for the 
assumption of a plenum, in which the ultimate atoms exist as 
the nuclei which determine its strains and motions.” To this 
passage Larmor appends a suggestive footnote. “ It is perhaps 
not superfluous to point out the argument here involved against 
any tendency we might have to assign to the aether itself an 
atomic structure.” 
It is to be remembered that these passages were written 
before the development of the principles of relativity, and no 
doubt their author would at the present time express them 
differently. 
A very interesting discussion of the question of continuity 
in relation to sub-atomic phenomena is to be found in Emile 
Borel’s stimulating volume on Space and Time* He propounds 
the question, whether, seeing that the motion of a solid body 
on which our geometry is based fails us completely on the sub 
atomic scale, we should not try to construct an entirely different 
geometry of a discontinuous character. He suggests that this 
might be a way of attacking the difficulties raised by the theory 
of quanta. 
“ Following up a suggestion made by Riemann, to which, 
however, he did not seem to attach much importance, we might 
also ask whether the property which space seems to possess, of 
being in a sense the more certainly Euclidean the smaller the 
region is which we consider, does not disappear when we reach 
atomic or sub-atomic dimensions. Very small regions may have, 
as it were, a granular structure, and the Euclidean properties 
only hold good as averages.” 
One possible way of describing the discontinuity required by 
the quantum theory is to make the hypothesis that time itself 
is discontinuous, “ Thus the universe would jump suddenly from 
one state to another, but in the interval between it would stand 
at rest. The different instants during which it stayed in the 
same state could not be distinguished from one another, so that 
we should be led to the discontinuous variation of time, to the 
atom of time” (Poincare). 
If, however, we adopt the view held by some supporters of 
the theory of relativity, that time ought not to be separated 
from space, we are led to the hypothesis that the space-time 
world is not a true continuum. With regard to such a sugges 
tion Jeans f remarks : “ The only type of atomicity which rela- 
* Borel, Space and Time (Blackie, 1926). 
t J. H. Jeans, Atomicity and Quanta, pp. 8, 55, 1926.