to each other), they will always go at the same rate, no matter where
and when they are again compared with each other at one place.--If
this law were not valid for real clocks, the proper frequencies
for the separate atoms of the same chemical element would not be
in such exact agreement as experience demonstrates. The existence
of sharp spectral lines is a convincing experimental proof of the
above-mentioned principle of practical geometry. This is the ultimate
foundation in fact which enables us to speak with meaning of the
mensuration, in Riemann's sense of the word, of the four-dimensional
continuum of space-time.

The question whether the structure of this continuum is Euclidean,
or in accordance with Riemann's general scheme, or otherwise,
is, according to the view which is here being advocated, properly
speaking a physical question which must be answered by experience,
and not a question of a mere convention to be selected on practical
grounds. Riemann's geometry will be the right thing if the laws
of disposition of practically-rigid bodies are transformable into
those of the bodies of Euclid's geometry with an exactitude which
increases in proportion as the dimensions of the part of space-time
under consideration are diminished.

It is true that this proposed physical interpretation of geometry
breaks down when applied immediately to spaces of sub-molecular
order of magnitude. But nevertheless, even in questions as
to the constitution of elementary particles, it retains part of
its importance. For even when it is a question of describing the
electrical elementary particles constituting matter, the attempt
may still be made to ascribe physical importance to those ideas
of fields which have been physically defined for the purpose