no means so radical as might appear from a hasty examination. For
it is not a difficult task to determine the physical state of a
measuring-rod so accurately that its behaviour relatively to other
measuring-bodies shall be sufficiently free from ambiguity to allow
it to be substituted for the "rigid" body. It is to measuring-bodies
of this kind that statements as to rigid bodies must be referred.

All practical geometry is based upon a principle which is accessible
to experience, and which we will now try to realise. We will
call that which is enclosed between two boundaries, marked upon a
practically-rigid body, a tract. We imagine two practically-rigid
bodies, each with a tract marked out on it. These two tracts are
said to be "equal to one another" if the boundaries of the one tract
can be brought to coincide permanently with the boundaries of the
other. We now assume that:

If two tracts are found to be equal once and anywhere, they are
equal always and everywhere.

Not only the practical geometry of Euclid, but also its nearest
generalisation, the practical geometry of Riemann, and therewith
the general theory of relativity, rest upon this assumption. Of the
experimental reasons which warrant this assumption I will mention
only one. The phenomenon of the propagation of light in empty space
assigns a tract, namely, the appropriate path of light, to each
interval of local time, and conversely. Thence it follows that
the above assumption for tracts must also hold good for intervals
of clock-time in the theory of relativity. Consequently it may be
formulated as follows:--If two ideal clocks are going at the same
rate at any time and at any place (being then in immediate proximity