SIDELIGHTS ON RELATIVITY

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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
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