The Gauss co-ordinate system has to take the place of the
body of reference. The following statement corresponds to the
fundamental idea of the general principle of relativity: "All Gaussian
co-ordinate systems are essentially equivalent for the formulation of
the general laws of nature."
We can state this general principle of relativity in still another
form, which renders it yet more clearly intelligible than it is when
in the form of the natural extension of the special principle of
relativity. According to the special theory of relativity, the
equations which express the general laws of nature pass over into
equations of the same form when, by making use of the Lorentz
transformation, we replace the space-time variables x, y, z, t, of a
(Galileian) reference-body K by the space-time variables x1, y1, z1,
t1, of a new reference-body K1. According to the general theory of
relativity, on the other hand, by application of arbitrary
substitutions of the Gauss variables x[1], x[2], x[3], x[4], the
equations must pass over into equations of the same form; for every
transformation (not only the Lorentz transformation) corresponds to
the transition of one Gauss co-ordinate system into another.
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