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We are now in a position to replace the provisional formulation

of the general principle of relativity given in Section XVIII by

an exact formulation. The form there used, "All bodies of

reference K, K′, etc., are equivalent for the description of

natural phenomena (formulation of the general laws of nature),

whatever may be their state of motion," cannot be maintained,

because the use of rigid reference-bodies, in the sense of the

method followed in the special theory of relativity, is in

general not possible in space-time description. 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._"