We are now in a position to replace the provisional formulation of the general principle of relativity given in Section 18 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 coordinate 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 Gaussion co-ordinate systems are essentially equivalent for the formulation of the general laws of nature.”