The following statements hold generally: Every physical description resolves itself into a number of statements, each of which refers to the space-time coincidence of two events _A_ and _B_. In terms of Gaussian co-ordinates, every such statement is expressed by the agreement of their four co-ordinates _x_1, _x_2, _x_3, _x_4. Thus in reality, the description of the time-space continuum by means of Gauss co-ordinates completely replaces the description with the aid of a body of reference, without suffering from the defects of the latter mode of description; it is not tied down to the Euclidean character of the continuum which has to be represented. XXVIII. EXACT FORMULATION OF THE GENERAL PRINCIPLE OF RELATIVITY 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._” 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 _x′, y′, z′, t′_, of a new reference-body _K′_. 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.