These are the results which we must weave into the general model of space-time, unless we reject Einstein’s postulate of equivalence, and maintain that fields of gravitation produced by matter have no more in common with fields of inertia than they have with electromagnetic fields, for instance. The postulate of equivalence, as we have seen, appears to be justified owing to the empirical fact that the two types of masses are identical. But we now propose to show that quite independently of this empirical fact, even if the postulate of equivalence had never been stated in a specific manner, a natural mathematical generalisation of the geometry of space-time would have led us indirectly to exactly the same identification of forces of inertia and gravitation. Accordingly, let us recall briefly the results we arrived at in Chapter XXIII when we examined the origin of forces of inertia in our space-time model. We remember that space-time was assumed to be perfectly flat, so that its geodesics were Euclidean straight lines when referred to Cartesian mesh-systems of equal four-dimensional cubes. These Cartesian mesh-systems, splitting up space-time into mutually perpendicular rectilinear directions, constituted the geometrical representations of our methods of breaking up space-time into space and time for purposes of referring our measurements to Galilean systems of reference. In these Cartesian mesh-systems the ’s of space-time maintained constant values throughout, and the numerical values of these ’s represented the potentials of the field of inertial force. These potentials being constants, remaining unchanged in value from [Pg 262] point to point in our Cartesian systems, no field of force could be present; and this was in full accord with what we know of Galilean systems, since these systems are characterised by the total absence of all such fields. Furthermore, as all free bodies and light waves followed geodesics in space-time according to the requirements of Least Action, and as these geodesics when referred to Cartesian systems were straight lines, free bodies and light waves would always appear to follow straight lines with constant speeds when observed from Galilean frames. This was in accord with Newton’s law of inertia.