It is easy to see that these physical conditions are precisely those which we have found to exist in a gravitational field produced by matter. The straightest type of mesh-system around a point (namely, a semi-Cartesian mesh-system) would correspond to that of the observer in the falling elevator or in the hollow projectile, since for an observer in a frame of this type the force of gravitation disappears in the immediate interior of his frame, but reappears at more distant points. Further, space-time being curved, its geodesics would no longer be Euclidean straight lines. They would still appear approximately straight when referred to a semi-Cartesian mesh-system in the immediate neighbourhood of the point for which the mesh-system was approximately one of equal four-dimensional cubes; but their curvature would become more and more apparent when we surveyed them from this same mesh-system in more distant regions. The physical interpretation of this geometrical fact would be afforded by the seemingly uniform and rectilinear motion of free bodies and rays of light in the immediate neighbourhood of the falling elevator when viewed by an observer situated in this falling frame, and by the apparent acceleration of these bodies in regions more distant from the falling elevator. It is therefore obvious that the existence of a non-Euclideanism of [Pg 264] space-time around matter would betray itself physically in exactly the same way as a field of gravitation produced by matter.[85] Assuming this generalisation to be correct, we see that no essential difference can exist between a field of gravitation and one of inertia. Both types of field arise from a relationship between the mesh-system adopted by the observer, and the fundamental structure of the space-time continuum. The only difference that exists is that in interstellar space far from matter, space-time being flat, it is always possible to select a Cartesian mesh-system corresponding to a Galilean system in which no field of force is present, whereas in the neighbourhood of matter, owing to the inherent curvature of space-time, the nearest approach to Galilean frames is given by semi-Cartesian or semi-Galilean frames (falling elevator). In such frames the field of force cannot vanish throughout the frame at more or less distant points.