An elementary illustration of this would be given by considering a curved surface of two dimensions, such as that of a sphere. On a sphere we can trace an infinite variety of mesh-systems, but none of these mesh-systems is made up of equal Euclidean squares. The nearest approach to a network of squares would be afforded by a mesh-system [Pg 263] of meridians and parallels. But even a mesh-system of this sort could be likened to a network of equal squares only in the immediate vicinity of the equator. As we examined our mesh-system at regions farther and farther removed from the equator, we should notice that the meridians had a tendency to run closer and closer together, so that the quadrilaterals bounded by the meridians and parallels would depart more and more in shape from those of Euclidean squares. In the general case, where we consider an arbitrarily curved surface and no longer a uniformly curved one, such as a sphere, it could be shown that the straightest type of mesh-system compatible with the surface was assimilable to one of squares only around a point, and not, as in the case of a sphere, along a line (such as the equator). The point could be selected arbitrarily, and our pseudo-straight mesh-system drawn around this point accordingly. We see, therefore, that if space-time is unevenly curved or unevenly non-Euclidean, the nearest approach to a Cartesian mesh-system around any given point could be approximately Cartesian only in a restricted region around this point. As we moved away from this point in our mesh-system, its curvilinear characteristics would become more and more pronounced. So far as the ’s of space-time are concerned, this would imply that in a region where curvature was present these ’s could maintain constant values only in the more or less immediate neighbourhood of a point. Expressed in terms of fields of force, this assertion is equivalent to stating that in a region of space-time curvature it would be quite impossible to rid ourselves of a field of force throughout space. We might annul it at the point and in its immediate neighbourhood, but the field of force would reappear for more distant regions.