And now let us revert to the space-curvature theory of gravitation. Inasmuch as the orbits of free bodies do not present a constant curvature, we should be in the presence of a space of variable curvature from place to place. This in itself is no drawback. But here comes the difficulty: Consider a point
above the earth’s surface, and let
be directed along a vertical. Then the geodesic surface perpendicular to
at
contains all the geodesics passing through