  I state and prove, in the context of a space having only the metrical and
affine structure imposed by the geometrized version of Newtonian gravitational
theory, a theorem analagous to that of Weyl's for a Lorentz manifold. The
theorem says that a projective structure and a suitably defined compatible
conformal structure jointly suffice for fixing the metric structure of a
Newtonian spacetime model up to constant factors, and for fixing its affine
structure as well. The theorem allows one to give a natural, physically
compelling interpretation of the spatiotemporal geometry of a geometrized
Newtonian gravity spacetime manifold, in close analogy with the way Weyl's
Theorem allows one to do in general relativity.
