  The equations of parallel transport for a non-linear connection on phase
space are examined. It is shown that, for a free-particle Lagrangian, the
connection term first-order in momentum reproduces the geodesic equation of
General Relativity and the term zeroth-order in the momentum reproduces the
Lorentz electromagnetic force law. Hence from one mathematical expression, a
non-linear parallel transport equation, one can derive the interaction laws for
both the gravitational and electromagnetic forces. These equations are free of
the difficulties associated with formalism of Weyl, which forms the basis for
the theory of Yang and Mills.
