A scalar-tensor theory of gravitation is constructed using the Weyl formulation of Riemannian geometry. The scalar field is given an important geometrical role to play and is related to the integrable change in length of a vector as it is transported from point to point in space-time. The geometry uses modified covariant derivatives and a metric tensor which is not covariantly constant. The field equations can be written down very simply in terms of a modified curvature tensor. The theory agrees with the usual Lagrangian formalism in its experimental predictions and offers a reformulation or reinterpretation of the transformation of units considered by Dicke.

• Received 15 July 1971

DOI:https://doi.org/10.1103/PhysRevD.5.284