In any theory of gravity in which free particles move along the geodesics of a four-dimensional metric tensor, a particular class of metrics can be defined which correspond to the fields of Newton's theory of gravity. In these Newtonian fields the metric coefficients which describe intrinsic properties of space and time are clearly separated from those that describe the gravitational field. This separation suggests an invariance in the gravitational field which is quite similar to the usual Lorentz invariance of electromagnetism. The infinitesimal form of the generalized Lorentz transformation is determined by the fact that the three-dimensional geometry remains Euclidian under the transformation. The finite form is determined so that the transformations form a group, and the group is found to be the usual Lorentz group. The transformation is then applied to fields that are not necessarily Newtonian. 21 pp. Ref. (Author)