  A new variational principle for General Relativity, based on an action
functional $I\/(\Phi,\nabla)\/$ involving both the metric $\Phi\/$ and the
connection $\nabla\/$ as independent, \emph{unconstrained\/} degrees of freedom
is presented. The extremals of $I\/$ are seen to be pairs $\/(\Phi,\nabla)\/$
in which $\Phi\/$ is a Ricci flat metric, and $\nabla\/$ is the associated
Riemannian connection. An application to Kaluza's theory of interacting
gravitational and electromagnetic fields is discussed.
