The spur \[ G = g^{\mu\nu} G_{\mu\nu} \Tag{(37.5)} \] is called the Gaussian curvature, or simply the \emph{curvature}, of space-time. It \index{Curvature!Gaussian}% \index{Gaussian curvature}% must be remembered, however, that the deviation from flatness is described in greater detail by the tensors $G_{\mu\nu}$ and $B_{\mu\nu\sigma\rho}$ (sometimes called \emph{components of curvature}) and the vanishing of~$G$ is by no means a sufficient condition for fiat space-time. Einstein's law of gravitation expresses the fact that the geometry of an empty region of the world is not of the most general Riemannian type, but is limited. General Riemannian geometry corresponds to the quadratic form~\Eq{(2.1)} with the $g$'s entirely unrestricted functions of the coordinates; Einstein asserts that the natural geometry of an empty region is not of so unlimited a kind, and the possible values of the $g$'s are restricted to those which satisfy the differential equations~\Eq{(37.3)}. It will be remembered that a field of force arises from the discrepancy between the natural geometry of a coordinate-system and the abstract Galilean geometry attributed to it; thus any law governing a field of force must be a law governing the natural geometry. That is why the law of gravitation must appear as a restriction on the possible natural geometry of the world. The inverse-square law, which is a plausible law of weakening of a supposed absolute force, becomes quite unintelligible (and indeed impossible) when expressed as a restriction on the intrinsic geometry of space-time; we have to substitute some law obeyed by the tensors which describe the world-conditions determining the natural geometry. %[** TN: Shortened running head] \Section[The field of an isolated particle]{38.}{The gravitational field of an isolated particle} \index{Gravitational field of a particle}% \index{Particle!gravitational field of}% We have now to determine a particular solution of the equations~\Eq{(37.3)}. The solution which we shall obtain will ultimately be shown to correspond to the field of an isolated particle continually at rest at the origin; and in seeking a solution we shall be guided by our general idea of the type of solution to be expected for such a particle. This preliminary argument need not be rigorous; \PageSep{83} the final test is whether the formulae suggested by it satisfy the equations to be solved.