The possibility of the existence of an electron in space is a remarkable phenomenon which we do not yet understand. The details of its structure must be determined by some unknown set of equations, which apparently admit of only two discrete solutions, the one giving a negative electron and the other a positive electron or proton. If we solve these equations to find \PageSep{154} the radius of the electron in any direction, the result must necessarily take the form \begin{quote} radius of electron in given direction $=$ numerical constant $\times$ some function of the conditions in the space into which the electron was inserted. \end{quote} And since the quantity on the left is a directed length, the quantity on the right must be a directed length. We have just found one directed length characteristic of the empty space in which the electron was introduced, viz.\ the radius of spherical curvature of a corresponding section of the world. Presumably by going to third or fourth derivatives of the~$g_{\mu\nu}$ other independent directed lengths could be constructed; but that seems to involve an unlikely complication. There is strong ground then for anticipating that the solution of the unknown equations will be \begin{quote} radius of electron in any direction $=$ numerical constant $\times$ radius of curvature of space-time in that direction. \end{quote} This leads at once to the law~\Eq{(66.3)}. As with the electron, so with the atom and aggregations of atoms forming the practical units of material structure. Thus we see that Einstein's law of gravitation is the almost inevitable outcome of the use of material measuring-appliances for surveying the world, whatever may be the actual laws under which material structures are adjusted in equilibrium with the empty space around them. Imagine first a world in which the curvature, referred to some chosen (non-material) standard of measurement, was not isotropic. An electron inserted in this would need to have the same anisotropy in order that it might obey the same detailed conditions of equilibrium as a symmetrical electron in an isotropic world. The same anisotropy persists in any material structure formed of these electrons. Finally when we \emph{measure} the world, i.e.\ make comparisons with material structures, the anisotropy occurs on both sides of the comparison and is eliminated. Einstein's law of gravitation expresses the \index{Einstein's law of gravitation!interpretation of}% result of this elimination. The symmetry and homogeneity expressed by Einstein's law is not a property of the external world, but a property of the operation of measurement. From this point of view it is inevitable that the constant~$\lambda$ cannot be zero; so that empty space has a finite radius of curvature relative to familiar standards. An electron could never decide how large it ought to be unless there existed some length independent of itself for it to compare itself with.