Just as we have generalised the equations of physics originally found for Galilean coordinates, so we could generalise the equations for the natural gauge by substituting the corresponding in-tensor equations applicable to any gauge. But before doing so, we stop to ask whether anything would be gained by this generalisation. There is not much object in generalising the Galilean formulae, so long as Galilean coordinates are available; we required the general formulae because we discovered that there are regions of the world where no Galilean coordinates exist. Similarly we shall only need the in-tensor equations of mechanics if there are regions where no natural gauge exists; that is to say, if no gauge-system can be found for which \PageSep{207} Einstein's formulae are accurately true. It was, I think, the original idea of Weyl's theory that electromagnetic fields were such regions, where accordingly in-tensor equations would be essential. There is in any case a significant difference between Einstein's generalisation of Galilean geometry and Weyl's generalisation of Riemannian geometry. We have proved directly that the condition which renders Galilean coordinates impossible \emph{must} manifest itself to us as a gravitational field of force. That is the meaning of a field of force according to the definition of force. But we cannot prove that the break-down of the natural gauge would manifest itself as an electromagnetic field; we have merely speculated that the world-condition measured by the vector~$\kappa_{\mu}$ which appears in the in-tensor equations may be the origin of electrical manifestations \emph{in addition} to causing the failure of Riemannian geometry.