Two possible ways of generalising our geometrical outlook are open. It may be that the Riemannian geometry assigned to actual space is not exact; and that the true geometry is of a broader kind leaving room for the vector~$\kappa_{\mu}$ to play a fundamental part and so receive geometrical recognition as one of the determining characters of actual space. For reasons which will appear in the course of this chapter, I do not think that this is the correct solution. The alternative is to give all our variables, including~$\kappa_{\mu}$, a suitable graphical representation in some new conceptual space---not actual space. With sufficient ingenuity it ought to be possible to accomplish this, for no hypothesis is implied as to the nature of the quantities so represented. This generalised graphical scheme may or may not be helpful to the progress of our knowledge; we attempt it in the hope that it will render the interconnection of electromagnetic and gravitational phenomena more intelligible. I think it will be found that this hope is not disappointed. In \Title{Space, Time and Gravitation}, Chapter~\Vol{XI}, Weyl's non-Riemannian geometry has been regarded throughout as expressing an amended and exact Natural Geometry. That was the original intention of his theory\footnotemark.\footnotetext {The original paper (\Title{Berlin.\ Sitzungsberichte}, 30~May 1918) is rather obscure on this point. It states the mathematical development of the corrected Riemannian geometry---``the physical application is obvious.'' But it is explicitly stated that the absence of an electromagnetic field is the necessary condition for Einstein's theory to be valid---an opinion which, I think, is no longer held.} For the present we shall continue to develop it on this understanding. But we shall ultimately come to the second alternative, as Weyl himself has done, and realise that his non-Riemannian geometry is not to be applied to \emph{actual} \index{Non-Riemannian geometry}% space-time; it refers to a graphical representation of that relation-structure which is the basis of all physics, and both electromagnetic and metrical variables appear in it as interrelated. Having arrived at this standpoint we pass naturally to the more general geometry of relation-structure developed in Part~II of this chapter.% \PageSep{198}%