’s in the generalised space-time structure. Accordingly, Weyl constructed an in-invariant which he suggested tentatively as the function of action of the world. In addition to the gravitational and electromagnetic equations which were derived therefrom, the stationary condition of the action (see [Chapter XXXV]) entailed certain electromagnetic equations bearing on the constitution of matter. In the light of these equations, and taking into consideration the fact that matter is always of positive density, Eddington concludes: “It would seem to follow that the electron cannot be built up of elementary electrostatic charges, but resolves itself into something more akin to magnetic charges.”
At this stage, a further generalisation of great elegance was given to Weyl’s geometry by Eddington. Here let us recall that whereas in Einstein’s theory the fundamental elements of space-time structure were ten in number (the ten
’s), and whereas in Weyl’s theory they were fourteen (the ten
’s and the four
’s), in Eddington’s still more general manifold we are confronted with 40 quantities (the forty
’s). It is not that Eddington has introduced new elements of structure into the manifold. Far from it: these elements were present in all the types of manifolds we have discussed. But they were crystallized by restrictions which removed them from the mathematician’s control; and what Eddington has done has been to loosen them. For instance, starting from Eddington’s generalised manifold, if we impose certain restrictions on the forty