and its ten separate components, as referred to any definite space-time mesh-system, defined such physical magnitudes as the density of matter at a point, its internal stresses, vis viva, and momentum in that mesh-system. Matter, as a source of gravitation, was obviously described much more completely by this tensor than was the case in classical science, where the mere mention of its density of mass was considered sufficient to determine its gravitational field. Thus, Einstein was in possession of the right-hand side of the equation of gravitation in the interior matter, that corresponding to
in Poisson’s equation (neglecting constants).
It remained to discover the left-hand side of the equation. Owing to the condition of covariance, this left-hand side had to be represented by a tensor of the same order and nature as the right-hand side, hence, in the present case, by a symmetrical tensor of the second order. Further, it would have to be built up of the ten
’s or potentials, expressing a relationship between these ten
’s at every point and at the neighbouring points. It is here that Riemann’s discoveries fit in with Einstein’s requirements; for Riemann and his successors had discovered tensors built up from the fundamental structural tensors of a continuum, namely, from the