Acceleration, on the other hand, is connected with the metrical
’s of space-time; and these, of course, subsist regardless of the presence or absence of matter, since they represent aspects of the structure of absolute space-time itself. We thus understand how it comes that acceleration manifests itself as absolute. Mach’s views lead us to ascribe the existence of these
’s of acceleration not to space-time itself, but to the totality of the matter of the universe. Under this aspect the
-distribution acquires the likeness of a species of ether conditioned by matter, which in turn conditions the behaviour of bodies in space and the evolution of phenomena in time. It should be emphasised, however, that rash philosophical conclusions on these and kindred subjects should be avoided. In the present state of our knowledge, even the most competent of scientists are far from having succeeded in solving all these arduous problems.
APPENDIX III
THE GRAVITATIONAL EQUATIONS
FROM a purely mathematical point of view, without any regard to physical applications, we may always select a co-ordinate system, or mesh-system, in a continuum regardless of whether the continuum be Euclidean or non-Euclidean. As referred to this co-ordinate system, the position of every point of the continuum is defined by its co-ordinates
