It is far beyond the scope of these lectures to report on the development of the ideas, first of Restricted, then of General, Relativity and to show how they are logically built on the outcome of a number of crucial experiments, as the aberration of the light of fixed stars, the Michelson-Morley experiment, certain facts regarding the light from visual binary stars, the Eötvös-experiments which ascertained to a marvellously high degree of accuracy the universal character of the gravitational acceleration—that is to say that in a given field it is the same for any test-body of whatever material.

Yet before going into details about the metrical (or Riemannian) continuum, I wish to point out the main trend of thought that suggests choosing such a one as a model of space-time in order to account for gravitation in a purely geometrical way. In this I shall not follow the historical evolution of thought as it actually took place, but rather what it might have been, had the idea of affine connexion already been familiar to the physicist at that time. Actually the general idea of it emerged gradually (in the work of H. Weyl, A. S. Eddington and Einstein) from the special sample of an affinity that springs from a metrical (Riemannian) connexion—emerged only after the latter had gained the widest publicity by the great success of Einstein's 1915 theory. Today, however, it seems simpler and more natural to put the affine connexion, now we are familiar with it, in the foreground, and to arrive at a metric by a very simple specialization thereof.