Page:Relativity (1931).djvu/139

XXIX

THE SOLUTION OF THE PROBLEM OF GRAVITATION ON THE BASIS OF THE GENERAL PRINCIPLE OF RELATIVITY

F the reader has followed all our previous I considerations, he will have no further diffculty in understanding the methods leading to the solution of the problem of gravitation.

We start off from a consideration of a Galileian domain, i.e. a domain in which there is no gravitational field relative to the Galileian reference-body $K$. The behaviour of measuring-rods and clocks with reference to $K$ is known from the special theory of relativity, likewise the behaviour of “isolated” material points; the latter move uniformly and in straight lines.

Now let us refer this domain to a random Gauss co-ordinate system or to a ‘‘mollusk” as reference-body $K'$. Then with respect to $K'$ there is a gravitational field $G$ (of a particular kind). We learn the behaviour of measuring-rods and clocks and also of freely-moving material points with reference to $K'$ simply by mathematical transformation. We interpret this behaviour as the

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