Page:The Meaning of Relativity - Albert Einstein (1922).djvu/125

1. The inert mass is proportional to $1+{\overline {\sigma }}$, and therefore increases when ponderable masses approach the test body.

2. There is an inductive action of accelerated masses, of the same sign, upon the test body. This is the term ${\frac {\delta {\mathfrak {A}}}{\delta l}}$.

3. A material particle, moving perpendicularly to the axis of rotation inside a rotating hollow body, is deflected in the sense of the rotation (Coriolis field). The centrifugal action, mentioned above, inside a rotating hollow body, also follows from the theory, as has been shown by Thirring.^[1]

Although all of these effects are inaccessible to experiment, because $\kappa$ is so small, nevertheless they certainly exist according to the general theory of relativity. We must see in them a strong support for Mach's ideas as to the relativity of all inertial actions. If we think these ideas consistently through to the end we must expect the whole inertia, that is, the whole $g_{\mu \nu }$-field, to be determined by the matter of the universe, and not mainly by the boundary conditions at infinity.

For a satisfactory conception of the $g_{\mu \nu }$-field of cosmical dimensions, the fact seems to be of significance that the relative velocity of the stars is small compared to the velocity of light. It follows from this that, with a suit-

1. That the centrifugal action must be inseparably connected with the existence of the Coriolis field may be recognized, even without calculation, in the special case of a co-ordinate system rotating uniformly relatively to an inertial system; our general co-variant equations naturally must apply to such a case.

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