the value of -1, which it had in flat space-time, we obtain approximately Newton’s law. It is then the deviation of
from the value -1 which is the distinguishing feature of Einstein’s law of gravitation. But it is obvious that
was not adjusted for the mere satisfaction of accounting for Mercury’s motion, since its value follows mathematically from the integration of
.
We may also add that the gravitational equations
are not linear. In ordinary language, this means that the resultant field produced by two masses cannot be obtained by superposing the two separate fields; additional cross-terms must also be taken into consideration. In the case of weak fields, however, these cross-terms may be neglected, so that in practice a superposition of separate fields is possible. Nevertheless, owing to this non-linearity of the gravitational equations, the problem of two bodies (when neither of the masses may be neglected) presents insurmountable mathematical difficulties. And so it happens that the problem of double stars, so easy to solve in Newtonian science, has as yet failed to receive a solution in the case of Einstein’s law of gravitation.