Finally, the general principle of relativity permits us to determine
the influence of the gravitational field on the course of all those
processes which take place according to known laws when a gravitational
field is absent _i.e._ which have already been fitted into the frame of
the special theory of relativity. In this connection we proceed in
principle according to the method which has already been explained for
measuring-rods, clocks and freely moving material points.
The theory of gravitation derived in this way from the general
postulate of relativity excels not only in its beauty; nor in removing
the defect attaching to classical mechanics which was brought to light
in Section XXI; nor in interpreting the empirical law of the equality
of inertial and gravitational mass; but it has also already explained a
result of observation in astronomy, against which classical mechanics
is powerless.
If we confine the application of the theory to the case where the
gravitational fields can be regarded as being weak, and in which all
masses move with respect to the coordinate system with velocities which
are small compared with the velocity of light, we then obtain as a
first approximation the Newtonian theory. Thus the latter theory is
obtained here without any particular assumption, whereas Newton had to
introduce the hypothesis that the force of attraction between mutually
attracting material points is inversely proportional to the square of
the distance between them. If we increase the accuracy of the
calculation, deviations from the theory of Newton make their
appearance, practically all of which must nevertheless escape the test
of observation owing to their smallness.
We must draw attention here to one of these deviations. According to
Newton s theory, a planet moves round the sun in an ellipse, which
would permanently maintain its position with respect to the fixed
stars, if we could disregard the motion of the fixed stars themselves
and the action of the other planets under consideration. Thus, if we
correct the observed motion of the planets for these two influences,
and if Newton s theory be strictly correct, we ought to obtain for the
orbit of the planet an ellipse, which is fixed with reference to the
fixed stars. This deduction, which can be tested with great accuracy,
has been confirmed for all the planets save one, with the precision
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