taking into consideration the following demands:
(a) The required generalisation must likewise satisfy the general postulate of
relativity.
(b) If there is any matter in the domain under consideration, only its inertial
mass, and thus according to Section 15 only its energy is of importance for its
etfect in exciting a field.
(c) Gravitational field and matter together must satisfy the law of the
conservation of energy (and of impulse).
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 21; 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