Now let us refer this domain to a random Gauss coordinate system or to
a mollusc 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 behaviour of
measuring-rods, clocks and material points under the influence of the
gravitational field _G_. Hereupon we introduce a hypothesis: that the
influence of the gravitational field on measuring-rods, clocks and
freely-moving material points continues to take place according to the
same laws, even in the case where the prevailing gravitational field is
_not_ derivable from the Galileian special case, simply by means of a
transformation of co-ordinates.
The next step is to investigate the space-time behaviour of the
gravitational field _G_, which was derived from the Galileian special
case simply by transformation of the coordinates. This behaviour is
formulated in a law, which is always valid, no matter how the
reference-body (mollusc) used in the description may be chosen.
This law is not yet the _general_ law of the gravitational field, since
the gravitational field under consideration is of a special kind. In
order to find out the general law-of-field of gravitation we still
require to obtain a generalisation of the law as found above. This can
be obtained without caprice, however, by 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 XV only its energy is
of importance for its effect in exciting a field.
(_c_) Gravitational field and matter together must satisfy the law of
the conservation of energy (and of impulse).
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