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of transmission c relative to the embankment and relative to the train
? This question leads to a quite definite positive answer, and to a
perfectly definite transformation law for the space-time magnitudes of
an event when changing over from one body of reference to another.

Before we deal with this, we shall introduce the following incidental
consideration. Up to the present we have only considered events taking
place along the embankment, which had mathematically to assume the
function of a straight line. In the manner indicated in Section 2
we can imagine this reference-body supplemented laterally and in a
vertical direction by means of a framework of rods, so that an event
which takes place anywhere can be localised with reference to this
framework. Fig. 2 Similarly, we can imagine the train travelling with
the velocity v to be continued across the whole of space, so that
every event, no matter how far off it may be, could also be localised
with respect to the second framework. Without committing any
fundamental error, we can disregard the fact that in reality these
frameworks would continually interfere with each other, owing to the
impenetrability of solid bodies. In every such framework we imagine
three surfaces perpendicular to each other marked out, and designated
as " co-ordinate planes " (" co-ordinate system "). A co-ordinate
system K then corresponds to the embankment, and a co-ordinate system
K' to the train. An event, wherever it may have taken place, would be
fixed in space with respect to K by the three perpendiculars x, y, z
on the co-ordinate planes, and with regard to time by a time value t.
Relative to K1, the same event would be fixed in respect of space and
time by corresponding values x1, y1, z1, t1, which of course are not
identical with x, y, z, t. It has already been set forth in detail how
these magnitudes are to be regarded as results of physical

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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