(Force) = (gravitational mass) x (intensity of the gravitational
field),
where the gravitational mass is likewise a characteristic constant
for the body. From these two relations follows:
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If now, as we find from experience, the acceleration is to be
independent of the nature and the condition of the body and always the
same for a given gravitational field, then the ratio of the
gravitational to the inertial mass must likewise be the same for all
bodies. By a suitable choice of units we can thus make this ratio equal
to unity. We then have the following law: The _gravitational_ mass of a
body is equal to its _inertial_ mass.
It is true that this important law had hitherto been recorded in
mechanics, but it had not been _interpreted_. A satisfactory
interpretation can be obtained only if we recognise the following fact:
_The same_ quality of a body manifests itself according to
circumstances as inertia or as weight (lit. heaviness ). In the
following section we shall show to what extent this is actually the
case, and how this question is connected with the general postulate of
relativity.
XX.
THE EQUALITY OF INERTIAL AND GRAVITATIONAL MASS AS AN ARGUMENT FOR THE
GENERAL POSTULATE OF RELATIVITY
We imagine a large portion of empty space, so far removed from stars
and other appreciable masses, that we have before us approximately the
conditions required by the fundamental law of Galilei. It is then
possible to choose a Galileian reference-body for this part of space
(world), relative to which points at rest remain at rest and points in
motion continue permanently in uniform rectilinear motion. As
reference-body let us imagine a spacious chest resembling a room with
an observer inside who is equipped with apparatus. Gravitation
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