perpendiculars can be determined by a series of manipulations with
rigid measuring-rods performed according to the rules and methods laid
down by Euclidean geometry.
In practice, the rigid surfaces which constitute the system of
co-ordinates are generally not available; furthermore, the magnitudes
of the co-ordinates are not actually determined by constructions with
rigid rods, but by indirect means. If the results of physics and
astronomy are to maintain their clearness, the physical meaning of
specifications of position must always be sought in accordance with the
above considerations.[5]
[5] A refinement and modification of these views does not become
necessary until we come to deal with the general theory of relativity,
treated in the second part of this book.
We thus obtain the following result: Every description of events in
space involves the use of a rigid body to which such events have to be
referred. The resulting relationship takes for granted that the laws of
Euclidean geometry hold for distances; the distance being
represented physically by means of the convention of two marks on a
rigid body.
III.
SPACE AND TIME IN CLASSICAL MECHANICS
The purpose of mechanics is to describe how bodies change their
position in space with time. I should load my conscience with grave
sins against the sacred spirit of lucidity were I to formulate the aims
of mechanics in this way, without serious reflection and detailed
explanations. Let us proceed to disclose these sins.
It is not clear what is to be understood here by position and
space. I stand at the window of a railway carriage which is
travelling uniformly, and drop a stone on the embankment, without
throwing it. Then, disregarding the influence of the air resistance, I
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