SIDELIGHTS ON RELATIVITY

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Let us imagine a point _S_ of our space, and a great number
of small spheres, _L'_, which can all be brought to coincide with
one another. But these spheres are not to be rigid in the sense
of Euclidean geometry; their radius is to increase (in the sense
of Euclidean geometry) when they are moved away from _S_ towards
infinity, and this increase is to take place in exact accordance
with the same law as applies to the increase of the radii of the
disc-shadows _L'_ on the plane.

After having gained a vivid mental image of the geometrical
behaviour of our _L'_ spheres, let us assume that in our space there
are no rigid bodies at all in the sense of Euclidean geometry, but
only bodies having the behaviour of our _L'_ spheres. Then we shall
have a vivid representation of three-dimensional spherical space,
or, rather of three-dimensional spherical geometry. Here our spheres
must be called "rigid" spheres. Their increase in size as they
depart from _S_ is not to be detected by measuring with