SIDELIGHTS ON RELATIVITY

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measuring-rods, any more than in the case of the disc-shadows on
_E_, because the standards of measurement behave in the same way as
the spheres. Space is homogeneous, that is to say, the same
spherical configurations are possible in the environment of all
points.* Our space is finite, because, in consequence of the
"growth" of the spheres, only a finite number of them can find room
in space.

* This is intelligible without calculation--but only for the
two-dimensional case--if we revert once more to the case of the disc
on the surface of the sphere.

In this way, by using as stepping-stones the practice in thinking
and visualisation which Euclidean geometry gives us, we have acquired
a mental picture of spherical geometry. We may without difficulty
impart more depth and vigour to these ideas by carrying out special
imaginary constructions. Nor would it be difficult to represent the