SIDELIGHTS ON RELATIVITY

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any meaning whatever. In fact the only objective assertion that can
be made about the disc-shadows is just this, that they are related
in exactly the same way as are the rigid discs on the spherical
surface in the sense of Euclidean geometry.

We must carefully bear in mind that our statement as to the growth
of the disc-shadows, as they move away from _S_ towards infinity,
has in itself no objective meaning, as long as we are unable to
employ Euclidean rigid bodies which can be moved about on the plane
_E_ for the purpose of comparing the size of the disc-shadows. In
respect of the laws of disposition of the shadows _L'_, the point
_S_ has no special privileges on the plane any more than on the
spherical surface.

The representation given above of spherical geometry on the
plane is important for us, because it readily allows itself to be
transferred to the three-dimensional case.