صفحة 136 من 212

In this case relations hold in the four-dimensional continuum

which are analogous to those holding in our three-dimensional

measurements.

However, the Gauss treatment for ds2 which we have given above is

not always possible. It is only possible when sufficiently small

regions of the continuum under consideration may be regarded as

Euclidean continua. For example, this obviously holds in the case

of the marble slab of the table and local variation of

temperature. The temperature is practically constant for a small

part of the slab, and thus the geometrical behaviour of the rods

is almost as it ought to be according to the rules of Euclidean

geometry. Hence the imperfections of the construction of squares

in the previous section do not show themselves clearly until this

construction is extended over a considerable portion of the

surface of the table.