Page:The Meaning of Relativity - Albert Einstein (1922).djvu/96

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84
THE MEANING OF RELATIVITY

We have, first, by (67),

In this, is the value of this quantity at the variable point of the path of integration. If we put

and denote the value of at by , then we have, with sufficient accuracy,

Let, further, be the value obtained from by a parallel displacement along the curve from to . It may now easily be proved by means of (67) that is infinitely small of the first order, while, for a curve of infinitely small dimensions of the first order, is infinitely small of the second order. Therefore there is an error of only the second order if we put

If we introduce these values of and into the integral, we obtain, neglecting all quantities of a higher order of small quantities than the second,

(85)

The quantity removed from under the sign of integration