Page:The Meaning of Relativity - Albert Einstein (1922).djvu/95

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THE GENERAL THEORY
83

is Euclidean (more generally, if by a suitable choice of co-ordinates the are constants) then the vector obtained at as a result of this displacement does not depend upon the choice of the curve joining and . But otherwise, the result depends upon the path of the displacement. In this case, therefore, a vector suffers a change, (in its direction, not its magnitude), when it is carried from a point of a closed curve, along the

curve, and back to . We shall now calculate this vector change:

As in Stokes' theorem for the line integral of a vector around a closed curve, this problem may be reduced to the integration around a closed curve with infinitely small linear dimensions; we shall limit ourselves to this case.