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Published online by Cambridge University Press: 24 October 2008
In this paper the method of infinitesimal transformations of coordinates, used by Weyl to determine conditions that a function of the tensors gik and φi, and certain of their derivatives, should be a scalar density, is applied (with certain modifications so as to give tensor relations) to functions of 
and 
. It is known that in order that such a function should be a scalar density it must be a homogeneous function, of degree ½n, of 
, and this must of course be deducible from the equations found by the infinitesimal transformations. In view of the part which these equations may play, as “equations of energy,” etc., in purely affine field theories, it seems desirable that the connection should be explicitly shown, and this is done in § 3.
* Cf. Weitzenböck, Invariantentheorie, p. 358.
(after Schouten)
† Cf. Weyl, , Raum, Zeit, Materie, 5te Aufl., pp. 111, 309Google Scholar; also Weitzenböck, , op. cit., p. 372Google Scholar; Pauli, , Relativitätstheorie, §23.Google Scholar
* When r>s, 
and 
stand for 
and 
.
† A[rs]=½(Ars−Asr) (after Schouten).
* Of. Einstein, , “Zur allgemeinen Relativitätstheorie,” Sitzungsber. der Preuss. Akad., 1928, p. 35.Google Scholar