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about a linear fractional transformation of the normal coordinates at every point. * NATIONAL, RESEARCH FULLOW IN MATHIMATICS. 1 Cf. 0. Veblen, these PROCEXDINGS, 8, 1922, p. 192. 2 H. Weyl, Gottinger Nachrichten, 1921, p. 99. 3 A type of normal coordinates invariant under the change (1.1) has been given by 0. Veblen and J. M. Thomas in these PROCEEDINGS, 11, 1925, p. 204. 4 0. Veblen, "Remarks on the Foundations of Geometry," Butt. Amer. Math. Soc., 31 (1925), p. 131. 5 Cf. 0. Veblen and T. Y. Thomas, "The Geometry of Paths," Trans. Amer. Math. Soc., 25, 1923, p. 557. This paper will be referred to as G. 6 G., p. 563. G., p. 562. 8 G., p. 571. 9G., p. 575, formula (12.1). 10 G., p. 560. 11 G., p. 577. 12 G., p. 579, formula (13.16). 13 G., p. 559, formula (5.10). 14 G., P. 559. 15 In an article which appeared after the present paper had been sent to the printer, J. A. Schouten gives the result contained in the first sentence of this theorem. Cf. Trans. Amer. Math. Soc., 27, 1925, p. 453.

A Simple Derivation of Kronecker's Relation among the Minors of a Symmetric Determinant