D O C U M E N T 2 4 6 A U G U S T 1 9 2 8 2 3 9 246. From Roland Weitzenböck[1] Laren (N. H.), Holland, “Klein Wohnfried,” 1 August 1928 Dear Colleague, I have read your two notes from the 7th and the 14th of June, 1928, in the Berlin Sitzungsberichten[2] with great interest, and I take the liberty of sending you some remarks about them here. For brevity, I refer to the notes as I and II. 1) The connection components in I, formula (7a), which you call , were first referred to in my Encyclopedia article III E1, in Comment 59 to No. 18 [3] in more detail in my theory of invariants (1923) (Groningen: Noordhoff), p. 317 ff.[4] The theory of the parallel displacement and that of the differential invariants based on an n-Bein frame are furthermore treated by: (1924) G. Vitali, Atti della Soc. Ligustica II, p 248–253[5] (1925) " " " " " " IV, p. 287–291[6] (1925) G.F.C. Griss, Dissertation Amsterdam p. 11, 25 ff.[7] (1926) M. Euwe, " "[8] (1927) E. Bortolotti, Proceedings Kgl. Ak. d. Wetenschappen 30,[9] (26. Feb. 1927) (1927) " " , Rendiconti Lincei V, 6a May 1927, p. 741–747 [10] and finally, (1927) L. P. Eisenhart, Non-Riemannian Geometry New York (Amer. Math. Soc.)[11] 2)[12] With regard to the rotational invariance that you require: It can be shown that every action function (“Hamilton function”), and thus every function I that is invariant under the generalized transform[ation] and under rotations, can be constructed from and the covariant derivatives obtained from the , of the tensor . I thus contains no more vectors explicitly. Furthermore, one can readily show that is the only function of zeroth or- der, and that there is no I of first order that is linear in the . All the I of first order which are quadratic in the are given by: (is found in your note I, p 7 and in II (1a)) ( " " " " " " in II, p. 6) x x h h a g , g = .... h a I h = I 1 g = I 1 g gg =