The authors consider her a generalization of known results relating to the curvature vectors of a pair of mutually orthogonal curve systems on a general two-dimensional surface S2 in hyperspace. Several phases of this generalization have been given in papers presented from time to time  but the more connected account here given seems desirable. The generalization is of a two-fold nature: first, to vector systems, or curve systems, in n dimensions, and second, to systems not necessarily orthogonal.
 The paper in the form here offered is the outgrowth of work begun in two papers presented to the Society: First normal spaces in Riemannian geometry, by Nola L. Anderson, presented at Lawrence, Kansas, December 1, 1928, and Invariant normals to a space Sn contained in a function space, by Nola L. Anderson and Louis Ingold, presented at Des Moines, Iowa, December 31, 1929. All the results had been secured and the general organization had been discussed, before the sad death of Professor Ingold on January 25, 1935.