In a recent paper Einstein has proposed a new type of geometry in which it is possible to give an arbitrary vector in the field a displacement which conserves parallelism at a distance. It may be briefly stated as follows:

Let the metric ofthe space, supposed to be of n dimensions, be given by

At each point of the space we consider a set of n unit vectors, denoted by the n2 quantities phq, which form an orthogonal ennuple such that