Quaternions applied to physics in non-euclidean space. 1 - The mathematical methods.

The utility of quaternions in mathematical physics in non-Euclidean space is much the same as in Euclidean, that is to say they are suitable for establishing fundamental relations. Details must be worked out by some system of scalar coordinates. It is hoped that the applications, to Physics, for which the methods of this paper have been prepared, will appear in subsequent papers; but, quite naturally, it has been found that the methods alone demand for exposition more space than can be placed at the writer's disposal for the first paper of the series.