1. W. R. Davis andM. K. Moss:Nuovo Cimento,38, 1531, 1558 (1965).
2. W. R. Davis andM. K. Moss:Nuovo Cimento,27, 1492 (1963).
3. In the previous papers of this series (ref. (1,2)), the term « symmetry property » referred to detailed functional form invariance at the co-ordinate level (described by Lie derivatives). However, in the present work the transformations considered do not involve a change of co-ordinates. Therefore, the question of whether a given quantity is altered as a function of the co-ordinates does not arise.
4. As a general reference to this Section, seeL. P. Eisenhart:Riemannian Geometry (Princeton, N. Y., 1926);Non-Riemannian Geometry (New York, 1927);J. A. Schouten:Ricci-Calculus, II Ed. (Berlin, 1954).
5. As a somewhat more general example of such prospective symmetry properties one has the so-called subprojective transformations discussed, for example, byJ. A. Schouten:Ricci-Calculus, II Ed. (Berlin, 1954).