Republication of: On the physical significance of the Riemann tensor (Reprinted from Acta Physica Polonica, vol 15, pg 389-405, 1956)

This Golden Oldie is a reprinting of a paper by F. A. E. Pirani first published in 1956. It is accompanied by a reprinting of a paper by J. L. Synge first published in 1934. Together these papers pointed the way to the interpretation of geodesic deviation and its relation to the curvature tensor. These two Golden Oldies are accompanied by an Golden Oldie Editorial containing an editorial note written by A. Trautman, and by the biography of F. Pirani written by himself and commented by A. Trautman.