The longitudinal oscillation of “light” springs carrying loads, in various combinations, has a well-established place in all mechanics textbooks, but none of the standard works appear to deal thoroughly with the oscillation of a spring whose mass is not negligible. The purpose of this note is to investigate the vertical longitudinal oscillation of a heavy spring, first by itself and secondly when carrying a load. It will be seen that in each case the motion consists not of a single S.H.M. (as for the light spring), but an infinite number of S.H.M.s ; when the spring oscillates by itself the frequency of these S.H.M.s are multiples of a fundamental frequency, but when the spring carries a load the frequencies are not so simply related.