In this paper the free period of an alternator is considered in relation to the other machines which may be coupled to the busbars, the following cases being examined:-(1) Two alternators working in parallel.(2) Two alternators working in parallel on an infinite busbar.(3) Two alternators working in parallel and connected to an infinite busbar through reactance.(4) Three alternators working in parallel and connected to an infinite busbar through reactance.(5) Three alternators working directly in parallel.(6) Three alternators working in parallel on an infinite busbar.(7) An alternator working on an infinite busbar driving a frequency-changer of the synchronous-motor type supplying an infinite busbar.In case (1) a formula is derived for the natural free period of two machines which may be compared with that of Mr. Everest, † and it is shown that the two machines together have only one resonant frequency.In case (2) it is shown that interaction between machines does not occur when working on an infinite busbar.In case (3) it is shown that two machines connected in parallel and joined to an infinite busbar through a reactance give a resonance, curve exhibiting two peaks.In case (4) the combination is found to be capable of resonant response to three frequencies, while in case (5) only two resonant frequencies appear.With three machines on an infinite busbar [case (6)], confirmation is obtained of case (2), three separate frequencies being present without interaction between the machines.In case (7) two resonant frequencies are found.*