The vibrations here referred to, are those which with their accompanying sounds were first observed by Mr Arthur Trevelyan, and communicated to this Society in a paper published in the 12th vol. of their Transactions. The author of the present paper undertook the inquiry as soon as the remarkable fact was announced by Mr Trevelyan, and was induced to prosecute it to a considerable extent experimentally, in consequence of being dissatisfied with the only plausible explanation yet offered,–that of the successive expansions of the cold metal by the hot one at the point of contact at each successive vibration, which was conceived to afford the necessary impulse or maintaining power.