In the author's paper on the Mechanical Action of Heat (Trans. Roy. Soc. Edin., Vol. XX., Part I), the calculations depending on the dynamical equivalent of temperature in liquid water were founded on the experiments of De la Roche and Bérard on the ratio of the apparent specific heat of atmospheric air under constant pressure to that of water. The equivalent thus obtained was about one-tenth part less than Mr Joule's. Since then, the author, having become acquainted with the details of Mr Joule's experiments, has come to the conclusion that Mr Joule's equivalent is correct to about of its amount, and that the discrepancy in question originates chiefly in the experiments of De la Roche and Bérard.