In March 1869 I communicated to the Society a paper entitled “Motion of a Palladium Plate during the Formation of Graham's Hydrogenium,” which appears in the Proceedings for Session 1868-69. When engaged with this subject many points of interest regarding the behaviour of palladium containing occluded hydrogen, suggested themselves for investigation, and in concluding the paper I remarked “ that careful determinations must be made of the electromotive force, latent heat, &c., of hydrogenium ” before we could arrive at any conclusion regarding the condition of the absorbed hydrogen. Subsequently Professor Tait made a series of determinations on the “ Electrolytic Polarisation of Palladium Electrodes,” devising a new and ingenious method for the purpose. Although at different times subsequent to my first communication, the problem of determining the physical constants of hydrogenium recurred, as my attention was in the meantime directed to the specific heat of carbon at high temperatures, no progress was made with the investigation until September 1872, when the results of my preliminary experiments were communicated to the “ Philosophical Magazine,” under the title, “ Note on the Specific Heat of Hydrogenium.” In that note it is stated that by means of a specially constructed calorimeter the specific heat of hydrogen in palladium is found to be 3.1 per atomic weight, nearly identical with that of gaseous hydrogen. The present paper deals with some of the physical constants of hydrogenium, more especially with the specific gravity, specific heat, and co-efficient of expansion.