The following paper contains the results of an inquiry which has occupied me at intervals for somewhere about ten years. It was carried out in part at the expense of the British Association, and I have already reported results to that body in 1869 and 1871. But these provisional reports referred to very short ranges of temperature only, and the experiments were made with faulty thermometers, for which I had not the corrections which had been carefully determined by Welsh at Kew. The inquiry arose from my desire to extend to other metals the very beautiful and original method which Principal Forbes devised, and which the state of his health prevented him from applying to any substance but iron. Forbes' experiments gave a result so very remarkable, and (as it seemed to me) so theoretically suggestive, that I wished to extend them to other pure metals, and also, in one or two cases at least, to alloys. I believe that Principal Forbes had at least two reasons for undertaking his investigations:—(1.) When he commenced his inquiry, there was no really accurate or trustworthy determination of the absolute conductivity of any body whatever for heat. (2.) FORBES had himself, in 1833 and subsequent years, pointed out a very remarkable analogy between the conducting powers of metals for electricity and for heat, and had shown that these were almost precisely proportional to one another—that is to say, that the list of the average relative conductivities of different metals for electricity differed, from that of their relative conductivities with regard to heat, certainly not more than did the several electric lists furnished by different experimenters, and certainly less than the corresponding thermal lists. Hence it was natural to suppose that temperature might have a marked effect on thermal conductivity, as it was known to have such an effect on electric conductivity.