Shortly after I read to the Society my paper on “Thermal and Electric Conductivity” (Trans. R. S. E., 1878), in which I stated that the results were “by no means final, even so far as my own work is concerned,” I was requested by Sir Wyville Thomson to undertake the examination of the “Pressure Errors of the ‘Challenger’ Thermometers.” This investigation led to another on the “Compression of Sea-Water,” and allied subjects, which is not yet finished. Meanwhile, though I had prepared everything for my promised repetition of the experiments on Thermal Conductivity, the bars formerly used having been nickelised, &c, I found that it would be impossible for me to carry out the investigation. I therefore asked Mr Mitchell, who, as Neil-Arnott Scholar, had already done good and careful work on Thermal Conductivity in my Laboratory, to repeat the experiments under the altered conditions. I put at his disposal all the apparatus which was employed in the former research. The Government Grant Committee allowed a sum for the payment of a computer to reduce the results, and the observations were at once commenced. The results are now laid before the Society, and are probably as good as the method and the thermometers employed can furnish.