In reference to the experiments of Dulong and Petit, on the relative expansions of air and mercury by heat, I have no doubt their results are good approximations to the truth. My former experiments were chiefly made in temperatures between 32° and 212°, and I found, as General Roi had done, the expansion of air to be somewhat greater in the lower half than in the upper half of that interval, compared with mercury. On a repetition of the experiments, I think the difference is less than I concluded it to be, and I find that the like coincidence of the air scale and mercurial, continues down to near freezing mercury; at least the difference will not be so great as my new table of temperature makes it at page 14. I have made some experiments on the expansions of air above 212°, which lead me to adopt the results of Dulong. On a comparison of the air and mercurial thermometer upon the laws which I pointed out, namely, the former expanding in geometrical progression to equal intervals of temperature, and the latter expanding as the square of the temperature reckoned from its freezing point, it appears that in the long range of 600° from freezing water to boiling mercury, the greatest deviation of the two thermometers does not exceed 22°. However, the great deviation of the scales between the temperatures of freezing water and freezing mercury, is sufficient to shew, as Dulong and Petit have observed, that their coincidence is only partial. Like the scales of air and mercury, which are so nearly coincident from -40° to 212° that scarcely any difference is sensible, though no one doubts of its existence; yet afterwards the differences become obvious enough, and the greater the farther we advance. _Expansion of Mercury._ See page 34, vol. I. I have overrated the expansion of glass bulbs (as will be seen presently,) and hence that of mercury; my expansion of mercury corrected on account of the glass, will be ¹/₅₃ nearly, which leaves it still greater than Dulong’s. The 2nd table of Dulong is valuable, on account of its affording us information of the rate of expansion in the higher degrees of temperature, from a given or standard air thermometer. _Iron, Copper, and Platina._