Some animadversions on the general laws relative to the phenomena of heat, announced in my elements of Chemical Philosophy (page 13) then follow, together with a table drawn up to show the discordance between the air thermometer and the mercurial thermometer, both being graduated in the manner I proposed in the said elements. On these points I may have to remark in the sequel. The first part of the Essay concludes with some remarks to shew why a preference should be given to the air thermometer, or more strictly, the thermometer whether of mercury or any other body, supposed to be graduated so as to correspond with an air thermometer of equal degrees. The Second Part of the Essay is on _The Laws of Refrigeration_. Adopting the air thermometer as the most eligible measure of temperature, Messrs. Dulong and Petit proceed to investigate the laws of the refrigeration of bodies, under a great variety of circumstances, in _vacuo_ and in air or gases of different kinds and densities. The inquiry abounds with experiments and observations evincing great skill and acuteness; but which it will not suit our purpose to detail. It may suffice for us to give a general summary of the Laws deduced by them from their experiments, at the same time recommending all those who feel sufficient interest in the subject to peruse the essay at large, which exhibits a profound philosophical train of experiments, the results of which are illustrated by the aid of mathematical generalization. “_Law 1._ If one could observe the cooling of a body placed in a vacuum, and surrounded by a vessel absolutely destitute of heat, or otherwise deprived of the power of radiating heat, the velocities of cooling would decrease in geometrical progression when the temperatures diminished in arithmetical progression.” “_Law 2._ The temperature of a vessel containing a vacuum being constant, and a body being placed in it to cool, the velocities of cooling for excesses of temperature in arithmetical progression, decrease as the terms of a geometrical progression diminished by a constant number. The ratio of this progression is the same for the cooling of all kinds of bodies, and is equal to 1.0077.” “_Law 3._ The velocity of cooling in a vacuum for the same excess of temperature, increases in geometrical progression, the temperature of the vessel circumscribing the vacuum increasing in an arithmetical progression. The ratio of the progression is the same as above, namely 1.0077 for all kinds of bodies.” “_Law 4._ The velocity of cooling due to the sole contact of a gas is entirely independent of the nature of the surface of the cooling bodies.” “_Law 5._ The velocity of cooling due to the sole contact of a gaseous fluid varies in a geometrical progression, while the excess of temperature itself varies in a geometrical progression. If the ratio of this second progression be 2, that of the first is 2.35, whatever be the nature of the gas and its elastic force.”