1821.] Phenomena of Heat, Gases, Gravitation, S)i\ 347 



sure at the temperature of water boiling as 8 to 11. Therefore^ 

 granting the truth of our principles, the temperature of water 

 freezing is to that of water boiUng in the subduphcate ratio of 

 8 to 1 1 ; that is, nearly in the ratio of 6 to 7 ; or, more nearly, in 

 that of 100 to 117, or that' of 579 to 679. 



Cor. 4. — Because the temperatures are in the same gas as the 

 velocities, the spaces occupied at equal elasticities are as the 

 square of the velocities. 



Cor. 5. — It has been demonstrated by the experiments of phi- > 

 Josophers, that the volumes of mercury and air, under the same 

 pressure, go on pari passu within certain limits ; namely, from 

 about — 36 of centigrade to nearly 150. There- 

 fore, let A B be a common mercurial thermome- 

 ter, of which F is the freezing and B the boiling 

 point of water; and let the tube, or a line by the 

 side of it, be continued to the point C, so that 

 B C : F C :: 11 : 8 ; and let C B be made the 

 axis of a parabola, whose vertex is C ; then will 

 any semiordinate M P, between the limits / 

 <~ 36) and L (nearly 150), drawn from the sur- 

 face M of the mercury, represent the tempera- 

 ture of the body in which the thermometer is 

 plunged ; and C M the volume, due to the ex- 

 pansion of air under the same temperature 

 pressure. 



From these circumstances it appears, that the measures which 

 have been taken by MM. Dulong and'Petit, in their late memoir 

 on the communication of heat, are not proportional to the tem- 

 peratures, as they imagine, but to the squares of the temper- 

 atures. 



Cor. 6. — Since, if the temperatures are the same, the volumes 

 are inversely proportional to the elasticities, it follows that the 

 volumes being the same, the squares of the temperatures are as 

 the elasticities. Hence, therefore, the same results would be 

 obtained by measuring the temperatures by the elasticities, under 

 an invariable volume, as by the volumes under an invariable 

 <iompression, which is conformable to what MM. Dulong and 

 Petit say they have found from experiment. This same inference 

 I had drawn from theory several years before Dulong and Petit 

 had made, or at least had published their experiments; and upon 

 this principle I had contrived a thermometer by means of hydro 

 gen and mercury, the description of which I have by me. 



Scholium. 



In the preceding theorems and their corollaries, we have not con* 

 sidered whether the media be homogeneous or not, or whether their, 

 particles be similar or dissimilar. The theorems are totally inde- 

 pendent of all considerations of homogeneity or similarity, and 



and a uniform 



