14 PRESSURE OF GASES 27 



experiment. This comparison leads to a definition of the 

 nature of temperature in reference to the conceptions under- 

 lying our theory. 



The empirical law, discovered nearly simultaneously by 

 Gay-Lussac 1 and Dalton, 2 which expresses the de- 

 pendence of the pressure of a gas on its temperature, is 

 contained in this amended form of Boyle's law, viz. : 



where p and p denote the pressure and density as before, 

 $ is the temperature C., k a constant, and a the thermal co- 

 efficient of expansion, or, more correctly, the coefficient of 

 increase of pressure. 3 



From this and the formula proved before, viz. 



p = 



we obtain the value of Jc by taking the temperature $ = 0, 

 thus finding 



k = i\ 



where denotes the mean molecular speed at the tempera- 

 ture 3 = 0; and it further necessarily follows that the 

 square of the molecular speed G increases in linear proportion 

 with the temperature 3, the relation between them being 



G 2 = 2 (1 + oS). 



We thus find that the square of the molecular speed of a gas, 

 and therefore the kinetic energy of its molecular motion, 

 increases proportionally with the temperature. The speed 

 itself is given by 



-I- aty- 



This law is in complete agreement with the conclusion 

 obtained in 9 from Bernoulli's theory, viz. that the 

 kinetic energy of the molecular motion is the mechanical 

 measure of heat and temperature. 



1 Annales de Chimie et de Physique, xliii. 1802, p. 137 ; Gilb. Ann. xii. 1802, 

 p. 257. 



2 Mem. of the Manch. Lit. and Phil. Soc. v. 1802, p. 595 ; Gilb. Ann. xii. 

 1802, p. 310. 



3 See 46. 



