64 THE DYNAMICAL THEORY OF OASES. 



Hence if the pressures as well as the temperatures be the same in two 



= (100), 



/>. P. 



or the mnnnnn of the individual molecules are proportional to the density of 

 the gas. 



This result, by which the relative masses of the molecules can be deduced 

 from the relative densities of the gases, was first arrived at by Gay-Lussac 

 from chemical considerations. It is here shewn to be a necessary result of the 

 Dynamical Theory of Gases ; and it is so, whatever theory we adopt as to 

 the nature of the action between the individual molecules, as may be seen by 

 equation (34), which is deduced from perfectly general assumptions as to the 

 nature of the law of force. 



We may therefore henceforth put - ! for -^ , where s u s, are the specific 



Oj JU. j 



gravities of the gases referred to a standard gas. 



If we use 6 to denote the temperature reckoned from absolute zero of a 

 gas thermometer, M, the mass of a molecule of hydrogen, F ' its mean square 

 of velocity at temperature unity, s the specific gravity of any other gas referred 

 to hydrogen, then the mass of a molecule of the other gas is 



M=M s (101). 



Its mean square of velocity, V* = - V*6 (102). 



Pressure of the gas, P = $-0V t * (103). 



We may next determine the amount of cooling by expansion. 



Cooling by Expansion. 



Let the expansion be equal in all directions, then 



du_dv_dw_ 1 dp 



and -r- and all terms of unsymmetrical form will be zero. 



