78 
ME. CLERK MAXWELL ON THE DYNAMICAL THEORY OE GASES. 
Hence if the pressures as well as the temperatures be the same in two gases, 
^ i =— 2 ( 100 ) 
Si ?! 
or the masses 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 consi- 
derations. It is here shown 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 indi- 
vidual 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 15 s 2 are the specific gravities of 
the gases referred to a standard gas. 
If we use 6 to denote the temperature reckoned from absolute zero of a gas thermo- 
meter, M 0 the mass of a molecule of hydrogen, V 2 its mean square of velocity at tempe- 
rature 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 0 s (101) 
Its mean square of velocity, 
Y 2 =iy^ (102) 
Pressure of the gas, 
P=i ?AV» (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 dv) 1 dg nod.) 
Ox dy ~dz 3gBP 
and ^ and all terms of unsymmetrical form will be zero. 
If the mass of gas is of the same temperature throughout there will be no conduction 
of heat, and the equation (94) will become 
fe(3^-|V*|=0, (105) 
or 
= (106) 
q V v 
or 
t=#4 ? (107 ' 
which gives the relation between the density and the temperature in a gas expanding 
