66 MOLECULAK MOTION AND ITS ENERGY 33 



33. Maxwell's Law for a Gas in Motion 



./ In the simple form in which we have hitherto used it, 

 Maxwell's law of distribution rests on the assumption that 

 the gas is in equilibrium and at rest as a whole. Hitherto, 

 we have always assumed that there is no other motion in 

 the gas than the invisible to-and-fro motion of its par- 

 ticles. Beside this molecular motion, the effect of which 

 we perceive only in the pressure and heat of the gas, there 

 should be no directly perceptible motion, no flow, no rota- 

 tion, no change of the volume occupied ; there should, 

 therefore, be no sort of cause for the centroid of the whole 

 mass of gas to change its position, nor, indeed, for that of 

 any portion of the gas of finite magnitude ; only the single 

 atoms -were endowed with independent motions, which they 

 executed without disturbing the equilibrium of the gas as 

 a whole. 



If we discard this assumption Maxwell's law must be 

 modified, and the necessary modification in a special simple 

 case is easy to see. If we impart to the whole mass of gas 

 and its containing vessel a uniform motion of translation, 

 there is no reason at all for any change in the to-and-fro 

 motion of the molecules. Both motions, the molecular and 

 the molar, will exist together without mutually disturbing 

 each other. If we compound them by the known rule of 

 the parallelogram of velocities, we get for each molecule the 

 direction and magnitude of the velocity with which it moves 

 when the gas as a whole is in translatory motion. Herewith, 

 then, the law of distribution for this case is determined. It 

 does not seem necessary to express here in mathematical 

 formulae l this more general law ; for the more general law 

 is easily to be deduced from Maxwell's known law of dis- 

 tribution. If we diminish, that is to say, the actual velocity 

 of a molecule by the velocity of translation of the centroid of 

 the gas as a whole, Maxwell's simple law for the probability 

 of a definite speed again comes to view. It is obvious that 

 the subtraction of the velocity of the centroid of the whole 

 gas from that of a molecule amounts to bringing the prin- 



1 See 16*, 17* of the Mathematical Appendices. 



