41 



CHAPTEE III 



MAXWELL'S LAW 



22. Unequal Distribution of Molecular Speed 



THE mean value of the molecular speed given in 13 

 is not the arithmetic mean of all the different values of the 

 speeds with which individual molecules move. The magni- 

 tude G by which the mean value in question is denoted 

 has been denned in 10 to be such that the mean energy 

 of the molecules which strike against the wall would be 

 unaltered if all of them possessed this same speed G instead 

 of their actually different speeds. From this it results that 

 with that equalised distribution the gaseous medium retains 

 the same energy and exerts the same pressure asjvith its 

 actual unequal distribution. 



So long as we are concerned only with the calculation of 

 the pressure and energy, therefore, it is sufficient to ascribe 

 this mean speed to all molecules. But if we wish to in- 

 vestigate more nearly the character of the gaseous state, we 

 have to ask ourselves whether a difference in the values of 

 the speeds is possible, and, further, how these different speeds 

 are actually distributed among the molecules. 



That the equilibrium of a swarm of gaseous molecules 

 in .no way depends on the speed of all the molecules being 

 the same, and that, on the contrary, there must really be a 

 non-uniform distribution of speed among the molecules, can 

 be seen without calculation. For it is easy to prove that if 

 all the molecules had exactly equal speeds at any moment, 

 this distribution of speed would be at once disturbed, and 

 in place of it a non-uniform distribution would be estab- 

 lished. 



Consider, for instance, the case of a moving particle 





