142 JAMES CLE11K MAXWKU, 



"There exists a positive function belonging to a 

 group of molecules which, as they settle themselves 

 into a steady state on the average derived from a 

 great number of configurations maintains a steady 

 downward trend. The Maxwell-Boltxinann steady state 

 is the one in which this function has finally attained 

 its minimum value, and is thus a unique steady state, 

 it still being borne in mind that this is only a pro- 

 position of averages derived from a great number of 

 instances in which nothing is conserved in encounters, 

 except the energy, and that exceptional circumstances 

 may exist, comparatively very few in number, in 

 which the trend is, at any rate, temporarily the 

 other way." 



This theorem, when applied to cases of motion, 

 such as that of a gas at constant temperature en- 

 closed in a rigid envelope impermeable to heat, 

 appears to be proved. For such a case, therefore, 

 the Maxwell-Boltzmunn law is the only one possible. 



But whether this be so or not, the h;w tirst intro- 

 duced by Maxwell is one of thoso possible, and the 

 advance in molecular science due to its introduction 

 is enormous. 



We come now to the second result, the equal 

 partition of the energy among all the degrees of 

 freedom of each molecule. Lord Kelvin has pointed 

 out a flaw in Maxwell's proof, but Boltzmann showed 

 (Philosophical Mayaz in <?, March, 189.T) how this flaw 

 can easily bo corrected, and it may be said that in all 

 cases in which the Bolumann-Maxwell law of the 

 distribution of velocities holds, Maxwell's law of the 

 equal partition of energy holds also. 



