52 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



definition of temperature. We see also from (7) that temperature 

 in a particular gas is directly proportional to either c 2 or [w 2 ]. 



MAXWELL further shows without any assumption as to the 

 nature of the molecules, or the forces acting between them, that 

 the derived law of distribution is valid for any gas mixture, but 

 that is it modified when the gas is exposed to the action of external 

 forces. 



BOLTZMANN found (Wien. Akad. Sitzber. LXXII B, 1875, p. 

 443) for monatomic gases that in spite of the effect of external 

 forces (a) the velocity of any molecule is equally likely to have 

 any direction whatever, (b) the velocity distribution in any element 

 of space is exactly like that in a gas of equal density and temperature 

 upon which no external forces act, the effect of the external forces 

 consisting only in varying the density from place to place as in 

 hydrodynamics. 



BOLTZMANN says this " normal " state is permanent (stationary) 

 for given external conditions because magnitude H does not 

 vary; such a normal state has many configurations, but all agree 

 in having same number of complexions. 



Also, " MAXWELL'S Velocity Distribution is not a state which 

 assigns to each molecule a particular place (locus) and a particular 

 velocity, which are reached say by the locus and velocity of each 

 molecule asymptotically approaching said assigned locus and 

 velocity. With & finite number of molecules MAXWELL'S state will 

 never be exactly but only approximately realized. MAXWELL'S 

 velocity is not a singular one which is confronted by an immense 

 number of non-Maxwellian velocity distributions. On the con- 

 trary, among the immense number of possible velocity distributions 

 by far the greater number possess the characteristics of the 

 MAXWELL velocity distribution." 



MAX PLANCK (Festschrift, p. 113) lucidly dwells on thermal 

 equilibrium, entropy and temperature, as follows: 



" The mechanical significance of the temperature idea is 

 most closely connected with the mechanical significance of entropy, 



