regarding Distribution of Kinetic Energy. 



467 



A 



Suppose now A, B, C to be all moving to and fro. The 

 collisions between B and the equal bodies A and C on its two 

 sides must equalize, and keep equal, the 

 average kinetic energy of A, immediately 

 before and after these collisions, to the ave- ^jilll-ir 

 rage kinetic energy of G. Hence, when the 

 times of A being in the space between H 

 and K are included in the average, the 

 average of the sum of the potential and kinetic 

 energies of A is equal to the average kinetic 

 energy of C. But the potential energy of A 

 at every point in the space H K is positive, 

 because, according to our supposition, the 

 velocity of A is diminished during every time 

 of its motion from H towards K, and in- 

 creased to the same value again during motion 

 from K to H. Hence, the average kinetic 

 energy of A is less than the average kinetic 

 energy of C ! 



This is a test-case of a perfectly represen- 

 tative kind for the theory of temperature, and 

 it effectually disposes of the assumption that 

 the temperature of a solid or liquid is equal 

 to its average kinetic energy per atom, which 

 Maxwell pointed out as a consequence of the 

 supposed theorem, and which, believed to be 

 thus established, has been largely taught, and 

 fallaciously used, as a fundamental propo- 

 sition in thermodynamics . 



It is in truth only for an approximately 

 " perfect " gas, that is to say, an assemblage 

 of molecules in which each molecule moves for 

 comparatively long times in lines very ap- 

 proximately straight, and experiences changes 

 of velocity and direction in comparatively 

 very short times of collision, and it is only 

 for the kinetic energy of the translatory ^ 

 motions of the molecules of the " perfect gas," 

 that the temperature is equal to the average kinetic energy 

 per molecule, as first assumed by Waterston, and afterwards 

 by Joule, and first proved by Maxwell. 



o B 



«.C 



