1891.] Doctrine regarding Distribution of Energy. 81 



afc the instant of contact of surfaces, while leaving unchanged the 

 absolute velocity of the centre of inertia of the two. Let any velocity 

 or velocities in any direction or directions be given to atoy one or more 

 of the atoms or of the shells or globules constituting the doublets. 

 According to the Boltzmann-Maxwell doctrine, the motion will become 

 distributed through the system, so that ultimately the time-average 

 kinetic energy of each atom, each shell, and each globule shall be equal ; 

 and therefore that of each doublet double that of each atom. This is 

 certainly a very marvellous conclusion ; but I see no reason to doubt 

 it on that account. After all, it is not obviously more marvellous 

 than the seemingly well proved conclusion, that in a mixed assemblage 

 of colliding single atoms, some of which have a million million times 

 the mass of others, the smaller masses will ultimately average a 

 million times the velocity of the larger. But it is not included in 

 Maxwell's proof for single atoms of different masses [(34) of his 

 " Dynamical Theory of Gases " referred to above] ; and the condition 

 that the globules enclosed in the shells are prevented by'the shells 

 from collisions with one another violates Tait's condition [(C) of 

 , 18 of "Foundations of K.T. Gases"], "that there is perfectly free 

 access for collision between each pair of particles whether of the 

 same or of different systems." An independent investigation of such 

 a simple and definite case as that of the atoms and doublets defined 

 in 3 5 is desirable as a test, or would be interesting as an illus- 

 tration were test not needed, for the exceedingly wide generalisation 

 set forth in the Boltzmann-Maxwell doctrine. 



6. Next, instead of only a single globule within the shell of 4, 

 let there be a vast number. To fix ideas let the mass of the shell be 

 equal to a hundred times the sum of the masses of the globules, and 

 let the number of the globules be a hundred million million. Let 

 two such shells be connected by a push-and-pull massless spring. 

 Let all be given at rest, with the spring stretched to any extent ; and 

 then left free. According to the Boltzmann-Maxwell doctrine, the 

 motion produced initially by the spring will become distributed 

 through the system, so that ultimately the sum of the kinetic 

 energies of the globules within each shell will be a hundred million 

 million times the average kinetic energy of the shell. The average 

 velocity* of the shell will ultimately be a hundred-millionth of the 

 average velocity of the globules. A corresponding proposition in the 

 kinetic theory of gases is that, if two rigid shells each weighing 

 1 gram, and containing a centigram of monatomic gas, be attached to 

 the two prongs of a massless perfectly elastic tuning fork, and set to 

 vibrate, the gas will become heated in virtue of its viscous resistance 



* The " average velocity of a particle," irrespectively of direction, is (in the 

 kinetic theory of gases) a convenient expression for the square root of the time- 

 average of the square of its velocity. 



VOL. L. G 



