Kinetic Theory of Gases. 97 



tends to an unequal distribution, for a considerable time at 

 all events, and this quite independently of the number of 

 degrees of freedom, or the continuity, of the molecules ; and 

 it is safe to state that no demonstration such as Sir William 

 Thomson has hinted at can be given as a result of dynamical 

 equations, in which a simultaneous reversal of velocities is 

 equivalent to a mere change in the sign of t. 



This may be tested by examining in a common-sense way 

 the case of a molecule striking a rigid wall, for it would be 

 too laborious to calculate the circumstances of the collision 

 even for the law of direct distance among the particles of the 

 molecule, because fresh equations would be necessary after 

 each collision of any particle of the molecule with the wall. 

 For, taking a molecule formed of two particles only, which 

 attract with any law of force, let the collision take place 

 against a wall perpendicular to X ; then, if when the first 

 particle P x hits the wall, the other particle P 2 happens to be 

 at rest relatively to the wall, it is evident that after P x has 

 hit the wall, <#, the ,v velocity of the Centre of Mass, is exactly 

 reversed (and should P 2 reach the wall, x will be increased). 

 Hence whether P 3 hit the wall or not, and whatever be the law 

 of force, the numerical value of ~x will be increased whenever 

 P 2 is moving from the wall at the instant P x hits it, and 

 similarly if P 2 were moving rapidly towards the wall when P x 

 hit it, and if P 2 did not hit the wall violently, then x would be 

 smaller than before the collision. In fact if to Pi and P 2 be 

 given the positions and reversed velocities that they have after 

 the collision, then the result would be a new collision after 

 which x would have its original value. Hence it is as likely 

 that the energy of the particle relative to its Centre of Mass 

 will be transformed into translational energy as that the 

 translational energy will be transformed into relative energy ; 

 and it seems evident that similar reasoning would apply to a 

 molecule formed of 3, or of 4, or of any number of particles. 

 The conclusion I draw from these observations is that no 

 success can attend an attempt to prove that the temperature- 

 equilibrium results from dynamical actions between molecules 

 alone. I can see no reason for supposing that, if the particles 

 of a t>as could be enclosed in a vessel not containing aether 

 (and such that no energy were transferred to the vessel 

 in its collision with the particles), the gas would ever attain 

 a temperature-equilibrium at all. If it did always attain such 

 an equilibrium, it would be to my mind a proof that the 

 ultimate particles of matter did not individually obey those 

 laws which they are known to obey when collected in the 

 Phil. Mag. S. 5. Vol. 30. No. 182. July 1890. H 



