16 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



is to make H diminish." [In essence BURBURY'S condition 

 A says no more than that Theory of Probabilities is applicable 

 for finding number of collisions.] Furthermore, "any actual 

 material system receives disturbances from without, the effect 

 of which coming at haphazard without regard to state of 

 system for the time being is, pro tanto, to renew or maintain 

 the independence of the molecular motions, that very distribu- 

 tion of co-ordinates (of collision) which is required to make 

 H diminish. So there is a general tendency for H to diminish, 

 though it may conceivably increase in particular cases. Just 

 as in matters political, change for the better is possible, but the 

 tendency is for all change to be from bad to worse." Here 

 BURBURY states what is practically true in all actual cases and 

 thus furnishes an additional reason, if that were needed, for the 

 legitimacy of the Probability method pursued by BOLTZMANN, and, 

 another explanation of why the results obtained are in such per- 

 fect accord with experience. 



As BURBURY'S remarks with respect to the nature of "elementary 

 chaos " under consideration are always illuminating, we will, 

 at the risk of repeating something already said, quote the following: 



" The chance that the spheres approaching collision shall 

 have velocities within assigned limits is independent of their 

 relative position, and of the positions and velocities of all other 

 spheres, and also independent of the past history of the system 

 except so far as this has altered the distribution of the velocities 

 inter se. In the following example this independence is satisfied 

 for the initial state and, for the assumed method of distribution, 

 has no past history. 



" Example. A great number of equal elastic spheres, each of 

 unit mass and diameter a, are at an initial instant set in motion 

 within a field 6 1 of no force and bounded by elastic walls. The 

 initial motion is formed as follows: (i) One person assigns com- 

 ponent velocities u, v, w to each sphere according to any. law 

 subject to the conditions that 2w= 2^=2^=0 and that 



