530 Mr. S. H. Burbury on 



velocities and positions of the other molecules for the tim(^ 

 being. We may express this also in the form that, whatever 

 the velocities may be, the molecules are distributed in space 

 at haphazard with respect to them. If this assumption be 

 regarded as the interpretation of Boltzmann's hypothesis, 

 that hypothesis comes before us, like the Ghost in Hamlet, in 

 a questionable shape. 



2. Jeans proceeds to show, rigfhtly as I think, that this 

 assumption A, the basis of the orthodox theory, is mathe- 

 matically impossible if the motion is continuous, that is, if the 

 state of the system at any instant is a necessary consequence 

 of its past history. I think 1 shall not be misinterpreting 

 Jeans if I put the argument thus : — If the 6K coordinates 

 and velocities of N molecules are given at any instant, and if 

 the motion be^ as above defined, continuous, the state of the 

 system at any other instant is completely determined in terms 

 of these 6N variables and the time t. There are then, 

 including t, only 6N + 1 independent variables. But if 

 assumption A is made at every instant, we are using in effect 

 an infinite number of independent variables. Therefore 

 assumption A is a mathematical impossibility. 



The coordinates and velocities of every pair of molecules 

 are necessarily correlated, because they are functions of the 

 same 6N + 1 quantities, and of no others. It is probably 

 true, if N be very great, that the correlation is a negligible 

 quantity, except for those pairs of molecules which happen 

 to be near each other. But it cannot be always negligible for 

 these. And it is for such pairs, and for such pairs only, that 

 the assumption A has to be made. It is untrue in the only 

 case for which we require to make it. 



3. Assumption A cannot then be accurate except in dis- 

 continuous motion, a motion, that is, which is continually 

 receiving disturbances at haphazard, which in fact takes a 

 fresh start from chaos at every instant. It is fair to say that 

 in nature disturbances are very frequently taking place. The 

 isolated system, with its HN variables left to its own forces, 

 hardly exists in practice. 



4. Having thus proved that assumption A is not a priori 

 consistent, Jeans goes on to show (art. 3) that it is not 

 justified a posteriori by its results, instancing the well-known 

 difficulty of Boltzmann's H theorem and the supposed reversed 

 motion. I agree with him in his view that the assumption is 

 not justified by its consequences, though I should not give 

 precisely the same explanation that he gives of the H theorem 

 difficulty. 



5. But Jeans having proved in arts. 2 and 3 that assumption 



