598 Mr. J. H. Jeans on the 



configuration. To overcome the difficulty of the initial con- 

 figuration being unknown we are compelled to regard the 

 whole question as one of probability. Not knowing the 

 positions of individual molecules of the gas, we have to argue : 

 " The probability that there is a molecule of a certain kind 

 within a certain region has such or such a value." The calcula- 

 tion of this value, in the orthodox treatment of the subject, rests 

 upon the u molekular-ungeordnet " assumption of Boltzmann. 



The assumption which Boltzmann announces that he is 

 making is tbat the gas is, and always remains, in a molekular- 

 ungeordnet state. It does not appear that any strict definition 

 of a molekular-ungeordnet state has ever been attempted. 

 Certainly Boltzmann does not give a definition. Two ex- 

 amples of a geordnet state are given in the Vorlesungen*, 

 and these are of such a special nature tbat the reader feels 

 convinced that it is legitimate to disregard the geordnet state 

 altogether. The form in which Boltzmann uses the assump- 

 tion is somewhat different. This has been pointed out by 

 Burbury, who has clearly stated the assumption in its working- 

 form, under the designation of ".Assumption A"j\ 



The effect of this assumption is to enable us to regard 

 certain probabilities at any given instant as independent, and 

 we then assume not only that the probabilities at a later 

 instant are inter se independent, but also that they are 

 independent of the events which took place at any earlier 

 instant. This assumption cannot be logically reconciled with 

 the fact that the motion of the system is continuous in time. 

 /. e., that the events which occur at any instant depend on 

 those which occurred at a previous instant. 



§ 3. The fundamental assumption, then, cannot be justified 

 a priori by its consistency. To show that it is not justified 

 a posteriori by its success, it will be necessary to examine 

 some of the consequences of the assumption. 



The assumption being granted, it is proved that a certain 

 function H must continually decrease as the time progresses. 

 From this follows the well-known objection of the reversal 

 of velocities J. Let A be a system such that the value of 

 H is H , and in the course of a small interval of time let it 

 change to a system B, for which H has the smaller value H^ 

 Then, if we reverse all the velocities in system B, we get a 

 second system in which the value of H is still H x . The 

 motion of this system must of necessity be through the 

 various configurations which were passed during the change 



* Vol. i. p. 20. 



t ' Kinetic Theory of Gases/ p. 9. 



X Boltzmann, Vorleswit/en, i. p. 42. 



