Kinetic Theory of Gases. 599 



from A to B, and so we arrive at a system which is identical 

 with A except that all the velocities are reversed. For this 

 system the value of H is H , and this is greater than Hi. How 

 is this to be reconciled with the theorem that H must always 

 decrease ? 



^"ow this theorem of H decreasing must have been im- 

 plicitly contained in the equations of motion and the 

 fundamental assumption. The H-theorem points to an 

 irreversible process. This irreversibility cannot have been 

 contained in the equations of motion, for these are essentially 

 reversible in time ; it must therefore have been introduced 

 in the molekular-ungeordnet assumption. The view of the 

 present paper, as will appear later, is that the molekular- 

 ungeordnet assumption is not a true assumption at all, but 

 amounts to a licence to misuse the calculus of probabilities. 

 The orthodox view is that the decrease in H is a consequence 

 of supposing the gas to be in a molekular-ungeordnet state, 

 and hence that a gas for which H increases must be geordnet. 

 By the time this result is reached there seems to be less 

 justification than before for supposing the typical gas to be 

 ungeordnet : it will be seen thnt to every ungeordnet state 

 there corresponds a geordnet state, so that only one-half at 

 most of all possible arrangements will be ungeordnet. Also 

 of the two corresponding states there does not seem to be 

 any reason why one should be labelled ungeordnet rather than 

 the other : in other words it would seem to be just as likely 

 that our results when applied to a real gas should be false as 

 that they should be true. For this reason the assumption 

 of a molekular-ungeordnet state does not seem to be justified 

 by success. 



The present paper contains an outline of a kinetic theory 

 based upon entirely different foundations. This new theory 

 is free from all assumptions, and the arguments are mathe- 

 matical instead of physical, so that if the reasoning is sound, 

 inconsistencies cannot occur. 



The proposed new Basis. 



§ 4. A simple illustration will best explain the course of 

 procedure which is to be followed. 



Suppose that we are concerned with a series of throws with 

 a die, this die being of the usual type, so that in each throw 

 the chances of each number from one to six being thrown 

 are exactly equal. Suppose that our problem is to find the 

 average value of the throw in an unknown series o\' throws. 



If we consider a series of 10 throws, ir can be shown thai 

 the " expectation " of the average throw (in other words, the 



2 S 2 



