56 



If we adopt tlie latter view, in other words if we say that the 

 log W of a sj'stem is almost the same as the sum of log w of its 

 parts, at the most a sign of inequality is changed into a sign of 

 equality. It is not justiliable, however, tó r^yé^r^^c the sign of inequality. 

 But this is just what happens when, for instance, the uniform 

 distribution of density in a gas is regarded as the most probable 

 state, and in order to calculate the probability of a distribution 

 slightly deviating from this the relation 



log W z= 2 log io, 

 is taken as the basis, for in this way each deviating distribution 

 appears as a less probable one ^). 



V. The above analysis is by no means intended to call into 

 question the validity of calculations similar to those indicated in the 

 preceding paragraph, as these rest on the thesis that the entropy of 

 the whole is equal to the sum of the entropies of the parts, a thesis 

 that probably is physically better justified than the combinatory 

 reasonings, at least in the circumstances in which they are applied. 

 The analysis is merely intended to make clear that the decision of 

 the question whether the probability of the state of a system has 

 reached its maxirnum or not, depends upon the point of vieio of the 

 investigator, and that tfie ideas formed from purely combinatory 

 reasonings do not form a satisfactory or conclusive foundation to 

 direct our choice amongst many different standpoints to any one in 

 particular; further that the choice of our standpoint is made on the 

 ground of various physical intuitions, which are outside the pale 

 of the combination-calculus as such. 



That is to say, that the combinational reasonings in question 

 cannot be deduced from a higher principle which may be said to 

 rule nature. 



VI. We can show this more particularly in the case of a gas. 

 Let us bring together two cubic centimetres of gas at different 

 temperatures. If it should depend upon the "probability principle" 

 which is to happen, it would be quite indetinite whether an equalisa- 

 tion of temperature would take place or not. It would depend upon 

 the question of which is more important in nature; one cubic 

 centimetre or trillions of cubic centimetres. In the latter case our 

 two cubic centimetres might just be those members of our trillion 



1) R. FüRTH. XJeber die Entropie eines realen Gases als Fimkiion der mittleren 

 raumlichen Temperatur- und Dichteverteilung. Phys. Zschr. 18, p. 395—400, 1917- 



