AND OF THE SECOND LAW 25 



probability that H decreases is always greater than that it increases. 

 In this connection we may add that BOLTZMANN looked forward 

 to a time," when the fundamental equations for the motion of 

 individual molecules will prove to be merely approximate formulas, 

 which give average values which, according to the Theory of 

 Probabilities, result from the co-operation of very many inde- 

 pendently moving individuals constituting the surrounding 

 medium, for example, in meteorology the laws will refer only to 

 average values deduced by the Theory of Probabilities from a 

 long series of observations. These individuals must of course be 

 so numerous and act so promptly that the correct average values 

 will obtain in millionths of a second." 



To further strengthen our faith we may point out that the 

 probability method has been successfully used to determine 

 unique results from complicated conditions and has been employed 

 for the general treatment of problems. In the case before us 

 it has solved the entropy puzzle which has exercised physicists, 

 as well as engineers, for decades, and it has thereby emancipated 

 the Second Law from all anthropomorphism, from all dependence 

 on human experimental skill. When we take the broadest 

 possible view of its character, this Calculus enables us to read 

 the present riddle of our universe, namely, why it is in its present 

 improbable state. We have therefore in this Calculus an engine 

 for investigation which is of great power and is likely to play a 

 large part in the future in the ascertainment -of physical truth. 

 Of course it must then be in the hands of masters. It is they 

 and they alone who can properly and adequately interpret such 

 a physical problem as the one before us. In scientific work our 

 last court of appeal must be Nature, and we therefore say: The 

 best justification for the use of the Theory of Probabilities in our 

 problem is that its results are in such complete accord with the 

 facts. 



In dealing with this physical engine of investigation, we must 

 again call attention to some of the features of haphazard necessary 



