24 THE PHYSICAL SIGNIFICANCE OF ENTROPY 



is attached to the theory of heat because the theorems of probability 

 are applied. One must not confuse an imperfectly proved proposi- 

 tion (whose truth is consequently doubtful) with a completely estab- 

 lished theorem of the Calculus of Probabilities; the latter represents, 

 like the result of every other calculus, a necessary consequence 

 of certain premises, and if these are correct the result is confirmed 

 by experience, provided a sufficient number of cases has been 

 observed, which will always be the case with Heat because of the 

 enormous number of molecules in a body." 



To become more specific we will mention some of the problems 

 to which the Theory of Probabilities has been profitably applied. 

 In business to life and fire insurance; in engineering to reducing 

 the inevitable errors of observations by the Method of Least 

 Squares; and in physics to the determination of Maxwell's Law 

 of the distribution of velocities. The results thus obtained are 

 universally trusted and accepted by experts. Why then should 

 this Calculus not be applicable to the more general natural events ? 



In this connection consider some of its good points: (a) It 

 eliminates from a problem the accidental elements if the latter 

 are sufficiently numerous; (b) it deals legitimately with averages; 



(c) it involves combination considerations other than averages; 



(d) it is available for non-mechanical as well as mechanical occur- 

 rences and thus (e) has a capacity for covering the whole range 

 of natural events, giving it a character of universality which is 

 now its most valuable asset. 



As an example of this we may instance BOLTZMANN'S deservedly 

 famous H-theorem, which establishes the one-sidedness of all 

 natural events. 1 Concerning it, this master in mathematical 

 physics says: 



" It can only be deduced from the laws of probability that, if the 

 initial state is not especially arranged ior a certain purpose, the 



1 The H-theorem considers a process (consisting of a number of separate,, 

 reversible processes) which is irreversible in the aggregate. 



