encountered in the Study of Thermodynamics. 213 



another form of the new fundamental substance which we 

 have to put into our reversible thermodynamics to make it. 

 applicable to real processes. After grasping this fact, the 

 mind trained in quantitative reasoning seeks instinctively for 

 some quantity — some function of the generalized coordinates 

 of the system — which characterises the instantaneous state 

 of the system, so that it may be possible to think of the 

 changes in state as characterised by the changes in this 

 quantity, which by its value expresses a certain property of 

 the system. That is why we rind men operating with en- 

 tropy, free energy, and thermodynamic potentials; it is the 

 desire to think of a change of state as measured by a single 

 quantity without the complicated machinery of a cycle, with 

 its tour or more separate operations to be considered sepa- 

 rately. And though it must be granted that these quantities 

 are defined onlv by reference to cyclic processes, and though 

 mathematically they are merely derived from something more 

 elementary, they do, in spite of that, to the man who has 

 once become familiar with them, present real advantages in 

 simplicity, as I think must be admitted by any man who has 

 eonstructed a model of the thermodynamic potential surface 

 for the region of the triple point of ice, water, and steam, or 

 for the critical point where the water-steam line comes to an 

 end. 



One man will prefer to work with entropy, as Professor Planck 

 seems to do ; another will use the free energy way of looking 

 at things, as Professor Nernst does: still another will think 

 altogether in terms of che thermodynamic potential, as 

 M. Duhein does. For me, the potential idea is the natural one; 

 I think of a natural process as going on because the system 

 involved in the process has not yet reached the bottom of a 

 potential slope ; and I think of a state of stable equilibrium 

 as a state such that the system is, so to speak, at the bottom 

 of a hollow of potential so that it cannot change its state 

 because to do so it would have to go up hill, which it cannot 

 do <>/ itself. But the particular form into which each man 

 casts hi- ideas is of small moment. What 1 have tried to 

 bring out is that beside regarding entropy, free energy, and 

 thermodynamic potentials as mere mathematical fictions which 

 complicate reasoning more simply performed by using only 

 cyclic processes, they, and perhaps other similar functions, 

 may have a real intrinsic value a- aids to clear thinking, and 

 may often be helpful in a way which is quite beyond the 

 power- of the cycle. 



I believe that it i< for the benefit of thermodynamics that 



