212 Mr. E. Buckingham on Certain Difficulties 



thermodynamic potentials are of very little significance ; it 

 is only a question whether the ideas are worth the trouble of 

 mastering them. Now one object of studying thermo- 

 dynamics is to be able to follow the literature, and the cur- 

 rent literature is written very largely by men who, wisely or 

 unwisely, do use free energy or thermodynamic potentials, 

 a usage which is characteristic of the modern developments 

 of the subject. For this reason, if for this alone, I think 

 that any text-book of thermodynamics which is not pro- 

 fessedly very elementary, should certainly, after showing how 

 problems may be treated by the use of cycles, also show how 

 they may be treated by other methods, and should, by the 

 juxtaposition of different proofs of the same proposition, try 

 to impress upon the student the fact that, though the mathe- 

 matical form be different, the underlying idea is the same. 



The question how a treatise should be written is not so 

 easily answered. We might turn to the treatises and com- 

 pare the good and the bad ; but are there any treatises on 

 thermodynamics? I do not know of a single book which 

 today deserves the title of " Treatise on Thermodynamics," 

 and the very few men who seem competent to write such a 

 treatise show no intention of doing so. We must leave the 

 question of the proper method for a treatise to the future 

 when the difficulties which now now beset us may have 

 vanished. 



But if each kind of writing should assume a form suitable 

 to the objects it has in view, we may yet ask whether, in our 

 private thinking about thermodyuamics, each method may 

 not have its advantages. For the treatment of problems of 

 pure equilibrium, where we do not have to consider irre- 

 versible processes, it seems to me merely a matter of personal 

 taste and habit what method we use. But when we come to 

 the inevitable problems where w^e can no longer be content 

 with the contemplation of states of equilibrium and nothing- 

 else, a treatment by cycles does not always give us the clearest 

 view or the firmest grasp of the subject. 



Every actual process does have a definite direction, and we 

 know experimentally, by the whole experience of our lives, 

 that if anything whatever happens in the physical world 

 about us, the mere fact that it did happen in a certain wav 

 proves that it could not, under precisely the same conditions, 

 have happened in the opposite way. There is something in 

 the nature of things which determines that any actual change 

 of state of a material system shall have a certain jiarticular 

 direction and not the opposite one. This statement is merely 



