260 PROCEEDINGS OF THE AMERICAN ACADEMY. 



tion like a perfect solution.^ As examples may be cited the mass 

 law, the law of change of solubility with the temperature, the law of 

 the lowering of vapor pressure by a solute, the law of Nernst for the 

 electromotive force of a concentration cell, and many other equally im- 

 portant generalizations. 



It is probable that no one of these laws is ever strictly true. As 

 approximations to the truth they have been of the greatest service. 

 But now that their utility has been demonstrated, the attention of a 

 progressive science cannot rest upon their acknowledged triumphs, 

 but must turn to the investigation of their inaccuracies and their limi- 

 tations. From the study of the deviations from the simple gas laws 

 has grown one of the most interesting chapters of chemistry. So from 

 a study of the deviations from such a law as the mass law we may ex- 

 pect results of the highest value. 



In such more exact investigations the old approximate equations of 

 thermodynamic chemistry will no longer suffice. We must either turn 

 to the precise, but rather abstruse, equations of entropy and the ther- 

 modynamic potential, or modify the methods which are in more com- 

 mon use, in such a way as to render them exact. 



The latter plan is the one followed in the present paper, the aim of 

 which is to develop by familiar methods a systematic set of thermody- 

 namic equations entirely similar in form to those which are now in 

 use, but rigorously exact. 



The following development is necessarily brief and concise, but I 

 have hoped, nevertheless, to make it intelligible to any chemist who is 

 familiar with the simpler theorems of elementary calculus. 



The Escaping Tendency. 



The meaning of the term "escaping tendency" maybe illustrated by 

 an analogy taken from another branch of applied thermodynamics, — 

 the theory of heat. 



The conception of temperature owes its utility to the existence of 

 two fundamental laws of heat exchange. When two bodies are brought 

 together and there is no transfer of heat from one to the other, they 

 are said to be at the same temperature ; but if such a transfer takes 

 place, the body which loses heat is said to be at a higher temperature 

 than the other. Now the two laws of temperature are the following : 

 (1) Two bodies which have the same temperature as a third, have the 



^ We may speak of a perfect solution as we speak of a perfect gas, that is, one 

 whicli obeys the laws of an infinitely dilute solution. 



