66 PROCEEDINGS OF THE AMERICAN ACADEMY. 



potential tt is established. Since we are discussing an ideal solution this 

 osmotic pressure is proportional to the fugacity of the ions. That is, 

 from equation (8), <// = p 11, and 



€Tr = RT\nxp- R T\np-\- K. 



DiflFerentiating at constant temperature and pressure we obtain the 



equation, 



f O RT\nip \ _ 



\ 5 TT Jt,P.... 



which is equation (28). 



Equations (20), (21), (27), and (28) comprise all cases in which 

 fugacity is known to depend upon the intensity of any form of energy. 

 The identity of these equations with equation (19) gives the highest 

 degree of probability to the supposition that the latter equation expresses 

 an exact law of nature and one possessing such universality as few 

 others possess. For this equation expresses the condition for any con- 

 ceivable change of state of any simple substance. Moreover, it will be 

 shown in the jjaper which is to follow this, that equation (19) not only 

 applies to chemically simple substances but, with a slight generalization 

 in the meaning of the symbols which it contains, applies to mixtures as 

 well, and further that it applies not merely to physical processes but also 

 to all chemical processes,* so that this law becomes the general law of 

 physico-chemical change. 



Finally, it will be shown that the adoption of the two functions \j/ and 

 RTlrnj/, which possess such peculiar importance, will remove many 

 obstacles in the search for the fundamental principles of energetics, in 

 which already so much progress has been made by the work of Helm, of 

 Ostwald, and of other investigators. I shall therefore offer in the last 

 section of this paper a further explanation of fugacity as a tangible, 

 physical quantity. 



V. 



The Fugacity of Imperfect Gases. 



The vapor pressure is determined for many substances and capable of 

 direct or indirect determination for all. Moreover the fugacity of a sub- 



* In the further extension of this theory, analogy will be seen between the 

 conception of fugacity and the driving tendency of chemical reaction as used by 

 T. W. Richards (These Proceedings, 35, 471 ; Jour. Pliys. Chem., 4, 385 (1900)). 

 It is a pleasure to recall how much I owe to the many conversations full of assist- 

 ance and encouragement which I had with Professor Richards during the early 

 development of the theory of fugacity or escaping tendency. 



