64 PROCEEDINGS OF THE AMERICAN ACADEMY. 



most important kinds of energy. The fugacity is also known to be a 

 function of a third energy-intensity, namely, surface tension. Let us 

 consider a drop of liquid containing n gram-molecules with a surface o- 

 and a surface tension t. The change in surface of the drop with a 



change in its content expressed in gram-molecules, that is, — — , has been 



an 



called the molecular surface, and we may designate it by s. If the 



quantity dn is taken from the drop and added to a large mass of the 



liquid the process is capable of yielding work. The amount has, I 



think, always hitherto been written equal to tela, the change in surface 



energy. This is not strictly true. The molecular volume in the drop is 



not exactly equal to but always slightly less than the molecular volume 



in the large mass. There is therefore always a small amount of work 



done against the atmosphere, and the total work capable of being done by 



the transference of dn gram-molecules is equal to t d cr + P (d v — d v), 



where dv represents the increase in the volume of the large mass, dv 



the decrease in the volume of the drop. If the transfer be made reversi- 



bly in any way the total amount of work obtained must be equal to the 



above. The transfer may be actually carried out reversibly as follows : 



Let a solvent be chosen in which the liquid in question is so slightly 



soluble that the solution may be regarded as an ideal one. The drop 



and the large mass of liquid will be in equilibrium * with the solution at 



two different osmotic pressures, II and II , respectively. We may now 



take the following steps reversibly: (1) dn gram-molecules of the drop 



dissolve into its saturated solution, (2) the same amount is diluted to the 



osmotic pressure II , and (3) passes out of solution into the large mass. 



The three steps yield the following amounts of work, in which d vj and 



d v' represent the volumes occupied by the amount d n in solution at the 



osmotic pressures II and II, respectively. 



Wi = Udv' - Pdv, 

 W 2 = dnRT\n^> 



W 3 = Pdv -Il dv>. 



The sum of these terms, written equal to the amount of work given 

 above, gives 



* In order not to affect the surface tension of the drop, it may be separated 

 from the solvent by its own vapor and thus pass into solution through the vapor 

 phase. 



