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 a- 

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



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



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

 quantity cf n 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 tda-^ 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 oi dn gram- molecules is equal to t d cr -\- P (d v\ — di>)^ 

 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, 11 and IIo, 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 n„, and (3) passes out of solution into the large mass. 

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

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

 osmotic pressures H^ and 11, respectively. 



Wi = li dv' - Pdv, 

 Wo = dnRr\n—, 



Ws^Pdv,-U,dvJ. 



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. 



