148 PROCEEDINGS OF THE AMERICAN ACADEMY. 



removed from A at pressure P l ; (2) it is compressed to P x + d P 1 ; 

 it is introduced into the secoud enclosure ;it A' against pressure 

 1\ -f- dP x : ill one gram of X^ is taken from the second enclosure at 

 ( ' at pressure P a + d P z \ (o) it is allowed to expand to P. 2 ; (6) it is 

 introduced into the first enclosure at (' against pressure P a . 



The system will have returned now by internal adjustment to its 

 original condition. The quantities of work done hy the system in the 

 ral steps are, 



)V l = P 1 a 1 , 



W i = -P 1 d<r l , 



W 9 = -(P 1 + dP 1 ) ((Ti-do-0, 



U\ = (P. 2 + dP,) (<T,-dn 



IV, = P 2 da 2 , 



n; =- p,a 2 , 



By writing the sum of these terms equal to zero, according to the 

 second law of thermodynamics, we obtain the equation, 



dP rr 



(Tod P., — ti dP x = 0; or, , " = — . (2) 



The meaning of this equation is obvious. When under any conditions 

 two phases of a substance are in equilibrium and the pressure is increased 

 upon one phase, then in order to maintain equilibrium the pressure must 

 be increased on the second phase; and the second change in pressure 

 must be to the first as the specific volume of the first phase is to that of 

 the second. For example, if ice and water are in equilibrium at atmos- 

 pheric pressure and an additional pressure of one atmosphere is put upon 

 the ice alone, then equilibrium can be maintained by an additional pres- 

 sure of 1.09 atmospheres upon the water, since 1.09 is the ratio of the 

 volumes of ice and water. 



The above law has been derived without any assumption whatever, 

 and is based only upon the second law of thermodynamics. It must be 

 considered, therefore, in the Bame degree aa the latter a universal and 

 exact law of nature. This law may be presented in another form. 



Thi i tendency for the particles ol everj phase to escape into M>me 



other phase. Liter a function \p will he so defined as to represent this 

 escaping tendency. Here it will be sufficient to consider ip merely a 

 quantity Bach that when two phases are in equilibrium, C ) in- the same 

 value in both ; when not in equilibrium,^ iter in the less stable 



