84 BUTLER ART. 1) 



perature and pressure, is zero or positive. It follows that it is 

 necessary for the equilibrium of two masses of the same com- 

 position, e.g., water and ice, which are in contact, that the 

 values of f for equal quantities of the two masses must be equal. 

 Thus, if the value of f for unit mass of ice were greater than the 

 value of f for unit mass of water, at the temperature and pres- 

 sure at which they are in equilibrium with one another, the 

 value of f of the system could be decreased by the change, ice -^ 

 water, at constant temperature and pressure. Since according 

 to (30) this is impossible, the values of f for unit masses of ice 

 and water in equilibrium with each other, must be equal. 

 Similarly for the equilibrium of three masses, one of which can 

 be formed out of the other two, it is necessary that the value 

 of f for the first mass should be equal to the sum of the values of 

 f for those quantities of the other masses, out of which the first 

 mass can be formed. For example, 100 grams of calcium 

 carbonate can be formed from 56 grams of lime and 44 grams 

 of carbon dioxide. When the three substances are in equilib- 

 rium with each other, the value of f for 100 grams of calcium 

 carbonate must be equal to the sum of the values of f for 56 

 grams of lime and 44 grams of carbon dioxide. Also if a solu- 

 tion composed of a parts of water and b parts of a salt is in 

 equilibrium with crystals of the salt and with water vapor, 

 the value of f for the quantity a + 6 of the solution is equal to 

 the sum of the values of ^ for the quantities a of water vapor 

 and h of the salt. 

 The definition 



X = e + py (31) 



may likewise be extended to any material system for which the 

 pressure is uniform throughout. If we consider two states of a 

 system at the same pressure, in which x has the values x' and 

 x", we see that 



x" - x' = 6" - e' + p{v" - v'), (32) [119] 

 or 



Ax = Ae + pAv = Qp , (33) 



