WILLARD GIBBS 355 



with its vapor, we have two phases P = 2, and therefore F=i, 

 that is, if anyone of the three conditions are decided upon, the 

 other two must follow. When we consider water, ice and vapor 

 altogether P = 3, and therefore F = o, that is, none of the variable 

 conditions can be chosen arbitrarily, for water, ice and vapor can 

 exist together at only one temperature (nearly o Centigrade) 

 and one pressure (4.6 millimeters of mercury). If the temperature 

 is lowered, all the water freezes; if the temperature is raised, all 

 the ice melts; in any event one of the phases disappears. 



By the use then of this simple little arithmetical rule involving 

 after the determination of the factors only the addition and sub- 

 traction of numbers usually less than three, the behavior of the 

 most complicated mixtures under all possible changes of condition 

 is made known when once a few data are obtained by experiment, 

 and it has found application in many widely diverse fields of 

 science and industry. The reader who is sufficiently interested in 

 the subject to follow it further is referred to the two books on the 

 Phase Rule by Bancroft and by Findlay. The Dutch chemists 

 were the first to make use of Gibbs' work, and Roozeboom, Van 

 der Waals, Van't Hoff, Schreinemakers and others have within 

 the last few years by the aid of the Phase Rule and other laws of 

 equilibrium immensely increased our knowledge of such difficult 

 matters as solutions, alloys and crystallizations. As examples 

 of its practical applications may be mentioned its use in the study 

 of sedimentary deposits, the metallurgy of iron and the igneous 

 rocks. The Stassfurt salt deposits which supply the world with 

 potash for fertilizers are composed of a curious and complicated 

 mixture of various sodium, potassium, magnesium and calcium 

 salts in layers aggregating a thousand feet in thickness. Professor 

 Van't Hoff and his pupils have been for the last eight years engaged 

 upon this problem, and have worked out the conditions under 

 which .these strata were deposited by the evaporation of sea water 

 in a land-locked sea. Iron has been most useful to man because 

 it is really several metals in one. By the addition of minute quan- 

 tities of carbon it can be changed from soft, malleable wrought- 

 iron, to hard, brittle cast-iron, or to steel which can be tempered in 



