324 A CENTURY OF SCIENCE 



"Phase-Rule" and is expressed by a very simple 

 formula. 



The application of this great discovery to chemical 

 theory was delayed for ten years, partly, perhaps, 

 because it was not sufficiently brought to the attention of 

 chemists, but largely it appears because it was not at 

 first understood, since its presentation was entirely 

 mathematical. 



It was Rooseboom, a Dutch chemist, who first applied 

 the phase-rule. It soon attracted profound attention, 

 and the name of Willard Gibbs attained world- wide fame 

 among chemists. When Nernst, who is perhaps the most 

 eminent physical chemist of the present time, was deliv- 

 ering the Silliman Memorial Lectures at Yale a few years 

 ago, he took occasion to place a wreath on the grave of 

 Willard Gibbs in recognition of his achievements. 



To understand the rule, it is necessary to define the 

 three terms, introduced by Gibbs, phase, degrees of free- 

 dom and component. 



By the first term, is meant the parts of any system of 

 substances which are mechanically separable. For 

 instance, water in contact with its vapor has two phases, 

 while a solution of salt and water is composed of but one. 

 The degrees of freedom are the number of physical con- 

 ditions, including pressure, temperature and concentra- 

 tion, which can be varied independently in a system 

 without destroying a phase. The exact definition of a 

 component is not so simple, but in general, the com- 

 ponents of a system are the integral parts of which it is 

 composed. Any system made up of the compound H 2 0, 

 for instance, whether as ice, water or vapor, contains but 

 one component, while a solution of salt and water con- 

 tains two. Letting P, F. and C stand for the three terms, 

 the phase-rule is simply 



F = C + 2 P 



that is, the number of degrees of freedom in a system in 

 equilibrium equals the number of components, plus two, 

 minus the number of phases. The rule can be easily 

 understood by means of a simple illustration. In a sys- 

 tem composed of ice, water and water-vapor, there are 

 three phases and one component and therefore 



