132 THE PATH OF SCIENCE 



to the study of reactions in homogeneous systems, the phase 

 rule of Willard Gibbs opened the door to the effective analysis 

 of heterogeneous systems in which the reacting substances are 

 present in more than one phase— as solids and liquids, for 

 instance. Willard Gibbs published his work in the trans- 

 actions of the Connecticut Academy. Because of this rather 

 obscure place of publication and the mathematical form in 

 which it was developed, chemists were slow to recognize its 

 value. It was not until Ostwald published his translation of 

 Gibbs' papers in 1891 and H. W. B. Roozeboom, at the 

 beginning of the twentieth century, studied heterogeneous 

 equilibria on the basis of Gibbs' phase rule that it became 

 generally known to chemists and physicists as a principle 

 of the highest value in the classification of heterogeneous 

 equilibria. 



In a general way, it may be stated that the effect of chang- 

 ing temperature, pressure, or concentration in any hetero- 

 geneous system would have to be considered a special prob- 

 lem for each system investigated were it not for the phase 

 rule. In any system, w^e have components— such as salt, water, 

 and acid; phases— gaseous, liquid, and perhaps several solid 

 phases; and variables— such as temperature, pressure, and con- 

 centration, which are known as degrees of freedom. The 

 phase rule, which states that the degree of freedom of the 

 system is equal to the number of components plus two minus 

 the number of phases present, enables any well-defined sys- 

 tem to be classified and analyzed without difficulty. This rule 

 has been of the greatest importance in many practical ap- 

 plications of chemistry, and, in particular, chemical engineer- 

 ing has made great use of it. All phenomena of precipitation, 

 evaporation, separation of salts, and compositions of alloys 

 are interpreted by Gibbs' phase rule. The great rise of in- 

 dustrial chemistry around 1900 was largely conditioned by 

 this chemical idea, which had remained in incubation for so 

 long a period between the time when it was conceived by 

 Gibbs and the time when it was generally adopted. 



In the years between Gibbs' writing and the application of 



