JOSIAH WILLARD GIBBS. xvii 



proceeds to show that the above condition for equilibrium, derived 

 from the two laws of thermodynamics, is of universal application, 

 carefully removing one restriction after another, the first to go being 

 that the substance shall be chemically homogeneous. The important 

 analytical step is taken of introducing as variables in the fundamental 

 differential equation, the masses of the constituents of the hetero- 

 geneous body; the differential coefficients of the energy with respect 

 to these masses are shown to enter the conditions of equilibrium in a 

 manner entirely analogous to the "intensities," pressure and temper- 

 ature, and these coefficients are called potentials. Constant use is 

 made of the analogies with the equations for homogeneous substances, 

 and the analytical processes are like those which a geometer would 

 use in extending to n dimensions the geometry of three. 



It is quite out of the question to give, in brief compass, anything 

 approaching an adequate outline of this remarkable work. It is 

 universally recognized that its publication was an event of the first 

 importance in the history of chemistry, that in fact it founded a new 

 department of chemical science which, in the words of M. Le Chatelier, 

 is becoming comparable in importance with that created by Lavoisier. 

 Nevertheless it was a number of years before its value was generally 

 known ; this delay was due largely to the fact that its mathematical 

 form and rigorous deductive processes make it difficult reading for 

 any one, and especially so for students of experimental chemistry 

 whom it most concerns; twenty-five years ago there was relatively 

 only a small number of chemists who possessed sufficient mathematical 

 knowledge to read easily even the simpler portions of the paper. 

 Thus it came about that a number of natural laws of great importance 

 which were, for the first time, clearly stated in this paper were subse- 

 quently, during its period of neglect, discovered by others, sometimes 

 from theoretical considerations, but more often by experiment. At 

 the present time, however, the great value of its methods and results 

 are fully recognized by all students of physical chemistry. It was 

 translated into German in 1891 by Professor Ostwald and into French 

 in 1899 by Professor Le Chatelier ; and, although so many years had 

 passed since its original publication, in both cases the distinguished 

 translators give, as their principal reason for undertaking the task, 

 not the historical interest of the memoir, but the many important 

 questions which it discusses and which have not even yet been worked 

 out experimentally. Many of its theorems have already served as 

 starting points or guides for experimental researches of fundamental 

 consequence; others, such as that which goes under the name of 

 the "Phase Rule," have served to classify and explain, in a simple 

 and logical manner, experimental facts of much apparent complexity ; 

 while still others, such as the theories of catalysis, of solid solutions, 



