GIBBS' PAPERS I AND II 55 



he who makes them may be least able to form a correct judgment. 

 It is, therefore, an especial satisfaction to find one's methods ap- 

 proved by competent judges. 



"The leading idea which I followed in my paper on the Equilibrium 

 of Heterogeneous Substances was to develop the roles of energy and en- 

 tropy in the theory of thermo-dynamic equilibrium. By means of 

 these quantities the general condition of equilibrium is easily expressed, 

 and by applying this to various cases we are led at once to the special 

 conditions which characterize them. We thus obtain the consequences 

 resulting from the fundamental principles of thermo-djTiamics (which 

 are implied in the definitions of energy and entropy) by a process which 

 seems more simple, and which lends itself more readily to the solution 

 of problems, than the usual method, in which the several parts of a 

 cyclic operation are explicitly and separately considered. Although my 

 results were in a large measure such as had previously been demon- 

 strated by other methods, yet, as I readily obtained those which were 

 to me before unknown, or but vaguely known, I was confirmed in my 

 belief in the suitableness of the method adopted. 



"A distinguished German physicist has said, — if my memory serves 

 me aright, — that it is the office of theoretical investigation to give the 

 form in which the results of experiment may be expressed. In the 

 present case we are led to certain functions which play the principal 

 part in determining the behavior of matter in respect to chemical equi- 

 librium. The forms of these functions, however, remain to be deter- 

 mined by experiment, and here we meet the greatest difficulties, and 

 find an inexhaustible field of labor. In most cases, probably, we must 

 content ourselves at first with finding out what we can about these 

 functions without expecting to arrive immediately at complete expres- 

 sions of them. Only in the simplest case, that of gases, have I been 

 able to write the equation expressing such a function for a body of vari- 

 able composition, and here the equation only holds with a degree of 

 approximation corresponding to the approach of the gas to the state 

 which we call perfect. 



"Gratefully acknowledging the very favorable view which you have 

 taken of my efforts, I remain, gentlemen, very truly yours, 



"J. WiLLARD GiBBS. 



"New Haven, Jan. 10, 1881." 



It is noticeable that with the exception of mere mention of 

 the chief divisions of the great memoir in the report recommend- 

 ing the award there is neither in the report nor in the address of 

 the chairman any reference to the content of that memoir, let 



