420 PROCEEDINGS OP THE AMERICAN ACADEMY 



"It is now my pleasant duty to present, in the name of the Acad- 

 emy and with their approving voice, the gold and silver medals to the 

 Recording Secretary, Professor Trowbridge, who has been commis- 

 sioned by Professor Gibbs to represent him on this occasion. I cannot 

 but thinli that if Count Rumford were living, he would regard with 

 peculiar pleasure this award. For the researches of Professor Gibbs 

 are the consummate flower and fruit of seeds planted by Rumford 

 himself, though in an unpromising soil, almost a century ago. In 

 transmitting these medals to Professor Gibbs, by which the Academy 

 desires to honor and to crown his profound scientific work, be pleased 

 to assure him of my warm congratulations and of the felicitations of 

 all the Fellows of the Academy, here assembled to administer Count 

 Rumford's Trust." 



In repl}'- to the President's address, the Recording Secretary 

 then read the following letter from Professor Gibbs : — 



"To THE American Academy of Arts and Sciences: — 



^^ Gentlemen, — Regretting that I am unable to be present at the 

 meeting to which I have been invited by your President, I desire to 

 express my appreciation of the very distinguished honor which you 

 have thought fit to confer upon me. This mark of approbation of my 

 treatment of questions in thermo-dynamics is the more gratifying, as 

 the value of theoretical investigation is more difficult to estimate than 

 the results obtained in other fields of labor. One of the principal ob- 

 jects of theoretical research in any department of knowledge is to find 

 the point of view from which the subject appears in its greatest sim- 

 plicity. The success of the investigation in this respect is a matter 

 which he who makes them may be least able to form a correct judg- 

 ment. It is, therefore, an especial satisfaction to find one's methods 

 approved by competent judges. 



" The leading idea which I followed in my pajier 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 con- 

 ditions which characterize them. We thus obtain the consequences 

 resulting from the fundamental j^rinciples of thermo-dynamics (which 

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

 which seems m-ore simple, and which lends itself more readily to the 

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



