OF ARTS AND SCIENCES. 419 



tlie writer in the London Spectator meant wlien lie called heat the 

 coniminiist of the universe, tlie final consummation of this dissipation 

 being a second chaos. Sir William Thomson has computed that the 

 sun has lost through its radiations hundreds of times as much mechani- 

 cal energy as is represented by the motions of all the planets. The 

 energy thus dispensed to the solar system, and from it to remoter 

 space, ' is dissipated, always more and more widely, through endless 

 space, and never has been, and probably never can be, restored to the 

 sun without acts as much beyond the scope of human intelligence as 

 a creation or annihilation of energy, or of matter itself, would be.' 

 Therefore, unless the sun has foreign supplies, in the fall of meteors or 

 otherwise, where its drafts will be honored, its days are numbered. 



" What I have attempted to state in language as little technical as 

 possible is tersely expressed by Clausius in two short sentences : ' The 

 energy of the world is constant.' ' The entropy of the world (that is, 

 the energy not available for work) tends constantly towards a maxi- 

 mum.' 



" Professor J. Willard Gibbs takes his departure from these two 

 propositions when he enters upon his investigation on the ' Equi- 

 librium of Heterogeneous Substances.' Any adequate theoretical 

 treatment of this complex subject must be, necessarily, highly mathe- 

 matical, and intelligible only to those familiar with the analytical 

 theory of heat. To assist the- imagination, Professor Gibbs has de 

 vised various geometrical constructions ; especially one, of a curved 

 surface, in which each point represents, through its thr^e rectangular 

 coordinates, the volume, energy, and entropy of a body in one of its 

 momentary conditions. The late Professor J. C. Maxwell (whose 

 early death is ever a fresh grief to science) devoted thirteen pages of 

 the fourth edition of his 'Treatise on Heat' to the elucidation and 

 application of these constructions ; and it is understood that he em- 

 bodied in a visible model the equations in which Professor Gibbs 

 expressed his strange surface. In a lecture delivered before the 

 Chemical Society of London, Professor Maxwell gave publicly the 

 endorsement of his great name to the merits of these researches which 

 we are now met to honor. He says : ' I must not, however, omit to 

 mention a most important American contribution to this part of thermo- 

 dynamics by Professor Willard Gibbs, of Yale College, U. S., who 

 has given us a remarkably simple and thoroughly satisfactory method 

 of representing the relations of the different states of matter, by means 

 of a model. By means of this model, problems which had long resisted 

 the efforts of myself and others may be solved at once.' 



