192 Josiah Willard Gihhs. 



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 catal^^sis, of solid 

 solutions, and of the action of semi-permeable diaphragms 

 and osmotic pressure, showed that many facts, which had 

 previously seemed mysterious and scarcely capable of explana- 

 tion, are in fact simple, direct and necessary consequences of 

 the fundamental laws of thermodynamics. In the discussion 

 of mixtures in which some of the components are present only 

 in very small quantity (of which the most interesting cases at 

 present are dilute solutions) the theory is carried as far as is 

 possible from a priori considerations ; at the time the paper 

 was written the lack of experimental facts did not permit the 

 statement, in all its generality, of the celebrated law which 

 was afterward discovered by van't Hoff ; but the law is dis- 

 tinctly stated for solutions of gases as a direct consequence of 

 Henry's law and, while the facts at the author's disposal did 

 not permit a further extension, he remarks that there are 

 many indications " that the law expressed by these equations 

 has a very general application." 



It is not surprising that a work containing results of such 

 consequence should have excited the profoundest admiration 

 among students of the physical sciences ; but even more 

 remarkable than the results, and perhaps of even greater 

 service to science, are the methods by which they were 

 attained ; these do not depend upon special hypotheses as to 

 the constitution of matter or any similar assumption, but the 

 whole system rests directly upon the truth of certain experi- 

 ential laws which possess a very high degree of probability. 

 To have obtained the results embodied in these papers in any 

 manner would have been a great achievement ; that they were 

 reached by a method of such logical austerity is a still greater 

 cause for wonder and admiration. And it gives to the work 

 a degree of certainty and an assurance of permanence, in form 

 and matter, which is not often found in investigations so orig- 

 inal in character. 



In lecturing to students upon mathematical physics, especi- 

 ally in the theory of electricity and magnetism, Professor 

 Gibbs felt, as so many other physicists in recent years have 

 done, the desirability of a vector algebra by which the more or 

 less complicated space relations, dealt with in many depart- 

 ments of physics, could be conveniently and perspicuously 

 expressed ; and this desire was especially active in him on 



