xviii JOSIAH WILLARD GIBBS. 



and of the action of semi-permeable diaphragms and osmotic pressure, 

 showed that many facts, which had previously seemed mysterious and 

 scarcely capable of explanation, 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 d 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 distinctly 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 conse- 

 quence should have excited the prof oundest 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 experiential 

 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 original in character. 



In lecturing to students upon mathematical physics, especially 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 departments of physics, could be conveniently and 

 perspicuously expressed ; and this desire was especially active in him 

 on account of his natural tendency toward elegance and conciseness 

 of mathematical method. He did not, however, find in Hamilton's 

 system of quaternions an instrument altogether suited to his needs, 

 in this respect sharing the experience of other investigators who have, 

 of late years, seemed more and more inclined, for practical purposes, 

 to reject the quaternionic analysis, notwithstanding its beauty and 

 logical completeness, in favor of a simpler and more direct treatment 

 of the subject. For the use of his students, Professor Gibbs privately 



