vi PEEFACE. 



Shortly before the author's death he had yielded to numerous 

 requests for a republication of his thermodynamic papers, and had 

 arranged for a volume which was to contain the Equilibrium of 

 Heterogeneous Substances and the two earlier papers, Graphical 

 Methods in the Thermodynamics of Fluids, and A Method of 

 Geometrical Representation of the Thermodynamic Properties of 

 Substances by means of Surfaces. To these he proposed to add 

 some supplementary chapters, the preparation of which he had hardly 

 more than commenced when he was overtaken by his last illness. 

 The manuscript of a portion of this additional material (evidently 

 a first draft) was found among the author's papers and has been 

 printed at the end of the first volume. It is believed that it will 

 be of interest and value in spite of its unfinished and somewhat 

 fragmentary condition. 



The remaining papers, which compose the second volume, are 

 divided between mathematical and physical science. Most of them 

 naturally fall under one of the following heads: Dynamics, Vector 

 Analysis and Multiple Algebra, the Electromagnetic Theory of Light, 

 and are so grouped in the volume in the order named. A fourth 

 section is made up of the unclassified papers. 



In the first section the short abstract of a paper read before the 

 American Association for the advancement of Science is worthy of 

 notice as showing that the fundamental ideas and methods of the 

 treatise on Statistical Mechanics were well developed in the author's 

 mind at least seventeen years before the publication of that work. , 



The second section includes the Elements of Vector Analysis, 

 privately printed in 1881-1884 for the use of the author's classes, 

 but never published. It contains in a very condensed form all the 

 essential features of Professor Gibbs's system of Vector Analysis, 

 but without the illustrations and applications which he was accus- 

 tomed to give in his lectures on this subject. Copies of this pamphlet 

 have been for many years past practically unobtainable. Here is 

 also placed a hitherto unpublished letter to the editor of Klinkerfues' 

 Theoretische Astronomic, on the use of the author's vector method 

 for the determination of orbits. 



Five papers on the Electromagnetic Theory of Light constitute 

 the third section. The fourth and last is composed of miscellaneous 

 papers, including biographical sketches of Clausius and of the 

 author's colleague Hubert A. Newton. 



The editors have spared no pains to make the reprint typographi- 

 cally accurate. In a few cases slight corrections had been made by 

 Professor Gibbs in his own copies of the papers. These changes, 

 together with the correction, of obvious misprints in the originals, 

 have been incorporated in the present edition without comment. 



