viii PREFACE 



papers that the methods and results of Gibbs will be intelligible 

 to and available for the use of all serious students of both chem- 

 istry and physics. The only exception to this mode of treat- 

 ment will be found in the interesting Article C of the present 

 volume, where our distinguished collaborator, Professor E. B, 

 Wilson, considered it more advantageous to give an outline of 

 Gibbs' own lectures on thermodynamics than a detailed discus- 

 sion of Papers I and II of Volume I of The Collected Works 

 of J. Willard Gibbs. Readers who have followed the reasoning 

 given by Gibbs in his lectures will find no difficulty in under- 

 standing the graphical developments of Papers I and II. 



In order further to lighten the work of the mathematically 

 inexpert reader, the present volume contains a short Article (B) 

 deahng with certain mathematical methods. In this connec- 

 tion reference may be also made to Chapter II of the Special Com- 

 mentary on Gibbs' Statistical Mechanics by A. Haas, dealing 

 with the algebra of determinants and contained in Volume II of 

 the Commentary. One of the objects of Article F of the pres- 

 ent Volume is to famifiarise students with certain mathematical 

 difficulties, e.g. the difference between Gibbs' use of the opera- 

 tors 8 and A. 



Some points of detail may now be considered. In the Table 

 of Contents and in the titles of the Articles of the present 

 Volume, the expression "Gibbs, I, pp." refers to the relevant 

 part of Volume I of The Collected Works of J. Willard Gibbs (two 

 volumes), Longmans, Green, and Co., 1928, or to the like- 

 numbered volume and page of The Scientific Papers of J. 

 Willard Gibbs, Longmans, Green, and Co., 1906.* This ap- 

 plies also to occasional references in the text. In each Article 

 the current numbers referring to the particular author's 

 equations are given between curved parentheses, whereas 

 the numbers referring to the equations as given by Gibbs in the 

 original paper are enclosed between rectangular brackets. When 



* The Collected Works is a reprint of the Scientific Papers, with iden- 

 tical pagination and contents except that it includes (in Volume II) 

 Gibbs' Elementary Principles in Statistical Mechanics, which was not 

 printed in the Scientific Papers. References to this particular portion, 

 however, occur in this Commentary only in Volume II and in Article 

 J of Volume I. 



