[ 433 ] 



XII. 'ike Kinetic Theory of a Gas Constituted of Spherically Symmetrical 



Molecules. 



By S. CHAPMAN, M.Sc., Trinity College, Cambridge; Chief Assistant, 

 Royal Ohservatory, 



Communicated by Sir JOSEPH L ARMOR, Sec. Jt.S. 



Received May 29, Bead June 29, Received after Revision and Alteration as indicated in the text, with 

 the addition of Part III., pp. 460-483, November 9, 1911. 



CONTENTS. 



Page 



Introduction 433 



Part I. General theory 434 



Part II. On certain special forma of molecular interaction 453 



Part III. Theoretical results, and comparison with experimental data 460 



Introduction. 



THE principal kinetic theories of a gas proceed either on the hypothesis that the 

 molecules are rigid elastic spheres, or that they are point centres of forces which v;iry 

 inversely as the fifth power of the distance. MAXWELL has worked out the 

 consequences of the latter hypothesis in his well-known theory,* which is unrivalled 

 in its high degree of accuracy and (after some improvements by BoLTZMANNt) in its 

 perfection of mathematical form. All the quantities not taken account of in the 

 theory (such as the time occupied by molecular encounters, and the effect of collisions 

 in which more than two molecules take part) are properly negligible under ordinary 

 conditions. The theory has the disadvantage, however, that the underlying 

 hypothesis is highly artificial (being chosen chiefly on account of mathematical 

 simplifications connected with it, rather than from any physical reasons), and does 

 not represent the real facts at all adequately. 



* 'Phil. Trans.,' 1867 ; 'Scientific Papers,' vol. iL, p. 23. For convenience we shall refer to a gas of the 

 type there contemplated as a Maxwellian gas. Of course, its molecules possess no internal energy, 

 t ' Vorlesungeu iiber Gastheorie,' vol. i. 



VOL. CCXI. A 482. 3 K 9-3.12 



