Mr. J. II. Jeans' Theorij of Gases. 535 



Now the above expression for ^ ^ is what I denoted l)y M 



in my Kinetic Theory of Gases, chapters v., vi. ; and I did 



/AT 

 solve the problem there stated by making -.^=0, that is, 



d'-(b . ' ^" 



-^ =0. I did not, however, define the energy of the stream 



motion. 



The Finite Dimensions of a Molecule. 



14. Jeans'' molecules may in the beginning of his paper be 

 conceived as elastic spheres having diameter 2B;. This he 

 expresses by equation (3), namely 



and his limits of integration are taken accordingly. His 

 view seems to be that by stating the fact, and remembering- 

 it in the limits of integration, he has given full account of all 

 the consequences which need be deduced from the fact stated. 

 It may be put on the shelf. Undoubtedly that view is true 

 for the discontinuous motion characterized by assumption A. 

 but not for continuous motion. For in continuous motion dis- 

 turbances may exist having greater or less permanence, such, 

 for instance, as the streams assumed to exist in the theory of 

 viscosity. At the point (<r, z) a positive stream kz parallel 

 to X, at (,r, —z) a stream —kz parallel to x. Now, as I have 

 said elsewhere, in presence of such continuing disturbances 

 a molecule which has finite dimensions, or as a centre of force 

 has finite sphere of action, is exposed to different influences 

 on different sides or parts of its surface, and its motion is 

 affected by these differences, and that may affect the mean 

 potential, the mean virial, and the question of stability. It is 

 true of course that molecular dimensions are exceedingly 

 small, but so is the scale on vrhich the disturbances take place. 

 Now unless assumption A be made, effects of this kind are 

 an essential part of the phenomena. We do not allow for 

 them by simply stating the fact that (for instance) a spherical 

 molecule has radius R, or two molecules have a potential % of 

 their mutual action, and then putting the question on the shelf. 

 If, on the other hand, we make assumption A, we assume the 

 non-existence of permanent or continuing disturbances ; and 

 in that case the simple statement of fact, and attention to it in 

 the limits of integration, is all that we want or can have. 

 And that is what Jeans has given us. For which reason I 

 think the theory developed in his paper is impliedly based, 

 like the orthodox theory, on assumption A. But as above 

 stated I admit that I may be mistaken. 



