Mr. J. II. Jiuns' Tlu'ovf/ of Gases, 533 



E boino- the total kinetic encroy, and that gives 



^laxwell's law ot' distribution of velocities, afterwards given 

 in its complete form in (34). 



Now either there exists or there does not exist some other 

 probable relation between the velocities and the coordinates 

 besides [a) and [h). If you assume that no such exists, you 

 make assumption A. If any such does exist, it is not true 

 that S/log/ being minimum characterizes the motion. 

 Maxwell's law does not follow. 



11. In art. 38 Jeans treats of a gas with ''mass velocity" 

 \] = \\. . .f.u . cLi' dy dz die do dw. The integration is intended 

 to include the whole gas under consideration. Now we may 

 conceive a state of things in which every molecule has, in 

 addition to its velocity in the ''normal state," the velocity U. 

 As an example U might be the earth's velocity in space. In 

 the equipartition of energy we do not include the energy of 

 the motion U. If assumption A be made, the only mass 

 motion that the system can possibly have is that simple one 

 formed from the normal state as above defined. For any 

 irregularities, such as some groups of contiguous molecules 

 having on average greater^ others less, momentum in direc- 

 tion denoted by U, if they exist at one instant, will under 

 assumption A cease to exist the next instant. They are 

 assumed to be non-existent. Jeans^ mass motion is then 

 exactly what we should have if we make assumption A. If 

 we do not make assumption A we cannot, except in the above- 

 mentioned case of infinite rarity, obtain Maxwell's law. We 

 must come to the law e~^^. where Q is the quadratic function 

 before defined. And from that it follows at once, if the 

 b coefficients be negative, that the velocities of neighbouring 

 molecules have, on average, the same sign. That is, we have 

 stream motion among the molecules of the gaSj a different thing 

 from Jeans' mass motion of the whole gas. Why should 

 stream motion not exist ? 



12. Such a motion is conceivable. If I mistake not it, or a 

 motion of the same kind, exists in the case of wind, which, as 

 we are told, is not mass motion of the simple kind allowed 

 by Jeans and by assumption A, but one in which the velocities 

 in the given direction vary very rapidly from instant to 

 instant, and from point to point at measurable distances in 

 space. For some, but not for all, purposes, this may be re- 

 presented by " mass motion '' U. Whether such streams exist 

 or not in fact is a proper subject for investigation. The 

 orthodox theory rejects them without investigation, because 

 they might not agree with the equipartition of energy. 



