382 MATHEMATICAL APPENDICES 16* 



for the number of molecules which move with such a velocity 

 and in such a direction that its velocity components are u, v, w. 

 Thus, too, the number of particles which have a component n, 

 independently of the components v and w, which remain un- 

 determined, is 



and similarly the numbers of particles whose velocities have the 

 components v and w respectively are 



N(TT ~ l km)*e ~ kmv "-dv, N(T 



The constant k which here occurs is connected with the mean 

 /kinetic energy E of molecular motion by the relation 



In these simplified formulae lies the law found by Maxwell, 

 which has been already pointed out in 24 the law, that is, that 

 the different values of the components of the molecular velocities 

 are distributed among the molecules considered according to the 

 same rule by which the errors of observation of different magni- 

 tudes are distributed among the observations in accordance with 

 the method of calculation by least squares. 



According to the formulae first given, this special case of a gas 

 at rest in space is distinguished from the more general case, in 

 which the gas flows as a whole with a certain velocity, only by 

 the velocity of flow having to be subtracted. The same law holds 

 good when we diminish the components u, v, w of the velocity of 

 a molecule by the components a, b, c of the velocity with which 

 the gas flows as a whole. The molecular motions will therefore 

 not be disturbed by a translatory motion being given to the gas as 

 a whole, but both motions combine simply together. 



17*. Gas in Rotation 



Just as simply stands the matter when the gas is not put into 

 translatory motion, but into rotation about an axis. 



In a review of a book 1 Maxwell has pointed_Qut that the 

 general theorems of mechanics mentioned inSll* are not the 



1 Notice of Watson's Kinetic Theory of Gases, Oxford 1876, in Nature 

 xvi. 1877, p. 242. 



