17* MAXWELL'S LAW 385 



is the velocity with which a particle at the point x, y, z advances 

 in the direction of the axis of x while rotating about the axis of y 

 from the -axis to the #-axis with the angular velocity 17, and also 

 about the axis of z from the #-axis to the ^/-axis with the angular 

 velocity . In exactly similar ways are the two other magnitudes 

 to be interpreted. The formulae therefore express motions of the 

 gaseous mass which correspond to those of a nut which moves on a 

 screw-spindle that itself moves along and turns about a second axis. 



These kinds of motion of the gaseous mass are, as our ex- 

 amination shows, to be simply subtracted from the molecular 

 motion present in order for us to arrive dipeclily at Maxwell's 

 law of distribution for the state of rest. Hence it follows that 

 the individual motions of the molecules are not disturbed if in 

 addition to a forward translatory motion of a gas there are also 

 rotations about any axis in which the gas as a whole takes part. 

 The actual velocities of a particle are thus made up of three 

 parts : firstly, of the motion which the particle would have in 

 accordance with Maxwell's law if the gas were at rest as a 

 whole ; secondly, of the velocity with which the centroid of the 

 whole gas moves ; and, thirdly, of the motions which it has in 

 taking part in the general rotation with the mean values , 17, of 

 the angular velocities. 



Thus the kinetic energy of the molecular motions breaks up 

 into ihree parts, and the mean energy of a molecule at the- point 



z$* + (c + yt-xtf}. 



When the whole amount of energy is known this formula may be 

 used for the determination of the constant k. 



In order to obtain Maxwell's law of distribution in its 

 simplest form, we have, according to the foregoing discussion, to 

 subtract from the components u, v, ID of the molecular velocity, no 

 always equal values of speed for all the different particles which 

 belong to the system, but for each particle the values of the 

 velocity-components which belong to the whole gas at the point 

 where it actually is. This remark discloses the possibility of 

 widening still further the limits of the region wherein Maxwell's 

 law holds good. 



In the simple cases which we have considered the validity 

 of this process would have been easy to see even without mathe- 



c c 



