44 MOLECULAR MOTION AND ITS ENERGY 23 



The arrangement that changes from moment to moment 

 and represents the distribution of the different speeds among a 

 limited number of molecules, oscillates therefore about a mean 

 regular state, and in such wise that the result which ensues 

 in the course of a considerable time is the same as if that 

 regular state had existed at each moment. In the calcula- 

 tion of the result we may therefore consider that regular 

 distribution of speeds as always existing instead of the actual 

 circumstances of constant change. 



24. Maxwell's Law 



/The law which regulates this distribution of speeds 

 among the gaseous molecules was discovered by James 

 Clerk Maxwell, 1 who thus made it possible to calculate, 

 by strict mathematical methods, the mean values of the 

 speeds which hitherto had been only estimated, and a know- 

 ledge of which was necessary for the development of the 

 theory of gases. 



Maxwell's law of distribution, the theoretical founda- 

 tion of which rests on the calculus of probabilities, agrees 

 exactly in form with another law which is also founded on 

 this calculus. The possible values which the components of 

 the molecular velocities can assume are distributed among 

 the molecules in question according to the same law as the pos- 

 sible errors of observation are by the method of least squares 

 distributed among the observations. 



According to this law the equilibrium of a gas depends, 

 of course, as was to be expected, in no way upon equality of 

 motion in all the particles. All values between and oo 

 occur for the components of velocity, and in such fashion 

 that small values occur oftener than large ones, just as 

 according to the method of least squares errors of small 

 magnitude should happen oftener than large ones. 



In order to give an idea of this law without having 

 recourse to mathematical formulae I will quote a few figures. 2 



1 Phil. Mag. [4] xix. 1860, p. 22 ; Scientific Papers, i. p. 377. 



2 Obtained from the values of the integrals 



( } dze- z "~ = 0-74682, f 2 <fee~* a = 0-13525, Vdze~** = 0-00413. 



