23 MAXWELL'S LAW 43 



the atoms which separate and combine again must at first 

 move confusedly about in irregular disorder till the new 

 regular arrangement is found. A still more striking example 

 of a regular law arising from chance events is afforded by 

 meteorological phenomena, the varied change of which 

 follows a law that is clearly recognisable from the means of 

 long periods. 



In all these cases, and in our theory as well, the regu- 

 larity arises only from the great number of the elementary 

 processes from which it results. If this number were not 

 so great, the result in similar cases would not always be 

 absolutely and fixedly one and the same, but there would 

 be different results conceivable of more or less probability. 

 But the greater this number, the greater the probability that 

 of all possible consequences a single perfectly definite one 

 would occur just as if it were directly caused by the opera- 

 tion of a fixed law of nature instead of by the play of 

 numberless casual events. 



Applied to our theory this general view teaches that in a 

 really infinite number of molecules of gas a condition must 

 exist, the law of which must admit of recognition and even 

 of mathematical expression, in spite of the chance character 

 of the motion of each individual molecule. We must there- 

 fore be able to determine how many molecules per thousand, 

 say, taken at random from the countless swarrn, have a 

 speed of a definite magnitude, or, in somewhat different 

 words, we must be able to express numerically the chance 

 that any given molecule in a region filled with an infinite 

 host of molecules should attain a speed of given value. 



In a gaseous mass consisting of a finite number of mole- 

 cules this condition of simple regularity will not be attained, 

 as in the case of an infinite number at least not at every 

 instant. In a finite system this law shows itself only if all 

 the states which occur with continual change in the course 

 of longish periods are taken into account together. The 

 particular condition of regularity which is exhibited at every 

 moment by an infinite swarm determines also for a finite 

 number of molecules its mean state during a considerable 

 period. 



