ON THE STATISTICAL VIEW OF NATURE. 591 



have to do with billions and trillions of particles, moving 

 with velocities varying from zero to many thousands 

 of miles per second : we have therefore to do with 

 numbers which practically mean infinity that is to 

 say, we have to do with that condition of things 

 where alone the laws of probability become strictly 

 correct. 1 



In this case, any deductions which can be made as to 

 the average condition or collective behaviour of an in- 

 finitely large assemblage of particles, whose individual 

 members move about with infinitely varying velocities 

 at infinitely varying speeds in infinitely varying direc- 

 tions, must be realised in the well - known laws of 

 gaseous bodies referring to pressure, volume, expansion, 

 molecular structure, and heat, assuming the latter to be 

 merely the sensible effect on our nerves of very numer- 

 ous impingements of infinitesimally small particles. It 

 is one of the greatest triumphs of the mathematical 

 methods applied in one of the most difficult instances, 

 that the average behaviour and collective properties of 



1 P. G. Tait ('Heat,' 1884, p. has its course changed. He thus 



355) says : " It is to Clausius that 

 we are indebted for the earliest 

 approach to an adequate treatment 

 of this question. He was the first 

 to take into account the collisions 

 between the particles, and to show 

 that these did not alter the pre- 

 viously obtained results. He has 

 also the great credit of introducing 

 the statistical methods of the 

 theory of probabilities, and of thus 

 giving at least approximate ideas as 

 to the probable length of the mean 

 free, path i.e., the average distance 



explains also the slowness of diffu- 

 sion of gases, and their very small 

 conductivity of heat. Clerk-Max- 

 well shortly afterwards improved 

 the theory by introducing, also from 

 the statistical point of view, the 

 consideration of the variety of 

 speed at which the different par- 

 ticles are moving ; Clausius having 

 expressly limited his investigations 

 by assuming for simplicity that all 

 move with equal speed. Clerk- 

 Maxwell explained gaseous friction, 

 and gave a more definite determina- 



travelled over by a particle before tion of the length of the mean free 

 it impinges on another, and thus path." 



