438 



SCIENTIFIC THOUGHT. 



38. 



Clerk Max- 

 well. The 

 statistical 

 view of 

 nature. 



well to develop the novel conceptions which here force 

 themselves upon us. Especially are we indebted to him 

 for the idea marking an epoch in the history of scientific 

 thought of the difference between historical knowledge 

 of natural phenomena and a merely statistical summary 

 of average results. 1 If the atomic view of nature has to 

 be adopted seriously, as the development of the kinetic 



1 See Clerk Maxwell's memoir, 

 ' Illustrations of the Dynamical 

 Theory of Gases' (1859: reprinted 

 in ' Scientific Papers,' vol. i. p. 377). 

 Clausius had in his second paper, 

 " On the average mean path of a 

 particle" (Poggendorf's 'Annalen,' 

 1858), given an expression for this 

 quantity as depending on the aver- 

 age distance of two particles and on 

 the average diameter of the sphere 

 of action of a particle. As these 

 quantities are all only mean or aver- 

 age quantities, he had been obliged to 

 resort to a method which was then 

 novel in physical science, the method 

 of averages and the calculus of prob- 

 ability, which is its mathematical 

 expression. He had calculated the 

 probability of a certain motion of a 

 particle. Maxwell, who had in 1856 

 been engaged in writing his Adams 

 prize essay " On the stability of the 

 motion of Saturn's rings," had there 

 considered the possibility of these 

 rings being composed of a cloud of 

 scattered particles moving with all 

 possible velocities towards each 

 other and round some attracting 

 centre : he was thus familiar with 

 physical problems in which the 

 given data could be only average 

 quantities. He now undertook to 

 develop systematically the methods 

 necessary for treating such prob- 

 lems, of which we have only statis- 

 tical knowledge, and he there de- 

 veloped his famous law which gives 

 the distribution of different veloci- 

 ties in a crowd of particles moving 



at random and in their collisions 

 obeying the condition of the con- 

 servation of energy. This investi- 

 gation marks an epoch in mathe- 

 matical physics and in the history 

 of the atomic view of nature. Like 

 all theorems connected with the 

 theory of probability, it has pro- 

 voked a large literature, the founda- 

 tions of the proof and the different 

 steps in the logic of the deductions 

 having been examined and criticised 

 in the most searching manner. The 

 expression given by Maxwell has 

 stood all these criticisms, " he has 

 demonstrated the possibility of 

 calculating in a strict manner the 

 averages which before him had only 

 been estimated, but which were 

 required for a further development 

 of the theory of gases." See 0. E. 

 Meyer, ' Die kinetische Theorie der 

 Gase,' 2d. ed.,vol. i. p. 45, &c., where 

 also a complete account is given of 

 the various steps by which the 

 doubts which attached to Maxwell's 

 theories and his proofs were at 

 length removed, and the "variety 

 of traps and pit - falls " avoided 

 " which are met with even in the 

 elements of the subject " (see Tait, 

 " On the Foundations of the Kinetic 

 Theory of Gases." 'Trans, of the 

 Royal Soc. of Edinburgh,' 1886, 

 vol. xxxiii. part 1, p. 66). In a 

 later chapter of this history I in- 

 tend to trace the development of 

 the statistical view of nature, and 

 shall then have occasion to revert 

 to this subject. 



