592 



SCIENTIFIC THOUGHT. 



28. 



Mathe- 

 matical rep- 

 resentation 

 of experi- 

 mental laws, 



such moving crowds turn out to be exactly those laws 

 which Boyle, Charles, Gay-Lussac, Dalton, and Avogadro 

 had found out by direct experiments with gaseous bodies. 

 James Clerk - Max well was the first to recognise the 

 great importance of the statistical methods, and to 

 apply them in an exhaustive manner.^ And we witness 

 here the same spectacle which presented itself in the 

 history of the theory of probabilities. Problems which 

 are to be solved by the mere application of a few rules 

 dictated by common-sense and an exercise of common 

 logic, present in their complexity such a multitude 

 of traps, snares, and pitfalls, that it required the suc- 

 cessive application of the highest intellects to free the 

 reasoning from insidious errors, and put the results on 



\/ 



^ The mauner in which Joule 

 dealt with the problem of a large 

 crowd of moving particles in his 

 memoir of 1851 was not strictly 

 statistical, inasmuch as he dealt 

 with an average velocitj' of the 

 molecules, and assumed that all the 

 molecules of a gas moved with the 

 same velocity. Clausius, in his 

 memoir of 1857, made use of as- 

 sumptions which were more in 

 conformity with nature : he had. 

 accordingly, to employ the calculus 

 of probabilities. Clerk - Maxwell's 

 occupation with the subject dates 

 from the year 1859, when he read 

 his paper, " Illustrations of the 

 Dynamic Theory of Gases," Part I. 

 (published in the ' Phil. Mag.,' 4th 

 series, vol. xix. p. 19, reprinted in 

 'Scientific Papers,' vol. i.) He 

 showed that " the velocities are 

 distributed among the particles 

 according to the same law as errors 

 are distributed among the observa- 

 tions in the theory of the method 

 of least squares. The velocities 

 range from to <x, but the number 



of those having great velocities is 

 comparatively small." If we leave 

 out Joule's imperfect attempt to 

 employ the statistical method, one 

 of the first applications of the 

 method of averages to a physi- 

 cal problem is to be found in 

 Sir G. G. Stokes's paper "On 

 the Composition of Streams of 

 Polarised Light from different 

 Sources" ('Camb. Phil. Trans.,' 

 1853), where he shows "what 

 will be the average effect of a very 

 great number of special sources 

 of light : thus giving one of the 

 earliest illustrations of the use, 

 in physics, of the statistical methods 

 of probabilities. . . . From this 

 point of view the uniformity of 

 optical phenomena becomes quite 

 analogous to the statistical species 

 of uniformity, which is now found 

 to account for the behaviour of the 

 practically infinite group of particles 

 forming a cubic inch of gas " (P. G. 

 Tait, 'Light,' 2nd ed., 1889, p. 

 237). 



