370 Lord Kelvin [April 27, 



which is the simplest illustration of the molecular dynamics of 

 Avogadro's law. It seems to me, however, that Tait's demonstration 

 of the Waterston-Maxwell law may possibly be shown to virtually 

 include, not only this vitally important subject, but also the very in- 

 teresting, though comparatively unimportant, case of an assemblage of 

 particles of equal masses with a single particle of different mass 

 moving about among them. 



§ 16. In §§ 12, 14, 15, " particle" has been taken to mean what 

 is commonly, not correctly, called an elastic sphere, but what is in 

 reality a Boscovich atom acting on other atoms in lines exactly through 

 its centre of inertia (so that no rotation is in any case produced by 

 collisions), with, as law of action between two atoms, no force at distance 

 greater than the sum of their radii, infinite force at exactly this distance. 

 None of the demonstrations, unsuccessful or successful, to which I have 

 referred would be essentially altered if, instead of this last condition, we 

 substitute a repulsion increasing with diminishing distance, according 

 to any law for distances less than the s-irm of the radii, subject only to 

 the condition that it would be infinite before the distance became zero. 

 In fact the impact, oblique or direct, between two Boscovich atoms thus 

 defined, has the same result after the collision is completed (that is to 

 say, when their spheres of action get outside one another) as collision 

 between two conventional elastic spheres, imagined to have radii 

 dependent on the lines and velocities of approach before collision 

 (the greater the relative velocity the smaller the effective radii) ; and 

 the only assumption essentially involved in those demonstrations is, 

 that the radius of each sphere is very small in comparison with the 

 average length of free path. 



§ 17. But if the particles are Boscovich atoms, having centre of 

 inertia not coinciding with centre of force ; or quasi Boscovich atoms, 

 of non-spherical figure ; or (a more acceptable supposition) if each par- 

 ticle is a cluster of two or more Boscovich atoms : rotations and changes 

 of rotation would result from collisions. Waterston's and Clausius' 

 leading principle, quoted in § 13 above, must now be taken into 

 account, and Tait's demonstration is no longer applicable. Waterston 

 and Clausius, in respect to rotation, both wisely abstained from saying 

 more than that the average kinetic energy of rotation bears a constant 

 ratio to the average kinetic energy of translation. With magnificent 

 boldness Boltzmann and Maxwell declared that the ratio is equality ; 

 Boltzmann having found what seemed to him a demonstration of this 

 remarkable proposition, and Maxwell having accepted the supposed 

 demonstration as valid. 



§ 18. Boltzmann went further * and extended the theorem of 

 equality of mean kinetic energies to any system of a finite number of 

 material points (Boscovich atoms) acting on one another, according to 

 any law of force, and moving freely among one another ; and finally, 



* 'Studien iiber das Gleichgewicht der lebendigen Kraft zwischcn bewcgten 

 rnateriellen runkten.' Sitzb. K. Akad. Wien., October 8, 1868. 



