ON OUR KNOWLEDGE OF THERMODYNAMICS. 89 



of steady flow of gases, viscosity, diffusion, heat conduction, chemical 

 action, &:c. Such questions form the subjects of investigations by Boltz- 

 mann,' Tait,'^ Burbury,^ Natanson,^ and other writers too numerous to 

 mention. A complete list of papers would probably require a Report to 

 itself, but the references in the accompanying footnotes may be of some 

 assistance to those specially interested in the subject. 



48. An entirely different class of problems has been treated by Lord 

 Rayleigh in illustration of the properties of colliding bodies in general, 

 considered especially with reference to the Kinetic Theory.'^ He con- 

 siders the law of distribution of energy in a number of large masses, each 

 of which is bombarded by streams of projectiles of much smaller mass 

 moving in both directions in a straight line. If the projectiles are all 

 moving with the same speed v, Lord Rayleigh finds that the velocities u 

 of the bombarded masses will assume the Boltzmann-Maxwell distri- 

 bution 



/(zA)=Ae-^"' 



where the mean kinetic energy of the masses is one half that of each pro- 

 jectile. 



If, however, the velocities of the projectiles themselves are distri- 

 buted according to the Boltzmann-Maxwell distribution, the same is true 

 of the bombarded masses, and the mean kinetic energies of the masses 

 and projectiles are equal. Hence the icltole system, consisting of the pro- 

 jectiles and masses, satisfies the Boltzmann-Maxwell distribution as 

 defined in § 34. Lord Rayleigh goes on to consider the case when the 

 free masses are replaced by pendulums under a one-sided or two-sided 

 bombardment, and also gives an interesting investigation of the rate of 

 progress towards the ' special ' state, the motion in every case being one- 

 dimensional. 



Collisions replaced by Encounters. 



49. Boltzmann has pointed out " that the effect of a collision between 

 material points or monatomic molecules may equally well be represented 

 by an encounter in which only attractive forces act. When the particles 

 are at a certain distance apait he supposes a very great impulsive attrac- 

 tion to act on them, so that their directions of relative motion are refracted 

 very nearly into the straight line joining them. "When, after passing close 

 together, they again come to the same distance, they undergo a second re- 

 fraction under an impulsive attraction equal and opposite to the first, and the 



' ' Zur Theorie der Gasreibung,' Sitzher. der It. Wiener Acad., Ixxxi. (ii.)> January 

 1880; Ixxxiv. (ii.), June 1881, December 1881. 'Zur Theorie der Gasdiffusion,' ibid., 

 Ixxxvi. (ii.), June 1882; Ixxxviii. (ii.), October 1883. 'Bemerkungen iiber die 

 Wiirmeleitung der Gase,' ibid., Ixxii. (ii.), October 1875. Other papers are in the 

 Sltzmigsberichte, Ivi. (ii.), November 1867, Ixxv. (ii.), January 1887, xcvi. (ii.), October 

 1887; Annalen der Pbysik und Clicnde, vol. xxii. 1884, p. 39. 



''■ ' On the Foundations of the Kinetic Theory of Gases,' Trans. Soy. Soc. Edin~, 

 1886. See also my first Report for fuller references. 



* Phil. Mag., October 1890, p. 306, &c. 



■* ' Sur rinterpretation cinetique de la Fonction de Dissipation,' Comptes Rendm, 

 October 23, 1893, &c. ; Bulletin de VAead. des Sciences de Cracovie, December 1893, 

 p. 348. 



^ ' DjTiamical Problems in Illustration of the Theory of Gases,' PJiil. Mag., 

 November 1891. 



' ' Deber die Moglichkeit der Begriindung einer kinetischen Gastheorie auf 

 anziehende Kriifte allein,' Annalen der Pliysik nnd Chende, xxiv. (1885"), p. 37. 



