24 Ladislaus Natanson on the Kinetic Theory 



N 

 along any isotherm, and must in fact be proportional to — : 



Therefore -srd must be constant, and consequently S also, since 

 ot cannot be regarded as dependent upon v. 



This conclusion can also be arrived at in the following 



AT 2"p ( f\ 



manner. Let — ! — — new molecules be formed during unit 



v 



time. In unit time ! Cl — collisions of two atoms take 

 v 



place ; therefore 'F 1 (t) ='&c 1 * / t, where c x is a constant factor. 



Now let us calculate how many molecules are decomposed in 



unit time, if hypothesis (a) be true. During unit time there 



take place between the molecules on the one hand, and either 



molecules or atoms on the other hand, 



collisions. Again, if «r 2 and -3t 12 denote the ratios of the 

 number of dissociating collisions to the corresponding total 

 number of collisions, and assuming that ot 2 and tn- 12 are indepen- 

 dent of the volume, so that «r 2 c 2 */t=¥ 2 {t), and vr^is *Jt = F 12 (t) , 

 the condition for equilibrium expressed in § 1 becomes 



N 1 2 Fa*)=N/F 2 (f) + N 1 N 2 F 12 (<), 



which is quite different from (C) § 1. 



§ 4. The equation (B) of § 1 is also, as I believe, incom- 

 patible with hypothesis (a), and for this reason, that then 

 Maxwell's law loses its meaning. The true meaning of this 

 law may be thus expressed : — " If two gases are mixed 

 together, whose mean kinetic energies are different, an ex- 

 change of energy takes place until the difference disappears ""*. 



If two colliding atoms enter into combination, their energy 

 divides into motion of the centre of gravity and relative 

 motion. The molecules formed have therefore a definite 

 mean value for the kinetic energy of the motion of the centre 

 of gravity, which we shall call molecular motion. 



Now there are two cases possible : — (i.) The molecular 

 energy may, just after the formation of the molecule, be 

 equal to that of the free atoms; this is the case, for example, 

 when aggregations are formed in imperfect gases, as I have 

 already pointed outf. Then Ej and E 2 are equal, because 

 this follows as a consequence of the laws of collision of atoms, 



* Tait, Trans. R. S. E. xxxiii. p. 82 (1886) ; cf. Wied. Ann. xxxiv. 

 p. 970 (1888). 



t Wied. Ann. xxxiii. p. 687 et sea. (1888). 



