Dynamical Theory of Heat and Light. 13> 



thus : Two atoms are said to be in collision during all the 

 time their volumes overlap after coming into contact. They 

 necessarily in virtue of inertia separate again, unless some 

 third body intervenes with action which causes them to 

 remain overlapping; that is to say, causes combination to 

 result from collision. Two clusters of atoms are said to be 

 in collision when, after being separate, some atom or atoms 

 of one cluster come to overlap some atom or atoms of the 

 other. In virtue of inertia the collision must be followed 

 either by the two clusters separating, as described in the last 

 sentence of § 19, or by some atom or atoms of one or both 

 systems being sent flying away. This last supposition is a 

 matter-of-fact statement belonging to the magnificent theory 

 of dissociation, discovered and worked out by Sainte-Clair 

 Deville without any guidance from the kinetic theory of 

 gases. In gases approximately fulfilling the gaseous laws 

 (Boyle's and Charles'), two clusters must in general fly 

 asunder after collision. Two clusters could not possibly 

 remain permanently in combination without at least one atom 

 being sent flying away after collision between two clusters 

 with no third body intervening *. 



§ 23. Now for the application of the Boltzmann-Maxwell 

 doctrine to the kinetic theory of gases : consider first a 

 homogeneous single gas, that is, a vast assemblage of similar 

 clusters of atoms moving and colliding as described in the 

 last sentence of § 19; the assemblage being so sparse that 

 the time during which each cluster is in collision is very 

 short in comparison with the time during which it is unacted 

 on by other clusters, and its centre of inertia, therefore, 

 moves uniformly in a straight line. If there are i atom> in 

 each cluster, it has 3/ freedoms to move, that is to say, free- 

 doms in three rectangular directions for each atom. The 

 Boltzmann-Maxwell doctrine asserts that the mean kinetic 

 energies of these Si motions are all equal, whatever be the 

 mutual forces between the atoms. From this, when the 

 durations of the collisions are not included in the time- 

 averages, it is easy to prove algebraically (with exceptions 

 noted below) that the time-average of the kinetic energy of 

 the component translational velocity of the inertial centre f y 

 in any direction, is equal to any one of the 3/ mean kinetic 

 energies asserted to be equal to one another in the preceding 

 statement. There are exceptions to the algebraic proof 



* See Kelvin's Math, and Phys. Papers, vol. iii. Art. xevn. § 33. In 

 this reference, for " scarcely " substitute " not." 



t This expression I use for brevity to signify the kinetic energy of the 

 whole mass ideally collected at the centre of inertia. 



