1900.] on the Dynamical Theory of Heat and Light. 873 



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 prases. 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 be- 

 tween two clusters with no third body intervening.* 



§ 23. Now for the application of the Boltzman-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 uni- 

 formly in a straight line. If there are i atoms in each cluster, it 

 has 3i freedoms to move, that is to say, freedoms in three rectangular 

 directions for each atom. The Boltzman-Maxwell doctrine asserts 

 that the mean kinetic energies of these 3i 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 in any direction, is equal 

 to any one of the Si mean kinetic energies asserted to be equal to one 

 another in the preceding statement. There are exceptions to the 

 algebraic proof corresponding to the particular exception referred 

 to in the last footnote to § 18 above ; but, nevertheless, the general 

 Boltzmann -Maxwell doctrine includes the proposition, even in 

 those cases in which it is not deducible algebraically from the 

 equality of the Si energies. Thus, without exception, the average 

 kinetic energy of any component of the motion of the inertial centre 



is, according to the Boltzmann-Maxwell doctrine, equal to — of the 



whole average kinetic energy of the system. This makes the total 

 average energy, potential and kinetic, of the whole motion of the 

 6ystem, translational and relative, to be 3i (1 -j- P) times the mean 



* See Kelvin's Math, and Phys. Papers, vol. iii. art. xcvn. § 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. 



