14 Lord Kelvin on the 



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 system, translational 

 and relative, to be 3z(l + P) times the mean kinetic energy 

 of one component of the motion of the inertial centre, where 

 P denotes the ratio of the mean potential energy of the 

 relative displacements of the parts to the mean kinetic energy 

 of the whole system. Now, according to Clausius' splendid 

 and easily proved theorem regarding the partition of energy in 

 the kinetic theory of gases, the ratio of the difference between 

 the two thermal capacities to the constant-volume thermal 

 capacity is equal to the ratio of twice a single component of 

 the translational energy to the total energy. Hence, if 

 according to our usual notation we denote the ratio of the 

 thermal capacity, pressure constant, to the thermal capacity, 

 volume constant, by k, we have, 



k-1 



3t(l + P)' 



§ 24. Example 1. — For first and simplest example, consider 

 a monatomic gas. We have i = l, and according to our sup- 

 position (the supposition generally, perhaps universally, made) 

 regarding atoms, we have P = 0. Hence, h — 1 = §. 



This is merely a fundamental theorem in the kinetic theory 

 of gases for the case of no rotational or vibrational energy of 

 the molecule; in which there is no scope either for Clausius' 

 theorem or for the Boltzmann-Maxwell doctrine. It is beau- 

 tifully illustrated by mercury vapour, a monatomic gas 

 according to chemists, for which many years ago Kundt, in 

 an admirably designed experiment, found k — 1 to be very 

 approximately §; and by the newly discovered gases argon, 

 helium, and krypton, for which also k— 1 has been found to 

 have approximately the same value, by Eayleigh and Ramsay. 

 But each of these four gases has a large number of spectrum 

 lines, and therefore a large number of vibrational freedoms, 

 and therefore, if the Boltzmann-Maxwell doctrine were true, 

 Jc— 1 would have some exceedingly small value, such as that 



