Dynamical Tlieory of Heat and Light. 15 



shown in the ideal example of § 26 below. On the other 

 hand, Clausius' theorem presents no difficulty ; it merely 

 asserts that h — \ is necessarily less than § in each of these 

 four cases, as in every case in which there is any rotational 

 or vibrational energy whatever; and proves, from the values 

 found experimentally for k — 1 in the four gases, that in each 

 case the total of rotational and vibrational energy is exceed- 

 ingly small in comparison with the translational energy. It 

 justifies admirably the chemical doctrine that mercury vapour 

 is practically a monatomic gas, and it proves that argon, 

 helium, and krypton, are also practically monatomic. though 

 none of these gases has hitherto shown any chemical affinity 

 or action of any kind from which chemists could draw any 

 such conclusion. 



But Clausius' theorem, taken in connection with Stokes' 

 and KirchhofFs dynamics of spectrum analysis, throws a new 

 light on what we are now calling a " practically monatomic 

 gas." It shows that, unless we admit that the atom can be 

 set into rotation or vibration by mutual collisions (a most 

 unacceptable hypothesis), it must have satellites connected 

 with it (or ether condensed into it or around it) and kept, 

 by the collisions, in motion relatively to it with total energy 

 exceedingly small in comparison with the translational 

 energy of the whole system of atom and satellites. The 

 satellites must in all probability be of exceedingly small mass 

 in comparison with that of the chief atom. (Jan they be the 

 "ions" by which J.J.Thomson explains the electric con- 

 ductivity induced in air and other gases by ultra-violet light, 

 Rontgen rays, and Becquerel rays ? 



Finally, it is interesting to remark that all the values of 

 h — 1 found by Rayleigh and Ramsay are somewhat less than 

 f; argon '64, '61; helium "652; krypton '666. If the devia- 

 tion from "667 were accidental they would probably have 

 been some in defect and some in excess. 



Example 2. — As a next simplest example let t=2, and as 

 a very simplest case let the two atoms be in stable equili- 

 brium when concentric, and be infinitely nearly concentric 

 when the clusters move about, constituting a homogeneous 

 gas. This supposition makes P = J, because the average 

 potential energy is equal to the average kinetic energy in 

 simple harmonic vibrations; and in our present case half the 

 whole kinetic energy, according to the Boltzmann-Maxwell 

 doctrine, is vibrational, the other half being translational. 

 We find &-l=f ='2222. 



Example 3. — Let i = 2 ; let there be stable equilibrium, 

 with the centres C, C of the two atoms at a finite distance a 



