130 Proceedings of Poyal Society of Edinburgh. 
[SESS. 
On Vibrating Systems which are not subject to the 
Boltzmann-Maxwell Law. By Dr W. Peddie. 
(MS. received February 23, 1906.) 
1. It is well known that the Boltzmann-Maxwell Law, which 
asserts average equi-partition of kinetic energy amongst the various 
motional freedoms, finite or infinite in number, of suitably con- 
ditioned systems, meets with apparently insuperable difficulties 
in its application to actual gases. Even in the case of gases 
showing complicated spectra, and therefore possessing numerous 
vibrational freedoms, the actual values of the ratio of the specific 
heats never deviate much from values which should, according 
to the law, he limited to very simple systems. Possible modes of 
evading this result, such as that supplied by J. J. Thomson’s 
suggestion (Arch. Neerlandaises, 1900, Ser. II. t. v.) that individual 
molecules may not he concerned in radiation, are too problematical 
to give much relief. 
Lord Kelvin (Baltimore Lectures , Appendix B) says that 
Clausius’ theorem regarding the specific heats, “ taken in connection 
with Stokes’ and Kirchhoff’s dynamics of spectrum analysis, throws 
a new light upon what we are now calling a ‘ practically monatomic 
gas.’ It shows that, unless we admit that the atoms can he set 
into rotation or vibration by mutual collisions (a most unacceptable 
hypothesis), each atom 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.” 
This asserts actual violation of the Boltzmann-Maxwell condition. 
Jeans’ recent suggestion (Nature, vol. lxxi., 1905) that the 
complete system must include the ether, and that radiation has 
hitherto prevented attainment, as between matter and ether, of 
that condition of statistical equilibrium, which the law requires, 
merely indicates a hypothetical mechanism necessitating Lord 
Kelvin’s conclusion, although it removes the law from direct attack 
on this side. 
