1900.] on the Dynamical Theory of Heat and Light. 375 



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 pro- 

 bability be of exceedingly small mass in comparison with that of tho 

 chief atom. Can they be the " ions " by which J. J. Thomson explains 

 the electric conductivity 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 7c — 1 

 found by Bayleigh and Eainsayare somewhat less than 5- ; argon "64, 

 •61; helium - 6L2; krypton '666. If the deviation from -667 were 

 accidental they would probably have been some in defect and some in 

 excess. 



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

 simplest case let the two atoms be in stable equilibrium when con- 

 centric, and be infinitely nearly concentric when the clusters move 

 about, constituting a homogeneous gas. This supposition makes 

 P = 1, 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 

 A-l = |= -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 asunder, and let 

 the atoms be always very nearly at this distance asunder when 

 the clusters are not in collision. The relative motions of the two 

 atoms will be according to three freedoms, one vibrational, consist- 

 ing of very small shortenings and lengthenings of the distance 

 C C, and two rotational, consisting of rotations round one or other of 

 two lines perpendicular to each other and perpendicular to C 

 through the inertial centre. With these conditions and limitations, 

 and with the supposition that half the average kinetic energy of the 

 rotation is comparable with the average kinetic energy of the vibra- 

 tions, or exactly equal to it as according to the Boltzmann-Maxwell 

 doctrine, it is easily proved that in rotation the excess of C C above the 

 equilibrium distance a, due to centrifugal force, must be exceedingly 

 small in comparison with the maximum value of C C — a due to the 

 vibration. Hence the average potential energy of the rotation is 

 negligible in comparison with the potential energy of the vibration. 

 Hence, of the three freedoms for relative motion there is only one 

 contributory to P, and therefore we have P = £. Thus we find 

 k- 1 = I = -2857. 



The best way of experimentally determining the ratio of the two 

 thermal capacities for any gas is by comparison between the observed 

 and the Newtonian velocities of sound. It has thus been ascertained 

 that, at ordinary temperatures and pressures, h — 1 differs but little 

 from • 406 for common air, which is a mixture of the two gases nitrogen 

 and oxygen, each diatomic according to modern chemical theory ; and 

 the greatest value that the Boltzmann-Maxwell doctrine can give for 

 a diatomic gas is the *2857 of Ex. 3. This notable discrepance 



