16 Lord Kelvin on the 



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, consisting of very small shorten- 

 ings and lengthenings of the distance C C, and two rotational, 

 consisting of rotations round one or other of two lines per- 

 pendicular to each other and perpendicular to C 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 vibrations, or exactly equal to it as according to the 

 Boltzmann-Maxwell doctrine, it is easily proved that in 

 rotation the excess of C 0' above the equilibrium distance a, 

 due to centrifugal force, must be exceedingly small in com- 

 parison with the maximum value of GC/ — a due to the 

 vibration. Hence the average potential energy of the rota- 

 tion 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 = i Thus we find &-l=f =*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, k — 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 dis- 

 crepance from observation suffices to absolutely disprove the 

 Boltzmann-Maxwell doctrine. What is really established in 

 respect to partition of energy is what Clausula* theorem tells 

 us (§ 23 above). We find, as a result of observation and 

 true theory, that the average kinetic energy of translation of 

 the molecules of common air is *609 of the total energy, 

 potential and kinetic, of the relative motion of the constitu- 

 ents of the molecules. 



§ 25. The method of treatment of Ex. 3 above, carried out 

 for a cluster of any number of atoms greater than two not in 

 one line, ^-j-2 atoms, let us say, shows us that there are three 

 translational freedoms; three rotational freedoms, relatively 

 to axes through the inertial centre; and ?>j vibrational free- 



j 1 



doms. Hence we have P = ^— -, and we find k — l= 0/1 , , . 



,7 + 2' 3(1+.; J 



The values of & — 1 thus calculated for a triatomic and tetra- 

 tomic gas, and calculated as above in Ex. 3 for a diatomic 



