376 



Lord Kelvin 



[April 27, 



from observation, suffices to absolutely disprove the Boltzmann- 



Maxwell doctrine. What is really established in respect to partition 



of energy is what Clausius' 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 constituents 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 3j vibrational freedoms. Hence we have 



?' 1 

 P = — I — , and we find It — 1 = —, — . The values of h — 1 thus 



y+2' m _ 3(i+i) 



calculated for a triatomic and tetratomic gas, and calculated as above 

 in Ex. 3 for a diatomic gas, are shown in the following table, and 

 compared with the results of observation for several such gases : 



It is interesting to see how the dynamics of Clausius' theorem is 

 verified by the results of observation shown in the table. The values 

 of h — 1 for all the gases are less than f, as they must be when 

 there is any appreciable energy of rotation or vibration in the mole- 

 cule. They are different for different diatomic gases ; ranging from 

 •42 for oxygen to *32 for chlorine, which is quite as might be 

 expected, when we consider that the laws of force between the two 

 atoms may differ largely for the different kinds of atoms. The 

 values of h — 1 are, on the whole, smaller for the tetratomic and 

 triatomic than for the diatomic gases, as might be expected from 

 consideration of Clausius' principle. It is probable that the differ- 

 ences of k — 1 for the different diatomic gases are real, although 

 there is considerable uncertainty with regard to the observational 

 results for all or some of the gases other than air. It is certain that 



