409-411] Dissociation 337 



This being so, it appears that the molecule has six degrees of freedom 

 the three translational degrees represented by the differentials dudvdw, and 

 the three internal degrees represented by the differentials dadfidy. 



We notice first that a, /3, <y, the components of F", enter similarly into 

 the law of distribution, so that for the velocity of a single atom relatively 

 to the centre of gravity of a molecule, all directions are equally probable. 

 There is no tendency for the atoms to fall into circular orbits. 



We notice next that as there are six degrees of freedom, the value of 7, 

 even if we neglect potential energy, must be 1, and will be less if potential 

 energy is taken into account. As we have seen that for diatomic molecules 

 7 is fairly uniformly equal to If, this suggests that we are on the wrong 

 track as regards underlying physical hypotheses. 



411. We have made practically no assumptions except that of conserva- 

 tion of energy, so that we are again led to examine what modifications have 

 to be made if dissipation of energy is taken into account. 



Since the atoms are known, from the evidence of spectroscopy, to be 

 capable of internal vibration, it seems extremely improbable that two atoms 

 could describe orbits about one another, and therefore exert varying forces 

 on one another, without "forcing" some at least of these vibrations. A 

 rough numerical calculation suggests that these forced vibrations would be 

 of considerable amplitude. The internal kinetic energy of the molecule, 

 raF 2 , can be written in the form 



m (r 2 -r r 2 2 + r 2 sin 2 0< 2 ), 



where r, 0, <f> are the polar coordinates of either atom referred to the centre 

 of gravity of the molecule. If there were no dissipation of energy, we 

 should have, from the law of equipartition, 



so that r is, on the average, comparable with C. The value of r, however, 

 increases and decreases alternately as the apses of the orbit are described, 

 and for a considerable number of the orbits the range of variation of r 

 will be small compared with the molecular diameter. It follows that the 

 time of oscillation of the value of r is small compared with the time which we 

 took in Chapter IX as the most probable duration of a collision, and hence, 

 by the analysis of Chapter IX, that the internal vibrations forced in the 

 atoms will be large. Thus any initial tendency to oscillations in the value 

 of r will be damped, and the atoms will describe circular orbits about one 

 another. 



There are now only five degrees of freedom for a diatomic molecule, 

 and the molecule is dynamically identical with the single rotating body 



j. 



22 



