276 Mr. R. H. M. Bosanquet on the Theory of Sound. 



two to rotation ; for by the hypothesis that the body is a solid 

 of revolution, perfectly hard and smooth, vis viva of rotation 

 about the axis of revolution is excluded. 

 The Clausius equation then takes the form 



which gives 



- = 12 or 1-40. 

 c °' 



The ratio of the specific heats for air, as deduced from the 

 value of sound, cannot, as we have seen, be assigned with great 

 accuracy from a comparison of experimental data ; all we can 

 say is that the value of the velocity of sound, deduced from 

 ratio 1*40, differs from our mean value by an amount insigni- 

 ficant compared with the difference of the mean value from the 

 results of the various experimenters. (Mean value =331*35 

 metres, value due to 140 = 331*2 metres.) 



If, then, Kundt and Warburg's result is worth any thing at 

 all, it is clear that the explanation of the ratio of specific heats 

 in air and allied gases may be placed on a perfectly analogous 

 footing. 



The relation is so obvious that it is impossible to suppose 

 that it has not occurred before to the eminent men who have 

 dealt with the subject. I will notice the points of objection 

 that occur to me ; there may be others of a more conclusive 

 character. 



It has been frequently assumed that if two or more atoms 

 are built up into a molecule, they must be connected in such 

 a manner that they can oscillate with respect to their common 

 centre of gravity. Every degree of freedom in such oscilla- 

 tions should, it appears, retain the same vis viva as a degree of 

 freedom of the motion of the molecule itself*. Under these 

 circumstances, if we supposed two spherical atoms joined by 

 elastic forces, the system would have more than five degrees 

 of freedom. 



If we ask, why must we suppose the two atoms joined by 

 elastic forces and not rigidly? we are told that it is the vibra- 

 tions of the atoms that do the work we see in the spectroscope 

 lines. But these lines occur in the vapour of mercury, for 

 which our explanation fails to suggest any collocation of atoms 

 more than one in the molecule. Why not, then, admit that the 

 lines are produced by something within the atom which we 



* Boltzmann, Ber. d. Wien. Akacl. vol. lxiii. 



