330 Sir William Thomson on the Ultramundane 



elastic, be much less rigid than that of the former, each glo- 

 bule that strikes one of the cage-bars mast (Thomson and Tait's 

 1 Natural Philosophy/ § 301) come away with diminished velocity 

 of translation, but with the corresponding deficiency of energy 

 altogether converted into vibration of its own mass. Thus the 

 condition required by Le Sage's theory is fulfilled without 

 violating modern thermo-dynamics ; and, according to Le Sage, 

 we might be satisfied not to inquire what becomes of those ultra- 

 mundane corpuscules which have been in collision either with the 

 cage-bars of mundane matter or with one another ; for at present, 

 and during ages to come, these would be merely an inconside- 

 rable minority, the great majority being still fresh with original 

 gravific energy unimpaired by collision. Without entering on 

 the purely metaphysical question, Is any such supposition satis- 

 factory ? I wish to point out how gravific energy may be natu- 

 rally restored to corpuscules in which it has been impaired by 

 collision. 



Clausius has introduced into the kinetic theory of gases the 

 very important consideration of vibrational and rotational energy. 

 He has shown that a multitude of elastic corpuscules moving 

 through void, and occasionally striking one another, must, on 

 the average, have a constant proportion of their whole energy in 

 the form of vibrations and rotations, the other part being purely 

 translational. Eyen for the simplest case — that, namely, of 

 smooth elastic globes — no one has yet calculated by abstract 

 dynamics the ultimate average ratio of the vibrational and rota- 

 tional to the translational energy. But Clausius has shown how 

 to deduce it for the corpuscules of any particular gas from the 

 experimental determination of the ratio of its specific heat, 

 pressure constant, to its specific heat, volume constant*. He 

 found that 



37—I 



if 7 be the ratio of the specific heats, and the ratio of the whole 

 energy to the translational part of it. For air, the value of y 

 found by experiment is 1*408, which makes /3 = 1*634. For 

 steam, Maxwell says, on the authority of Raukine, /3 " may be 

 as much as 2'19; but this is very uncertain. - " If the molecules 

 of gases are admitted to be elastic corpuscules, the validity of 

 Clausius's principle is undeniable ; and it is obvious that the 

 value of the ratio /3 must depend upon the shape of each mole- 

 cule, and on the distribution of elastic rigidity through it, if its 

 substance is not homogeneous. Further, it is clear that the 

 value of /3, for a set of equal and similar corpuscules, will not be 



* Maxwell's ' Elementary Treatise on Heat, 5 chap. xxii. Longmans, 1871. 



