THE KINETIC THEORY OF MATTER. 139 



According to a theorem due to Boltzmann, if a molecule be regarded 

 as a mechanical system having n " degrees of freedom " or such different 

 modes of motion that it requires the knowledge of n different quantities 

 to specify its position and configuration at any instant, the energy must 

 be equally shared between the different modes when the distribution 

 of velocities and of internal energy is permanent. A purely translational 

 motion has three degrees of freedom, say the motions parallel to three 

 perpendicular axes. If there are other degrees of freedom implying 

 possibility of change of internal arrangement, making with the three 

 translational degrees n in all, we have 



translational energy 3 3/ , x , -. 2 



- J = - = ~(y I), whence y = 1 + 

 total energy n 2 n 



If n = 8 we have the case of mercury vapour, helium, and argon. 

 We may, merely for illustration, picture the molecules in these gases as 

 small perfect spheres, perfectly smooth if they come in contact at collision, 

 or else in an encounter never actually touching. Then their mutual 

 actions always pass through their centres, so that there never can be any 

 interchange of energy between the tvanslational and the rotational forms, 

 and we need not consider the co-ordinates necessary to specify the con- 

 figuration of the sphere. Of course this is a very crude illustration, but 

 it serves to show that it is conceivable that there may be degrees of 

 freedom like those expressing the rotation of the spherical molecules 

 which may be omitted from consideration, since the forces producing or 

 destroying that rotation do not come into play in encounters. 



For oxygen, hydrogen, and nitrogen, 



y = 1 *4 very nearly. 

 Then n = 5 



We may here picture the molecules as pairs of atoms rigidly attached 

 and forming, as it were, dumb-bells. If the actions at encounters always 

 pass through the axis of symmetry the co-ordinates expressing the 

 orientation round that axis may be omitted and the position and con- 

 figuration of a molecule is sufficiently given by the three co-ordinates of 

 its centre of gravity and the two angles giving the direction of the axis 

 of symmetry, thus accounting for w = 5. 



If the distance between the atomic pair is variable, n = 6 and y = 1 -33, 

 a value possessed by some gases. 



As n increases, y approaches 1, and observation shows that for more 

 complex gases this is true. 



It may be observed that if the omission of any degree of freedom is 

 admissible through its force not coming into play at collision, then if 

 motion in that degree is produced by the absorption of radiation of a 

 given wave-length passing through the gas, sucli radiation will not affect 

 the energy of translation but only the molecular configurations. Thus 

 we may suppose that the pressure of argon against the side>s of the con- 

 taining vessel will not be appreciably altered if it is exposed to radiation 

 which it can absorb. 



But the questions here discussed or rather indicated are still 

 open. It is held by many that Boltzmann's theorem does not really 



