206 SCIENCE PROGRESS. 



7. It is worth while to analyse more closely the con- 

 ception of an elastic sphere. Our elastic spheres are sup- 

 posed to have each three degrees of freedom, namely, that 

 of motion of translation in space. The three angular 

 velocities of which each sphere is also capable are to be 

 ignored, because, the spheres being perfectly smooth, these 

 velocities will not be affected by collisions. Again, if our 

 spheres collide with each other, they must separate with 

 their combined kinetic energy unaltered, none of it being 

 dissipated, i.e., converted into heat or vibrations. This is 

 essential if the system is to have the properties of a per- 

 manent gas. For otherwise it would change its condition 

 by collisions among the spheres without any influence of 

 external bodies. It would appear then that a sphere, or 

 molecule, such as the theory requires, cannot consist of 

 parts capable of vibrations or other relative motion inter se, 

 for otherwise such relative motion would be set up on col- 

 lision. Therefore, also, that it cannot of itself be either hot 

 or cold, that is, cannot possess the quality temperature as 

 commonly understood. But the whole system of moving 

 spheres has temperature, which, according to the above 

 form of the theory, either is, or is proportional to, the mean 

 kinetic energy of the spheres. 



8. It is evident that a body of such very simple struc- 

 ture cannot be expected to discharge all the duties which 

 the chemist requires of the molecules of a gas. Further 

 we know from the phenomena of the spectroscope that the 

 molecules, or atoms, of every gas must be capable of exe- 

 cuting vibrations of one or more kinds. It seems then that 

 our system of elastic spheres, though it satisfies with more 

 or less accuracy certain physical properties of permanent 

 gases, which depend on pressure, density and temperature, 

 cannot be expected to explain those phenomena which 

 depend on chemical composition. 



9. The following extension of the theory was given 

 originally by Boltzmann, and afterwards in the most general 

 form in the first edition of Dr. Watson's book. For the 

 elastic sphere with its three degrees of freedom we may 

 substitute a molecule of n co-ordinates, q It q 2 , q„, and cor- 

 responding momenta/,,^,/,,, and in the permanent state 



