THK DYNAMICAL KVIDBNCK OF THE 



Now. we have already shewn that the pressure of a gas is two-thirds of the 

 kinetic energy in unit of volume. Henoe, if the pressure as well as the tem- 

 penUurv be the some in the two gases, the kinetic energy per unit of volume 

 m the "fj, as well as the kinetic energy per molecule. There must, therefore, 

 be the mm** number of molecules in unit of volume in the two gases. 



Thi result coincides with the law of equivalent volumes established by Gay 

 LUBMC. This law, however, lias hitherto rested on purely chemical evidence, 

 the relative masses of the molecules of different substances having been deduced 

 from the proportions in which the substances enter into chemical combination. 

 It i* now demonstrated on dynamical principles. The molecule is defined as 

 that *rn*l\ portion of the substance which moves as one lump during the motion 

 of agitation. This is a purely dynamical definition, independent of any experi- 

 menta on combination. 



The density of a gaseous medium, at standard temperature and pressure, 

 is proportional to the mass of one of its molecules as thus defined. 



We have thus a safe method of estimating the relative masses of molecules 

 of different substances when in the gaseous state. This method is more to be 

 depended on than those founded on electrolysis or on specific heat, because our 

 knowledge of the conditions of the motion of agitation is more complete than 

 our knowledge of electrolysis, or of the internal motions of the constituents of 

 a molecule. 



I must now say something about these internal motions, because the greatest 

 difficulty which the kinetic theory of gases has yet encountered belongs to this 

 part of the subject. 



We have hitherto considered only the motion of the centre of mass of the 

 molecule. We have now to consider the motion of the constituents of the 

 molecule relative to the centre of mass. 



If we suppose that the constituents of a molecule are atoms, and that each 

 atom is what is called a material point, then each atom may move in three 

 different and independent ways, corresponding to the three dimensions of space, 

 so that the number of variables required to determine the position and con- 

 figuration of all the atoms of the molecule is three times the number of atoms. 



It is not essential, however, to the mathematical investigation to assume 

 that the molecule is made up of atoms. All that is assumed is that the position 

 and configuration of the molecule can be completely expressed by a certain 

 number of variables. 



