AND MODERN PHYSICS. 



which at any time have a given velocity, and this, 

 when simplified by the assumption.? of the former 

 papers, reduces to the form already found. He also 

 shows that the average kinetic energy corresponding 

 to any one of the variables which define his system 

 is the same for every one of the variables of his system. 

 Thus, according to this theorem, if each molecule 

 bo a single small solid body, six variables will be re- 

 quired to determine the position of each, three 

 variables will give us the position of the centre of 

 gravity of the molecule, while three others will deter- 

 mine the position of the body relative to its centre of 

 gravity. If the six variables be properly chosen, the 

 kinetic energy can be expressed as a sum of six 

 squares, one square corresponding to each variable. 

 According to the theorem the part of the kinetic 

 energy depending on each square is the same. Thus, 

 the whole energy is six times as great as that which 

 arises from any one of the variables. The kinetic 

 energy of translation is three times as great as that 

 arising from each variable, for it involves the three 

 variables which determine the position of the centre 

 of gravity. Hence, if wo denote by K the kinetic 

 energy due to one variable, the whole energy is C K, 

 and the translational energy is 3 K ; thus, for this 

 case 



Or, again, if we suppose that the molecule is such that 

 m variables are required to determine its position 

 relatively to its centre of gravity, since 3 are 

 needed to fix the centre of gravity, the total number 



