MOLECULAR CONSTITUTION OF BODIES. 431 



Let us call this number n, 



Of these variables, three are required to determine the position of the 

 centre of mass of the molecule, and the remaining n 3 to determine its con- 

 figuration relative to its centre of mass. 



To each of the n variables corresponds a different kind of motion. 



The motion of translation of the centre of mass has three components. 



The motions of the parts relative to the centre of mass have n 3 com- 

 ponents. 



The kinetic energy of the molecule may be regarded as made up of two 

 parts that of the mass of the molecule supposed to be concentrated at its 

 centre of mass, and that of the motions of the parts relative to the centre 

 of mass. The first part is called the energy of translation, the second that of 

 rotation and vibration. The sum of these is the whole energy of motion of the 

 molecule. 



The pressure of the gas depends, as we have seen, on the energy of translation 

 alone. The specific heat depends on the rate at which the whole energy, kinetic 

 and potential, increases as the temperature rises. 



Clausius had long ago pointed out that the ratio of the increment of the 

 whole energy to that of the energy of translation may be determined if we 

 know by experiment the ratio of the specific heat at constant pressure to that 

 at constant volume. 



He did not. however, attempt to determine & priori the ratio of the two 

 parts of the energy, though he suggested, as an extremely probable hypothesis, 

 that the average values of the two parts of the energy in a given substance 

 always adjust themselves to the same ratio. He left the numerical value of this 

 ratio to be determined by experiment. 



In 1860 I investigated the ratio of the two parts of the energy on the 

 hypothesis that the molecules are elastic bodies of invariable form. I found, to 

 my great surprise, that whatever be the shape of the molecules, provided they 

 are not perfectly smooth and spherical, the ratio of the two parts of the energy 

 must be always the same, the two parts being in fact equal. 



This result is confirmed by the researches of Boltzmann, who has worked 

 out the general case of a molecule having n variables. 



He finds that while the average energy of translation is the same for 

 molecules of all kinds at the same temperature, the whole energy of motion 

 is to the energy of translation as n to 3. 



