MOLECULAR CONSTITUTION OF BODIES. 433 



And here we are brought face to face with the greatest difficulty which 

 the molecular theory has yet encountered, namely, the interpretation of the 

 equation n + e = 4'9. 



If we suppose that the molecules are atoms mere material points, incapable 

 of rotatory energy or internal motion then n is 3 and e is zero, and the ratio 

 of the specific heats is 1*66, which is too great for any real gas. 



But we learn from the spectroscope that a molecule can execute vibrations 

 of constant period. It cannot therefore be a mere material point, but a system 

 capable of changing its form. Such a system cannot have less than six variables. 

 This would make the greatest value of the ratio of the specific heats 1'33, which 

 is too small for hydrogen, oxygen, nitrogen, carbonic oxide, nitrous oxide, and 

 hydrochloric acid. 



But the spectroscope tells us that some molecules can execute a great many 

 different kinds of vibrations. They must therefore be systems of a very con- 

 siderable degree of complexity, having far more than six variables. Now, every 

 additional variable introduces an additional amount of capacity for internal 

 motion without affecting the external pressure. Every additional variable, there- 

 fore, increases the specific heat, whether reckoned at constant pressure or at 

 constant volume. 



So does any capacity which the molecule may have for storing up energy 

 in the potential form. But the calculated specific heat is already too great 

 when we suppose the molecule to consist of two atoms only. Hence every 

 additional degree of complexity which we attribute to the molecule can only 

 increase the difficulty of reconciling the observed with the calculated value of 

 the specific heat. 



I have now put before you what I consider to be the greatest difficulty 

 yet encountered by the molecular theory. Boltzmann has suggested that we 

 are to look for the explanation in the mutual action between the molecules 

 and the Eetherial medium which surrounds them. I am afraid, however, that 

 if we call in the help of this medium, we shall only increase the calculated 

 specific heat, which is already too great. 



The theorem of Boltzmann may be applied not only to determine the dis- 

 tribution of velocity among the molecules, but to determine the distribution of 

 the molecules themselves in a region in which they are acted on by external 



forces. It tells us that the density of distribution of the molecules at a point 



_! 

 where the potential energy of a molecule is t/f, is proportional to e where 6 is 



VOL. II. 55 



