1895.] Energy among the Degrees of Freedom of Atoms. H13 



case. Professor Schuster has suggested that the numerous lines 

 need not involve the same number of degrees of freedom, as it is 

 possible that there may be connections between them such that one 

 or two -co-ordinates would define a motion which when analysed into 

 its Fourier components, as is done by a grating or prism, would pro- 

 duce a very complex system of lines. However, even one degree of 

 internal freedom would interfere very seriously with the observed 

 value of the ratio of specific heats, and the object of this letter is to 

 explain how this difficulty may be surmounted without supposing 

 that the theorem as to equal partition of energy is untrue, for it is 

 not by any means disproved because a certain form of proof fails in 

 certain cases. 



It has been long held that the motion of the electrons on neigh- 

 bouring atoms is very much controlled by the ether between them. 

 The wave-length of light is generally many times as great as the 

 molecular distances, so that the ether is a practically rigid connector 

 between neighbouring electrons. Suppose now, as a particular 

 example, that 10 6 atoms are in this sense, and so far as the motion of 

 electrons is concerned, within one another's control. In this case 

 the motion of these 10 6 electrons might be defined by means of, say, 

 three co-ordinates. Hence, if the atoms were spheres, there would 

 be 3 x 10 6 degrees of freedom plus these three degrees defining the 

 motions of all the electrons. Now, if the total energy be equally 

 distributed among all these degrees of freedom, each atom will only 

 have its share of the electromotions, and its energy of external 

 motion will only be diminished by 3 x 10~ 6 th part owing to the 

 existence of the internal motion of its electrons. I need hardly say 

 that our methods of calorimetry are by no means sufficiently delicate 

 to detect anything of this kind. There might be a thousand such 

 internal degrees of freedom, and yet the ratio of specific heats would 

 agree with observation. 



There is some analogy between this suggestion and the case of a 

 sphere moving in a liquid. The presence of the liquid, although 

 apparently endowed with an infinite number of degrees of freedom, 

 does not really increase the degrees of freedom at all, because its 

 motion is entirely defined by the motion of the sphere. In a some- 

 what similar manner, I would suggest that the presence of the 

 million electrons does not sensibly increase the degrees of freedom of 

 motion of the million atoms, as all their motions may be defined in 

 terms of the motion of a few of them. That the ether would so 

 control the motions of electrons seems almost certain from what we 

 know of the rapidity with which electromagnetic actions are trans- 

 mitted by it, showing how completely it behaves in respect of them 

 as a system of rigid connections. 



