82 Mr. J. H. Jeans [March 30, 



the to-and-fro motion of the two atoms of which the molecule is 

 formed, probably the latter. 



The instances so far mentioned are sharply divided into cases of 

 complete success of the theorem and case of complete failure. But 

 every scientific investigator will recognise that our chances of 

 unravelling the causes of failure will be enormously improved if we 

 can find a case of gradual transition from truth to failure. 



An interesting case of failure of exactly this kind has been 

 disclosed by recent investigations on specific heats at low temperature. 

 If the principle of equipartition held, even as regards the atomic 

 motions in a solid, the atomic heats ought to be the same for all 

 elements. They are so at high temperatures, but there is a steady 

 falling off as the temperature decreases. The specific heats of silver, 

 copper, and aluminium at low temperatures, as measured by Nernst 

 and Lindemann, are shown in Fig. 1. 



I 2 



Graph of 



Fig. 2. 



Debye, attacking the question mathematically, has shown that the 

 observed values of the specific heats, both for these and other 

 suljstances, are exactly what they would be if the energy were not 

 rationed out equally amongst the different waves, as demanded by 

 the principle of equipartition, but according to the law 



where x stands for hvjBT, v being the frequency of the vibration, 

 T the absolute temperature, and li and h being constants. Fig. 3 

 shows the theoretical curve deduced by Debye from this law, together 

 with the observed values of Nernst and Lindemann for three 



