634 SCIENCE PROGRESS 



In other words, the solid melts, and the atoms are free to 

 move from place to place. 



It has long been known that the atomic heats of solid 

 elements, especially metallic elements, at ordinary temperature 

 are very nearly the same quantity, namely six calories — the 

 well-known Law of Dulong and Petit. Boltzmann, many 

 years ago, showed that this value was to be expected if the 

 mechanical principle of equipartition of energy between degrees 

 of freedom held good. Boltzmann based the numerical result 

 upon atomic vibration, possessing three degrees of freedom, 

 the view still held. It was known, however, that several of 

 the elements, notably the element carbon, did not possess the 

 value six for the atomic heat, but a smaller quantity. Further 

 it was shown later that, on lowering the temperature, the 

 atomic heats of all the elements investigated diminished con- 

 siderably. This result could not be explained on the basis 

 of the classical mechanics employed by Boltzmann, for the 

 classical theory requires absolute constancy in the value of 

 the atomic heat. It was only when Einstein introduced the 

 quantum theory, as already mentioned, into the problem, 

 that a way out of the difficulty presented itself. It would 

 hardly be possible, however, to follow this line of argument 

 further in the present instance. We shall turn, therefore, to 

 the second line of investigation, namely, that of crystal struc- 

 ture by means of X-rays. 



X-rays are now known to consist of vibrations of exactly 

 the same nature as light, with this difference, however, that 

 the wave length of X-rays is incomparably shorter than, say, 

 visible light. Thus yellow light has a wave length of about 

 5,900 x io" 8 cm., whilst that of X-rays is of the order io" 8 cm. 

 itself. From what has been said in connection with molecular 

 dimensions it will be realised, that the average wave length 

 of the X-ray is just about the same order of magnitude as the 

 diameter of a molecule, and therefore of an atom. This acci- 

 dental comparability in size has made possible the investiga- 

 tion of crystal structure by means of the rays. 



Since X-rays possess the properties of light it would be 

 expected that a beam of the rays could be dispersed into a 

 spectrum provided we had at our disposal a diffraction grating 

 of suitable dimensions. For ordinary light it has been found 

 possible to produce a spectrum by means of fine lines ruled 



