262 Mr. W. Sutherland on the 



molecule has a certain average period of vibration from one 

 encounter with a neighbour to the next. Now if this period 

 of intermolecular vibration were to become the same as a 

 natural period of internal vibration belonging to the molecule, 

 then by resonance the molecules would all be set aswing with 

 a tine accord, the translatory vibrations keeping time with 

 the internal elastic vibrations. Such a state of affairs is 

 favourable to the escape of each molecule from the restraint 

 of its neighbours, that is, to melting. Thus it comes to pass 

 that the periods of vibration of the molecules of the elements 

 of the Li family at the melting-points are as 1, 2, 3, 4*5, and 

 6 because the internal periods of vibration stand in these 

 harmonic relations to one another. 



Now it is possible by the Kinetic Theory of Solids to 

 •calculate the periods of the elastic vibrations of the metallic 

 molecules in the following way. It is shown that these 

 molecules are practically incompressible ; but as the rigidities 

 are given for a number of metals at the absolute zero of 

 temperature, it follows that these rigidities are those of the 

 molecules. The molecule of a metal vibrates, therefore, as a 

 body which is deformable. but incompressible, and has there- 

 fore a fundamental internal mechanical period of vibration 

 depending chiefly on the rigidity and linear dimensions of 

 the molecule and partly on its shaped 



Let N be the rigidity of a metal at absolute zero as tabu- 

 lated (Phil. Mag. [5] xxxii. p. 41), let m be the mass of its 

 atom which may be taken to be identical with its molecule, 

 and p its density. Then the mean linear dimension of the 

 atom is (??i//>)s, and the velocity of a deformation in the atom 

 is (N//o)*, so that the period of vibration of the atom is of the 

 order 



2(»/p)*/(N/p)* (16) 



Now (ibid. p. 547) it is shown that if b is the mean coeffi- 

 cient of linear thermal expansion of the metal, and c its specific 

 heat, 2lNbm/Jcmp is approximately the same for all metals 

 (Zn and Gd have values double the average). 



Again (Phil. Mag. [5] xxx. p. 319), I have given the 

 empirical relation bTm^= 0*044, where T is the melting- 

 point measured from absolute zero. Using these two results 

 along with our expression (16) for the period of vibration, we 

 find this period is proportional to 



w%*T2 (17) 



But the expression originally used to calculate relative 



