On the Kinetic Theory of Solids. 673 



not easily explain the heat expansion of the body. If heat 

 be a form of motion, it is clear that the motion of the atoms 

 must have something to do with the force of repulsion. 

 I have, therefore, assumed that the repulsion is of the nature 

 of an impulse due to what are called impacts in the Kinetic 

 Theory of Gases. The problem thus becomes a dynamical 

 one and the mathematics much more difficult. 



Again, in order to allow impacts, it is necessary to assume 

 that rhe mutual distances of molecules are not large enough 

 for free vibration. For simplicity I have assumed that the 

 amplitude is small in comparison with the atomic dimen- 

 sions. The results obtained completely bear out with the 

 assumption. 



It may be pointed out that the phraseology used is that of 

 the Kinetic Theory of Gases. Use has, therefore, been 

 made of terms such as impacts, radius of atoms, which in 

 the light of modern researches on the structure of matter 

 will have to be accepted in a generalized sense. 



The numerical values have been taken from Kaye and 

 Laby, 



1. Some numerical values. 



Let N be the number of molecules in a metal supposed 

 monatomic per c.cm., and / the average distance between 

 the centres of two adjacent ones. Then N/ 3 =l *. 



The number of molecules of gas per c.cm. at N.T.P. 



= 2-75 xlO 19 . 



Let W be the atomic weight, and D the density of the metal. 

 Let w be the weight of one molecule of the standard gas 

 (0 = 16). 

 Then 

 D = wt. of 1-c.cm. of the metal = N.W.-^io. 



wt. of 1 c.cm. of oxygen = 2'75 x 10 19 x 16w = 1*429 x 10" 3 . 



NW 



.-. ^-=6-16xl0 23 



= the number of atoms in one gram atom of the metal 

 = e say. 



* Strictly speaking this relation holds only for the cubical arrange- 

 ment of the molecules. But for the fare-centred cubical arrangement 

 the equation ouuht to be lsl 3 = >J2. This would increase the valu- of I 

 given in the table by about 11 per cent. But there will be no occasion 

 to use the arithmetical values of I. All that we need trouble about is 

 the order of magnitude of I. 



Phil. Mag. S. 6. Vol. 43. No. 256. April 1922. 2 X 



