682 On the Kinetic Theory of Solids. 



It is known that the value of Young's modulus for the- 

 comraon metals is of the order 10 12 . Taking the case of Cu 

 by way of illustration, the first term = 5 X 10 12 roughly. 



The experimental value = 1* 23 X 10 12 . 



.'. jf'Q) is of order 10 12 , which makes /"(I) of order 10 4 . 



The potential energy term in the equation of energy in 

 art. 4 is therefore of order 10~ 16 . 



11. Residual Rays. 



We can make a rough calculation of the frequency of 

 vibration of the molecules at the surface. We know that 

 for a Cu molecule, 



Y is of order 10 4 , 

 M „ „ 10- 22 , 

 F „ „ 10- 5 . 

 Neglecting the variations of the force, the frequency 



F 



v= ~ MV , which is of order 10 12 . 



This agrees with the experimental values *. 



12. Conclusion. 



We have, therefore, arrived at a consistent theory of the 

 solid state. Starting from known values of the specific 

 heat, compressibility, and the coefficient of linear expansion, 

 we have investigated the amplitude of molecular vibration 

 and the inter-molecular forces. The partition of the gain 

 of thermal energy has been dealt with. We have found 

 that for Cu, for example, 



(1) 2 - 02 x 10 ~ 16 erg is absorbed by each molecule to 

 increase the energy of translational motion, 



(2) 1*2 x 10~ 16 erg is absorbed by the rotational motion, 

 and presumably increases the energy of the electrons, 



(3) *76xl0~ 16 erg is absorbed in doing work against 

 the inter-molecular forces. 



The cases of cubical and face-centred cubical crystals 

 have been dealt with in the next paper ; the results obtained 

 do not differ materially from those obtained here. 



* McLewis, ' Physical Chemistry/ vol. ii. p. 58. 



