Mr. W. Sutherland on a Kinetic Theory of Solids. 525 



got to be compatible with the behaviour of isotropic bodies. 

 The true solution of the difficulty lies in taking account of 

 the kinetics of the molecules. The motion of the molecules 

 is a fundamental part of the phenomenon of elasticity of 

 solids as of gases. 



The subject-matter of the kinetic theory of solids will be 

 taken in the following order : — 



1. Establishment of the characteristic equations of solids. 



2. Testing of the equations on the supposition that the 

 molecules are unalterable. 



3. Testing of equations on the supposition that the mole- 

 cules alter somewhat with change of temperature. 



4. Further evidence of the alteration of molecules with 

 change of temperature. 



5. Periods of vibration of the molecules of metals. 



6. Comparison of the theoretical variation of Young's 

 modulus with temperature with the experimental. 



7. Rigidity according to the kinetic theory. 



8. Ratio of lateral contraction to elongation in Young's 

 experiment. 



9. Dulong and Petit's law, Joule and Kopp's law, and the 

 equation for compound solids. 



10. The parameter of molecular force. 



1. Establishment of the characteristic Equations of Solids. — 

 In the kinetic theory of gases molecules are supposed to 

 exercise pressure on an external body by colliding against its 

 molecules, and the molecules are supposed to collide with 

 one another. Let us imagine, then, a number of molecules of 

 equal mass and size moving amongst one another under the 

 influence of an attractive force <f(f) exerted by each, and 

 colliding and rebounding with coefficient of restitution unity. 

 If the molecules are close enough together, it is evident that 

 each separate molecule is hemmed in by its neighbours, so 

 that it cannot change its position beyond vibrating about in 

 its own limited share of space which I call its domain. Such 

 a collection of molecules has one characteristic property of a 

 solid body. Liquefaction occurs when each molecule ceases 

 to be hemmed in and just manages to wriggle through 

 amongst its neighbours. In the solid body each molecule as 

 it knocks about in its domain has its mean position preserved, 

 just as if it were held there by central repulsive forces 

 emanating from all the other molecules, or only from its 

 immediate neighbours, while it itself by colliding with its 

 neighbours many times a second in all directions acts vir- 

 tually as a centre of repulsion to them. There is this much 



