Kinetic Theory of Solids. 551 



still clearer when taken in conjunction with that of Joule and 

 Kopp, that the molecular heat of a solid compound is the sum 

 of the atomic heats of the component atoms. This means 

 that the freedom of the atom within the molecule is such that 

 each atom vibrates independently of the others. On this 

 basis it is easy to sketch the investigation of the equations 

 for a solid compound. Let us consider a compound whose 

 molecule consists of n y atoms of an element A 1? n 2 of A 2 , and 

 so on. Suppose a cubical arrangement of molecules at dis- 

 tance e apart, then the number of molecules per unit area is 

 1/e 2 , and hence the number of atoms A 1 per unit area is 

 n-fi/e 2 . Let m ly m qi and so on be the masses of the atoms, 

 and Vi, v 2 their mean velocities, then the collisional pressure 

 per unit area due to the atoms A x is n^m^/e 2 ^, if a x is the 

 full swing of the atom in its domain. For the total colli- 

 sional pressure we have the sum of such pressures for the 

 different sorts of atoms. For the pressure due to molecular 

 attraction it does not matter whether we consider the attrac- 

 tions of the atoms separately or of the entire molecules; if we 

 take the entire molecules, then we get the former expression 

 ^rcf)(r)/6e 3 . For a solid compound submitted to hydrostatic 

 pressure p we have the equation 



Kinetically, then, a compound in the solid state behaves 

 like a mechanical mixture of its component atoms, because 

 the molecules are almost as close to one another as the atoms 

 in the molecule. It is evident that a complete kinetic theory 

 of compounds must be a very complicated affair. 



10. The Parameter of Molecular Force. — Hitherto we have 

 managed to dispense with a close knowledge of the molecular 

 attraction because we have always managed to eliminate it by 

 using the fact that when the external pressure is small we 

 can put 



2^W/6e 3 =2D/3e 2 (e-E), 



which is the fundamental equation for a solid free from ex- 

 ternal force. But it is desirable to obtain an independent 

 estimate of molecular force for comparison with that given by 

 this equation, and Quincke's measurements of the capillary 

 tensions of the metals at their melting-points give an excellent 

 opportunity (Pogg. Ann. cxxxv. and cxxxviii.). 



I have shown (Phil. Mag. 5th ser. vol. xxvii.) that if the 

 law of molecular force is 3Awi 2 /r 4 then the surface-tension is 

 proportional to Am?p%. Let us denote the surface-tension by 



