Kinetic Theory of Solids. 527 



The same equation will now be established from Clausius's 

 equation of the virial, taking account of the virial of the 

 repulsions during collision as Lorentz does (Wied. Ann. xii.) 

 in the case of gases. Let F be the repulsive force between 

 two molecules in collision when their centres are distance E 

 apart, then the equation of the virial is 



t 



s 7 — < 



1 Jo 



= \ . i $1- f rtfr) clt- \.\t\$ ®Fdt + terms 



which vanish when the motion is stationary and t is large 

 enough. As E is practically constant during collision, 



j*EF<ft=EJF<ft. 



Now suppose each encounter to last a time t, then, since 

 each molecule in time t experiences vt/u collisions, we have 



and then 



Jo « Jo « 



rf-U«*w-}.SS 



2 2^ rv/ 2 2 



, S =i'(, + 5) = ^^„, 



Now E is the mean distance apart of the molecules when 

 in contact, and accordingly 



E + u = e; 

 hence, as before, 



a. 2 2 2 e T 



In the usual theory of gases the molecules are treated as 

 elastic spheres, in which case E is constant ; but as change of 

 temperature is known to produce changes inside the molecule, 

 it will be safer to consider E as possibly a function of the 

 temperature ; E can hardly depend appreciably on the pres- 

 sure, except in cases where, by the application of external 

 pressure, the number of collisions per second becomes great 

 enough to influence the internal structure of the molecule, as, 

 for example, when great pressure produces crystallizations 

 and combinations. In the most general case, then, we have 



