1328 
Q = Ay Ap ae ee 
In this equation we must take for q¢,,9,..-.qs the values as they 
are in the heat motion such as it really is. As now in the case of 
oscillations the mean value of each coordinate g over a long interval 
of time is O, the term A, may be omitted. 
As to A,, this term represents the value of the force Q that would 
be required for maintaining the assumed value v of the volume, in 
case all the coordinates g,,...qs were 0, so that there would be no 
heat motion. For this foree we may find an expression if we 
introduce the volume v, that the body would have at the absolute zero 
if it were free from external forces. In order to maintain at this 
same temperature the volume v, which we shall suppose to be 
greater than v,, a negative pressure would have to be exerted on 
the body. It may be represented by 
v—v, 
pe ag Cee EN 
xv 
where x is a certain mean coefficient of cubical compressibility. 
Substituting this in (4) we find 
3 (vv) 
QS 
} x 
and this is the value of A,. Thus, if there is a heat motion, we 
have according to (7) 
3 3 (ev) ) 
Q= + A,. 
x 
If finally we want to know what volume the body will occupy 
in the case of a heat motion, and in the absence of an external 
pressure, we have only to put Q=0O. We then find 
v0, EE NA Sle eee 
for the connection between the heat motion and the volume, which 
it was our object to deduce. 
§ 5. As to the meaning of A, we must remember that the part 
of the potential energy which contains terms of the second order 
with respect to 9,,9,---@s, will be 
2 (2,9," ae 492 EN ars as qs”) =i qA, 
when the volume has increased to the extent determined by q. 
After this expansion to the volume (l + 3q)v the coordinates 
Gi» Jo --- Qs need no longer be normal coordinates as they were for 
the volume v; so that A, may also contain products g q;. As 
however the fundamental vibrations which constitute the heat motion, 
