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body a homogeneous expansion at a given temperature, so that 
é, == ==, 6, = 6, = ¢, — 0. This force consists of two parts. 
In the first place one may give the required expansion to the solid 
body at the absolute zero and thereupon supply at constant volume 
the energy necessary to give the solid body the required tempe- 
rature. Therefore the thermal pressure as calculated in our first 
contribution has to be added to the elastic tension at the absolute 
zero. 
Now in order to calculate the first part we use the expression 
for the energy 
EY pO) a OR EE 8 8 
It is immediately clear that the invariants have the following 
values 
Be valken, SE 
so that the energy takes the form: 
e= (OA + 3Be? + (27C + 9D + He? 
For the tension at the absolute zero we find consequently 
S= = = (64 VID ATC UL Gp = Bye. 
For the thermal pressure (Sp) we found in Contribution I the 
expression ; 
Uae te AE Ea 
6A 6B i 
Now A, B, C, and D are constants which ‘are relative to the 
non-deformed substance. In our case however we must replace these 
constants by their values in the strained condition when calculating 
the thermal pressure. But as the solid in that condition remains 
isotropic, the given formula still holds. We will neglect the variation 
of C and D with e as this variation is determined by terms of 
higher order in the energy, which were neglected by us. The average 
energy of the longitudinal and the transversal vibrations may change 
also. When we have to do with so high a temperature that the 
theorem of equipartition is true, that change is zero as the 
number of degrees of freedom does not change by the expansion. 
For lower temperatures where the quantum-theory must be taken 
into consideration, the change of ¢&, and ¢,. has to be taken into 
account. 
The variation of A and B with e can be found in the following 
manner. The strain can be represented by 
== 
1) Conf, for the rotations Contribution 1, 
. 
