1307 
limit of the integral in the expression (196), which is given by 
Born for the energy does not come into account. Then we have to 
take into consideration for the thermal pressure in formula (2) not 
only the variation of A and B with e, but also that of the longi- 
tudinal and the transversal energy. 
By application of the formulae which Born has given in $ 21, 
we find after a simple calculation as equation of state 
S= (6A + 2B)e+ (2704+ 9D + He zel 
„{BOCH2D) — HIDE — (6) 
a TL aan | \ 
into which may be introduced the values for the energy of the 
longitudinal and the transversal vibration. From this the modulus 
of compression can afterwards be calculated. We find thus 
_§A+2B  5(9C+2D)*— 5(8D + LE) — | 
UZ EL — Er — 
3 re EB 
(27C4+9DHE) \9C ee zn 5 | ) 
944+3B BA a | 
2. Now we can try to deduce the shearing stresses and their 
dependence on temperature in a way analogous to the one that 
has been used for the thermal pressure. For this purpose we can 
. de 
determine the space-time average of the force oe 
4 
We have 
= i. 3 B 4 = 5 E (ese, —,€,) Ts. z D (ee, + e¢ 16504): 
Now we have to determine the mean force when the solid body 
has a given strain e, =e in the initial condition. Thus, if we call 
again e’,...e’, the deformations from the strained condition, 
we get 
X, SSS ra, 3 B (e-+e,)+ 7 Elese, wi ey! (e +é,’) ) re 2 D (e,'+ é, +6) (e+ e‚). 
Now we have to find the space-time-average of this force. It should 
be taken into consideration that ¢,’—=e,’ =e,’ =e,’ =0, whence 
Xx, =—3 Bet} E (e, ele, ee,) = 3 D (e,'e, aD ee, Hent (8) 
The mean values e’, e’, ete. which vanish in the case the body 
remains isotropic will now, by the existence of the initial shearing 
e,—=e, have values deviating from zero in consequence of the 
fact that the body presently bebaves like a rhombic erystal. Thus 
far the calculation corresponds with that of the thermal pressure. 
The force calculated is indeed the force required to keep a certain 
deformation given at the absolute zero unchanged when the tempe- 
