1314 
4. Besides the dynamic way we developed above, there is another 
method in which the results of Born’s general theory about the 
specific heat as well as known thermodynamic relations are used. 
This method shows a certain conformity with the one used by 
DeBYr-v. EVERDINGEN, but enables us to put the problem more 
strictly, whereas it has in common with the method given above 
the advantage that it can introduce or not the theory of the quanta 
of energy and may be easily extended to the temperatures where 
the approximations of v. EVERDINGEN prevail no more. Moreover it can 
easily be extended to a theory of the equation of state of a crystal of 
any class of symmetry. Instead of using a characteristic temperature 
as v. Everpincen does — who also introduces the incorrect approxi- 
mation that there is only one characteristic temperature — the 
specific heat itself is used. Hence the approximation which 
v. EverDINGEN introduces on p. 35 of his dissertation, the conse- 
quences of which it is impossible fully to survey, viz. the application 
of formulae which prevail for the isotropic body to a aeolotropic 
body, can be avoided. 
Now the principle of our method is as follows. When the defor- 
mations e, e, e‚ are given to the body A, may be represented (as 
is demonstrated in (2)) e.g. by 
X, = X, + ae, + be, + 4) 
in which X; is the thermical pressure for the isotropic body for 
e, =e, —¢,=—0, and a and 6 are functions.of temperature. On 
account of the isotropy in X, the coefficient of e, has to be equal 
to that of e,; Y, and Z, hence follow by cyclic interchange. 
X, ete., on account of the isotropy, are at the given deformation zero. 
Now the specific heat can be calculated by application of the 
formulae of Born to the rhombiedric crystal with the e’s given 
above. As we start from an isotropic body the development of the 
specifie heat in terms of e, e, e, will only depend on tke invariants. 
So we may put 
Ce Cp iat, “ipa En. 
in which C, means the specific heat at constant e, e, e,, C‚o that 
fori rb). 
Now we can apply the thermodynamic relation 
OC, a? Xe 
de, dT? 
This gives 
d’ Xt d'a db 
a+ We +4 He) +7 He) =De + e+ on 
