887 
this too. First for the case of rest and no gravitation this potential 
must take the form [J easasasya of the ordinary kinetic 
a t 
potential dependent on quantities that characterize the deformation 
and on the entropy. In the system of coordinates S° the equation 
f Pp — Qs, Bij) a, eN ee ne Ae see ey 
must therefore hold, if ¢ is the entropy per unit of the normal 
volume and if at rest the six deformations e;; are determined by 
the following equations (equations (16) of HerGrorz): 
2 2 2 \ 
bf rey a A eo ss 
9 
Deeg, Ag Oet an EET ee 
ite. / 
The quantities e;; show how the form of an element of the body, 
when at rest, differs from the normal form. 
Secondly ® must be invariant with respect to arbitrary transform- 
ations. Thus the general expression for ® is obtained by trans- 
forming equation (11) from S° to an arbitrary system. 
At this transformation the connexion 
de? 
a 5 dap. 
ke Ox}: 
must be used. We then obtain from (7) and (8). 
= 0x°; 02°; a Ow, dz? : (13) 
Ye — TT == = -y 5 5 4 Z 
i=3 Ox; dx; 
ws 
vi — 2 - (14) 
Further (5) gives 
(On; 
Goyette Oey Lae ven a Sg peek) 
: k Di 
while for the expressions (12) may be written 
l ER 5 ~ Oz, Ox, dx’, Oz". Oz°, at 
ao, = aes A Olt =—- = ES ee Coie 
me Is, l lov, Oa) Ov: Ox Oxy, Oa] 
so that according to (14) 
1+ 2e, = — = an An Yl, 
2.5 — D Ak2 A13 Ykls 7? + ° . ° . . (16) 
kl 
etc, 
If the expression (9) for y,, is introduced and if we put 
