888 
Agel = — 3 gw Auk Al = — & VI yy (Auk Gt + An Ge), « (17) 
jy? [2,7 
then the expressions: for the deformations at rest are finally obtained 
in the form: 
Ar 
De 
AA 
an te ees Oe 18) 
eh a nee ( fs 
285 ager rat 
Ane 
etc. 
These expressions look just like the corresponding equations (16) 
of Hererorz. Here however the quantities Aj; have a wider meaning. 
By introducing into (1!) the expressions (18) for the deformations 
at rest and by taking into consideration that: 
ds EA aes Soo hee oi tee Ea 
we obtain for ® a function of ¢ and the A;z’s only. We may 
however also consider @ as a function of the quantities & aj; , Jy». 
DD (& Ay) = DAE, Aij Ip) A ee 
The a;;s and the g,,’s occurring in the expressions Aj, only, 
there exists the expression 
Op 0p O@ 
“Za | a Soe 
— Ain — = Jin 
> = as 
n ain n Od jn 0nj 
OP 
ZE 2 nd Oman . . (21) 
n Od jn 
which is of much interest for the following investigation. This 
equation is easily proved by taking on both sides the differential 
quotients of @ first with respect to the Ajz;’s and only then with 
respect to the a;,’s or g;,’s. At this last differentiation gj, and gnj 
| 0p 
are not identical, if j=f=», and in order that ee be equal to 
Jin 
Jj 
Pp 
a the last expression (17) for Aj; has to be used. This gives: 
Inj 
ee OAT id Ò A, 
> ain = — A J Gil — 451 ZS Yui duke = 2 = Jin os 
° y yp. n Din 
and by means of this equation (21) is easily proved. 
We must remark that the right-hand side of (21) represents the 
(2) component of a mixed tensor. By dividing the equation by the 
determinant ; 
Det ay hy. Se eee eee 
volume tensors are obtained on both sides, for 
pia’ =p 
