885 
and by varying the q(o9)’s he finds a system of equations for the 
field of the matter on which however he does not dwell. 
~The assumptions Einstein makes on the character of the quantities 
with respect to transformations are sufficient to determine the function 
; 
G*. As Je must be a scalar quantity we find that at transform- 
ations both parts of equation (2) behave as “covariant volume- 
tensors’ 
The quantity 
Eat ns al 
poh cen eng eee ay Bak VANCE ag NED) 
which oceurs in Ernsrein’s equation (21) as momentum and energy 
is therefore a mixed volume tensor. 
In this paper will be shown that the same volume tensor 3, is 
obtained as tension-energy tensor if HeRGLoTZ’s mechanics for deform- 
able bodies*) are extended in the way required for EINSTEIN's 
theory 7). | 
For incoherent masses the problem has already been solved by 
Prof. Lorertz *). The problem may however also be solved for 
arbitrary elastic bodies if -Hrreiorz’s formulae for a system of coor- 
dinates, in which the g,,’s have their normal values, are transformed 
to an arbitrary system of coordinates. 
HerGrorz denotes the cartesian coordinates belonging to the point 
of matter, when the body was in its normal state, by é,, &, &,. Here 
the property of the normal state has to be added that the gs have 
their normal values + 1 and 0. Then an arbitrary system of coor- 
dinates may be introduced in which the point of tbe matter (&,, &,, §,) 
may have at the time t— #, the coordinates 2,,.v,, 2, in space. If 
still an arbitrary time &, is introduced 
§, =S, (Si: Sos §3, 4); 
then the four equations 
ZR (Gr, Sey Bas Gales Evert Ket ne meen ee ee) 
describe the motion of the body. Further we put, just as Hrreiorz did 
On; a 
NEET ad ee. Sinton et ren «CNO 
nj 
1) G. Hererorz. Uber. die Mechanik des deformierbaren Körpers vom Stand- 
punkt der Relativitiitstheorie. Ann. d. Phys. 36, 1911, p. 493. 
2) If there exists an electro-magnetic field, then £ contains of course still an 
electro-magnetic term, which must be treated separately. 
8) H. A. Lorentz, Hamitron’s principle in Ersrem’s theory of gravitation. 
These Proc. XIX, p. 751. 
