1062 
that apart from the sign, we need not distinguish between covari- 
ant, contravariant and mixed components of the energy-tensor *). Theore- 
tically there will be a difference, but this difference will be of the same 
order of magnitude as the small deviations of the g,,’s from the 
é,, 8, and small terms of this order have already been neglected in 
the establishment of the formulae (18). 
In the former we have fixed the properties of a rigid body with 
an approximation, sufficient for our purpose. Let us now imagine 
such a body at a certain time to be placed in a stationary field of 
gravitation in such a way, that its centre of gravitation is at rest 
and coincides with a point P of the field, where all the derivatives 
ò, 
en are equal to zero, and we propose to discuss the influence, which 
Lie 
the stationary field of gravitation will have on the motions, which 
will be executed by the body. We will begin by proving, that the 
centre of gravity will remain at rest in P. For this purpose we will 
use the equations of energy and impulse of matter: 
Ohta entier | 
Haes } Ju Tw —= 0, Rw) zZz Te —gq, . . rate (19) 
02) Ou, 
where g represents the determinant of the quantities g,,. We will 
assume, that by means of a suitable transformation of the form (1) 
the- coordinates in P are made to fulfill the conditions (9). Then the 
gus may in the neighbourhood of P be represented by 
02,02 
Jok = (Jok,m) P&n + 4 (gom) P Gin Cyto es ans neee (20) 
Oh) = Ex + 4 (art, mn)P Um Une | | 
Oyu» 
Joo = Foo + } (Joo,mn) P Um Uny Ypv‚mn = 
Here we have assumed for the sake of simplicity, that the coordinates 
» &, and x, are equal to zero in the point P and have neglected 
small terms of the order of magnitude «*, z* ete, that is, terms 
which would contain products of three or more «’;’s. 
Let us now consider a closed surface in the «,-#,-«,-space, which 
encloses the body under consideration, and in the inside of which 
the relations (20) hold, and let us integrate both sides of (19) over 
the space inside this surface. Then we get, denoting the space element 
dx, de, de, by dS: 
x 
1 Ok ’k yt 7 der 00 ry my ; 
yee = 71; aE nr ff = 1 = Too =m. 
vO 
