An te (Ei) () | 
G Ox, Joo Oz, Joo 
rot (t)-Poae 
Ox, \7 de, \T 
and analogous expressions for the components /? and 2. With 
neglect of small terms of the same order of magnitude as the square 
of the velocities of the masses we have further the formulae 
n 
where m is the density of mass of matter, and v,,v,,v, denote the 
components of the velocity of matter. If we substitute these values 
in the expression found above, we get 
== Fen MN, T, == mv,, is 
oe, 
01 
00 02 
(ve) Vz — (re) V5 dS ' 
R' = 2x Im 
(15) 
ze 
and correspondingly #? and &*. This formula teaches, that the con- 
tribution of every mass particle to the rotation-vector in point P is 
equal to the moment of momentum of the mass particle with respect 
to the point P, divided by the cube of the distance from P, and 
multiplied by twice the gravitation constant of EINSTEIN. 
Formula (15) can be applied to a problem which has been treated 
by H. Tuirrinc') in order to illustrate the influence of rotating 
masses on the field of gravitation. A homogeneous spherical shell 
with mass J/ and radius « rotates with constant angular velocity 
w in a space, in which no other matter is present, and for which the 
quantities g,, approach to ¢,, at infinite distance from the centre. 
It is asked to determine the influence of the spherical shell on the 
motion of a mass point, which is lying just at the centre OQ. The 
field of gravitation produced by the shell is stationary. From symmetry 
we may further conclude that in O a mass point can remain in 
i ze San end 
equilibrium; that means that in this point the quantities ae dis- 
ee 
appear. Approximately, that means omitting small terms proportional 
to w’, g,, will even be constant in the space within the shell, and 
0744, | 
02,02)" 
point at rest just outside O, will in general be proportional to w?*, 
but cannot be determined if the constitution of the shell has not 
which determine the force exerted on a mass 
the quantities 
1) H. TuHirriNG, Phys. Zeitschr. XIX,-p. 33 (1918). 
