1061 
on the result of Foucautt’s experiments must be expected, but we 
will not enter here into this problem. 
§ 3. Influence of a stationary field of gravitation on the motion 
of a rigid body round its centre of gravitation. 
In the former § we have given an example of the appearance of 
the rotation-vector; the present § forms a direct continuation of § 1 
and gives the necessary preparation for the treatment of the problem, 
which will be discussed in § 4, and which deals with the influence 
of the sun’s field of gravitation on the precession of the axis of 
the earth. 
If in the following we speak of a rigid body, we mean only a 
body, which is practically rigid, and which can move in the way 
well known from classical mechanics, characterised by 6 degrees of 
freedom, without changes of form or the appearance of enormously 
high stresses. Thus we will assume that the linear dimensions of 
the body are so small, that the “geometry” inside the body, which 
is determined by the quantities g,, and their derivatives deviates 
very little from the Euclidean geometry, and also that the relative 
velocities, which the different parts of the body possess relative to 
each other, are very small compared with the velocity of light. For 
such a rigid body it is possible directly to determine the values of 
the components of the energy-tensor of matter to an approximation, 
which may be exactly defined. In fact, if we introduce such a 
system of coordinates that in every point within the body. the line 
element only differs very little from ds* = d«,*—d2x,’—dz2,’—da,? 
— as a consequence of the above mentioned assumptions this will 
always be possible — and if we denote by v a small quantity of 
dap 
vy 
parts of the body, we have — neglecting small terms, which relative 
to the main terms are of the order v? and of the same order as 
the small deviations of the g,,’s from the ¢,,’s (see (8)) —: 
dat}, 
dx, 
while the quantities 7’, (4,/= 1, 2,3) which are connected with the 
stresses existing in the body, and which can only be determined, if 
the constitution of the body is known more closely, will be small 
compared with the quantities 7%, and may be considered as being 
of the order of magnitude v?. The quantity m in the formulae (18) 
represents the mass per unit of volume. Further it may be remarked, 
69 
of the different 
the same order of magnitude as the velocity 
(18) 
1 ’ 
e= fj Tor == — m 
Proceedings Royal Acad. Amsterdam. Vol. XXIII. 
