1054 
small displacement contravariant). From the invariance of the 
expression (4) we may thus conclude, that the quantities *) 
Joel 9 (901 Ò (gok 
Rn LA laki Sh a a. Gene 
; G Ou}. (=) Ow) (=) ( 
where k‚lan again may assume the sets of values 1, 2,3 and 2, 3,1 
and 3, 1, 2, with regard to the transformation (1) are the contra- 
variant components of a vector in the three-dimensional extension 
with the invariant line-element do? = Gj,da,da,;. The invariant ab- 
solute value of this vector is given by R=V Gy, RER! 
If the components 2” are everywhere equal to zero, we have to 
do with a static field of gravitation. In fact, from (5) follows that 
in this case the quantities gor/g,, may be deduced from a potential 
p in such a way that gor == Yeo but from this follows again, 
(pp 
Dar,’ 
that the line element may be written in the form ds? = — Gij derde + 
+ gsde,*, where x, = x, + Pp. 
If the components Rr" are not equal to zero, these quantities deter- 
mine in every point what might be called the “rotatory” properties 
of the stationary field of gravitation. This may be illustrated by 
considering the motion of a masspoint, the velocity of which is small] 
compared with the velocity of light. In general the ‘‘worldline” of 
a masspoint is determined by the equations 
dv) | uv ) de, de, 0 
ee azo A HOUTE 
ds? (2 ds ds 
If now we assume, that by a suitable transformation of the kind 
(1), the line-element has been given the form ds? = da,’°—dx,*?—dw,’?— 
dr,’ at a given point P of the worldline, it may be easily verified 
that the equations (6), looking apart from small terms of the same 
‘order of magnitude as the square of the velocity, in the point P 
assume the simple form: 
lk Ae (2 dn =) ETE EN 
de,” Ue dx, Ow} 
where klm just as before may assume the sets of values 1, 2, 3 
and 2, 3, 1 and 3, 1, 2. From these equations we learn that the 
“force” which the field of gravitation in the point P exerts on a 
mass point of unit mass may be described as the sum of a Corio- 
lis-force perpendicular to the velocity and proportional to it and of 
a force, which may be derived from the potential 4 ,,. 
1) If we admit only such transformations, for which the functional determinant 
is positive, we may by the root-sign in this expression always understand the 
positive root. 
