1055 
If next we consider the motion of a mass-point in a conservative 
field of force, such as would take place according to Newtonian 
mechanics, we obtain equations of motion of the same form as (7), 
if the Cartesian coordinates describing the position of the mass-point 
refer to a system of coordinates which rotates uniformly in the 
space. In fact, if the equations of motion in the non-rotating system 
of coordinates. possess the form 
/ 
they obtain in a system of coordinates vl, et! which rotates 
round an axis through the origin with an angular velocity which, 
considered as a vector, possesses the components — #', — FR? and 
— R*,*) the form: 
du!) pl d'n de | 0 (p—w) 
= 5 == 2 R oe re Fins = ee Fi 3 
dt dt Ox ke 
Yp =$ (LJ (wt He Helt) — HRE! + Re, + Rk a) 
rm 
which coincides exactly with the form of the equations (7), if we 
put t=a, and gy —w=b3g,,. The essential difference with the 
equations of motion in the non-rotating system of coordinates lies 
consequently in the appearance of the Coriolis-forces, and we are 
justified in denoting in the following the vector RE as the “rotation- 
vector”. 
The character of the rotation-vector may also be examined in the 
following way. We will try by a transformation of coordinates of 
the form (1) to give the line-element of a stationary field of gravi- 
tation such a form, that in a given point P not only the relations 
Ins = Ems are valid, where the quantities «,, are defined by 
Ei FS oe ey Srl, Ent Ap) pf 5 8) 
4 
but that at the same time the quantities e= Ju,k AS many of 
them as possible become equal to zero. If it was possible to make all 
the latter quantities equal to zero, we should obtain in this way a 
system of coordinates, which is “geodetic” in P. Now it is always 
possible in many ways by means of a transformation (1) to make 
the quantities y,, assume the values &,, in the point P, but in general 
it will not be possible to make all quantities Ju,k equal to zero. In 
!) Here and in the following we will assume the usual rule, that to a 
rotation in a plane corresponds a direction of the normal of this plane in 
such a way, that, for a rotation in the X|, Xg-plane from the positive X-axis 
to the positive x-axis through an angle smaller than z, the corresponding 
„normal points to the same half-space as the positive x-axis. 
