1068 
e= ME dln eg alle fo: SD 
where x again denotes the constant of gravitation (see p. 1058). 
Let us now introduce a new system of coordinates, which rotates 
round the axis of the original system of coordinates with an angular 
velocity w. The line element in the new coordinates may then be 
calculated by means of the transformation 
p=ttotr 
This gives 
ise = (1 eae a r* sin? 0) ai? 
i. 
— 2r7 sin? Fw dpdl — 
(28) 
dr* 
— rt (d9* + sin? 9 dp”) | 
pps | 
% | 
The field of gravitation corresponding to this line element is 
stationary. We will first try to find a point P, where a mass-point 
can remain in equilibrium. In such a point the first derivatives of 
a 3 . : . 
grr = 1 ——7" sin? Jo" are equal to zero. This gives the following 
7 
conditions, which must be fulfilled by the coordinates of P: 
0 0 
TP ares 2r sin? JF w? —=0, Er = — 2r’ sin 3 cos 3 w° =—0. 
Or "? 09 
From this we see, that a mass-point can remain at rest at every 
point P, which lies in the equatorial plane he and for which 
the distance A from the sun fulfills the relation 
2 AP wt 5+ staten ne en) 
This relation gives us therefore the connection between the angular 
velocity and the orbital radius of a planet, which moves in a circle 
round the sun. 
In order to discuss the rotation of such a planet round its 
axis we shall begin by calculating the rotation-vector in P. In 
order to find, by means of (5), its contravariant components we 
want to know the value of the determinant G of the quantities 
Gi = — Jui + ates 
We find 
