1060 
been defined in nearer details. The rotation-vector in O, however, 
may directly be calculated approximately by means of (15). Its 
direction is of course parallel to the axis of rotation. We intro- 
duce a system of Cartesian coordinates «, y, z, the origin of which 
coincides with O, and the z-axis of which coincides with the axis 
of rotation. Let the mass of unit surface of the shell be denoted by 
m. The contribution to the value of A? which is due to a ring of 
the shell, the angular distance of which to the z-axis is equal to 9, 
will then be equal to 
2x X 2x a’? sin BAD Km A od dn sin? 9 dd 
a 
a’ 
and for A itself we thus get 
xMo (. 4x M 
kz = fein van =O foie eas MEN 
a da 
0 
From this we learn that if in O we introduce a system of coor- 
dinates, which rotates uniformly in the same sense as the shell with 
4M. ee 
an angular velocity equal to ae times that of the shell, the Coriolis- 
a 
forces will disappear from the equations of motion for a mass point 
in O. This result is in agreement with the results obtained by 
THiRRING in his above mentioned paper. 
Another application of formula (15) may be obtained in connection 
with the following problem. Let us imagine a uniformly rotating 
sphere, such as eg. the earth, and let us suppose that the 
FoucauLt’s pendulum experiments are performed at the northpole. 
Then it will be found, that the plane in which the pendulum 
moves, will not remain at rest with respect to the fixed stars, but 
will rotate slowly in the same sense as the earth. The angular 
velocity of this slow rotation is given by the absolute value of the 
rotation vector at the pole, which by means of (15) may be found 
by simple integration. We find 
ce cee Oe Mele) Le 
where M denotes the mass of the earth, which is supposed to be 
homogeneous, while a and w represent the radius and the angular 
dx M 
velocity of the earth. The factor ~~ is of course so small (circa 
5.10 10), that it will be impossible to detect this rotation of the 
plane of the pendulum. Also at lower latitudes a similar influence 
