(3) [mu]1 [~=] gMh/G' = An^2/CR,
the same for all inclinations, and this is the precession observed in
the spinning top and centrifugal machine of fig. 10 This is true
accurately when the axis OC' is horizontal, and then it agrees with
the result of the popular explanation of S 2.
[Illustration: FIG. 10.]
If the axis of the top OC' is pointing upward, the precession is in
the same direction as the rotation, and an increase of [mu] from [mu]1
makes N negative, and the top rises; conversely a decrease of the
procession [mu] causes the axis to fall (Perry, _Spinning Tops_, p.
48).
If the axis points downward, as in the centrifugal machine with upper
support, the precession is in the opposite direction to the rotation,
and to make the axis approach the vertical position the precession
must be reduced.
Centrifugal machine.
This is effected automatically in the Weston centrifugal machine (fig.
10) used for the separation of water and molasses, by the friction of
the indiarubber cushions above the support; or else the spindle is
produced downwards below the drum a short distance, and turns in a
hole in a weight resting on the bottom of the case, which weight is
dragged round until the spindle is upright; this second arrangement is
more effective when a liquid is treated in the drum, and wave action
is set up (_The Centrifugal Machine_, C. A. Matthey).
Similar considerations apply to the stability of the whirling bowl in
a cream-separating machine.