so that the stability requires
K2 > 4gAMa.
(7)
Here A denotes the moment of inertia about a diametral axis through the centre of gravity; when the point of the fly-wheel is held in a small smooth cup, b = 0, and the condition becomes
(A + Ma2) n2 − Kn + gMa = 0,
(8)
requiring for stability, as before in § 3,
K2 > 4g (A + M2) Ma.
(9)
For upright spinning inside a spherical surface of radius b, the sign of a must be changed to obtain the condition at the lowest point, as in the gyroscopic horizon of Fleuriais.