L = l/½ (z1 − z3),

(21)

suspended from a point at a height ½ (z1 + z3)l above O, in such a manner that a point on the pendulum at a distance

½ (z1 − z3) l = l2/L

(22)

from the point of suspension moves so as to be always at the same level as the centre of oscillation of the top.

The polar co-ordinates of H are denoted by ρ, ῶ in the horizontal plane through C; and, resolving the velocity of H perpendicular to CH,

ρdῶ/dt = An2 sin θ cos KCH.

(23)

ρ2dῶ/dt = An2 sin θ·CK = An2 (G′ − G cos θ)