(54)
from (8) (9) § 3; and the apsidal angle is
| μ | ½π | = | Aμ | · | n | ·½π = | ON | · | 2√ (OM·ON) | ·½π = | ON | π, |
| m | An | m | √ (OM·ON) | MN | MN |
(55)
and the height of the equivalent conical pendulum λ is given by
| λ | = | g | = | n2 | = | OM | = | KC | = | OL | , |
| l | lμ2 | μ2 | ON | KC′ | OC′ |
(56)
if OR drawn at right angles to OK cuts KC′ in R, and RL is drawn horizontal to cut the vertical CO in L; thus if OC2 represents l to scale, then OL will represent λ.
9. The gyroscope motion in fig. 4 comes to a stop when the rim of the wheel touches the ground; and to realize the motion when the axis is inclined at a greater angle with the upward vertical, the stalk is pivoted in fig. 8 in a lug screwed to the axle of a bicycle hub, fastened vertically in a bracket bolted to a beam. The wheel can now be spun by hand, and projected in any manner so as to produce a desired gyroscopic motion, undulating, looped, or with cusps if the stalk of the wheel is dropped from rest.
As the principal part of the motion takes place now in the neighbourhood of the lowest position, it is convenient to measure the angle θ from the downward vertical, and to change the sign of z and G.