(12) 2Z{E} = -{(G'- GE)/An}^2,
if II denotes the apsidal angle of [~omega], and T the time of a single
beat of the axle, up or down,
_z3
GT / [root](-2Z_E) dz
(13) II + -- = | ------------- ----------,
2A _/z2 z - E [root](2Z)
= 1/2[pi]f + KznfK',
in accordance with the theory of the complete elliptic integral of the
third kind.
Interpreted geometrically on the deformable hyperboloid, flattened in
the plane of the focal ellipse, if OQ is the perpendicular from the
centre on the tangent HP, AOQ = amfK', and the eccentric angle of P,
measured from the minor axis, is am(1 - f)K', the eccentricity of the
focal ellipse being the comodulus [kappa]'.