(16)
Along the path of a liquid particle ψ′ is constant, and putting it equal to ½Uc2,
(r2 − a3/r) sin2 θ = c2, sin2 θ = c2r / (r3 − a3),
(17)
the polar equation; or
y2 = c2r3 / (r3 − a3), r3 = a3y2 / (y2 − c2),
(18)
a curve of the 10th degree (C10).
In the absolute path in space
cos ψ = (2 − 3 sin2 θ) / √ (4 − sin2 θ), and sin3 θ = (y3 − c2y) / a3,