x + yi = c√[ sin (ξ + ηi) ]
(17)
the function
ψ = Qc sh ½ (η − α) sin ½ (ξ − β)
(18)
will give motion streaming past the fixed cylinder η = α, and dividing along ξ = β; and then
x2 − y2 = c2 sin ξ ch η, 2xy = c2 cos ξ sh η.
(19)
In particular, with sh α = 1, the cross-section of η = α is
x4 + 6x2y2 + y4 = 2c4, or x4 + y4 = c4