At infinity
| U = − | m | e−a cos β = − | m | cos β, |
| c | a − b |
| V = − | m | e−a sin β = − | m | sin β, |
| c | a − b |
(9)
a and b denoting the semi-axes of the ellipse α; so that the liquid is streaming at infinity with velocity Q = m/(a + b) in the direction of the asymptote of the hyperbola β.
An ellipse interior to η = α will move in a direction opposite to the exterior current; and when η = 0, U = ∞, but V = (m/c) sh α sin β.
Negative values of η must be interpreted by a streaming motion on a parallel plane at a level slightly different, as on a double Riemann sheet, the stream passing from one sheet to the other across a cut SS′ joining the foci S, S′. A diagram has been drawn by Col. R. L. Hippisley.
The components of the liquid velocity q, in the direction of the normal of the ellipse η and hyperbola ξ, are
−mJ−1 sh (η − α) cos (ξ − β), mJ−1 ch (η − α) sin (ξ − β).