φ1 + ψ1i = −½ iR (x + yi)2 a2 / (a2 + b2),
(10)
φ2 + ψ2i = ½ iR (x + yi)2 b2 / (a2 + b2),
(11)
and for the interspace, the ellipse α being fixed, and α1 revolving with angular velocity R
φ1 + ψ1i = −1⁄8 iRc2 sh 2 (η − α + ξi) (ch 2α + 1) / sh 2 (α1 − α),
(12)
φ2 + ψ2i = 1⁄8 iRc2 sh 2 (η − α + ξi) (ch 2α − 1) / sh 2 (α1 − α),
(13)
satisfying the condition that ψ1 and ψ2 are zero over η = α, and over η = α1