]>Velocity Induced by a Plane Uniform Vortex Having the Schwarz Function of Its Boundary with Two Simple Poles : Table 2
Table 2: Behaviour with respect to the second property, consequences on the map 𝐳 𝐱 and corresponding constraints on the poles 𝐳 1 , 𝐳 2 .

Kind 𝐱 ( 𝒜 ) Position of 𝒞 Constraints on 𝐳 1 , 𝐳 2

1Inside 𝑃 Internal to 𝒞 One inside and one outside 𝒞
External to 𝒞 Both inside 𝒞

2Outside 𝑃 Internal to 𝒞 Both outside 𝒞
External to 𝒞 One inside and one outside 𝒞