\frac{1}{r}
+\frac{2 K_1(r \epsilon )}{\epsilon 
 K_0(\epsilon )}
 \right] \sin (\theta ) \label{streamfn}$$ We note some interesting facts about this expression. First, it has the [*right*]{} behaviour as $r \rightarrow \infty$ provided $\epsilon >0$, as the Bessel function of $r$ decays exponentially. Second, if we keep $r$ fixed and finite and let $\epsilon \rightarrow 0_+$ we obtain $$\psi \sim \frac{\sin\theta}{\log(2/\epsilon) - \gamma}  \left(r \log r - \frac{1}{2}r + \frac{1}{2r}\right) \label{nearcyl}$$ and we recover a multiple of Stokes’ (1851) solution satisfying the boundary conditions on the sphere (but not at infinity), and, furthermore, the multiple is now reminiscent of that arising from the methods of matched asymptotic expansions. The claim therefore is that it is Eq. (\[streamfn\]) that essentially resolves the paradox, as all the boundary conditions are satisfied, but the low Reynolds number limit for finite $r$ does not. The third observation is that in the neighbourhood of the surface of the sphere, $$\psi \sim \sin\theta (r-1)^2 \frac{\epsilon K_1(\epsilon)}{K_0(\epsilon)}$$ and that for small $\epsilon$ this is given by $$\frac{(r-1)^2 \sin (\theta
   )}{-\log (\epsilon )+\log (2)-\gamma
   }+O\left(\epsilon ^2\right)$$ We also note that the limit as $\epsilon \rightarrow \infty$ is just the potential flow limit: $$\psi \sim (r - \frac{1}{r}) \sin \theta$$ [*Mathematica*]{} 