Solution
= Solution
<Stokes flow> obeys $-\nabla p+\mu\nabla^2u=0$, $\nabla\cdot u=0$. Reversing all applied forces reverses $u$ while leaving <streamlines> unchanged. Reflection in the vertical plane containing the cylinder axis rules out rotation normal to that plane; reflection combined with reversibility rules out rotation within it and spin about the axis. Thus its orientation remains fixed.