When the applied fields and the total charge on each conductor are known, the solution of the London equations for a superconductor in the steady state is completely determined by requiring the continuity of the magnetic field and of the tangential components of the electric field. This result is incompatible with the somewhat prevalent notion that the lines of current flow rotate with the conductor. The solution for a nonsteady state is uniquely determined by the additional specification of E, H, J throughout the system at some particular time.