Fan's treatment [Phys. Fluids 10, 1756 (1967)] of the plane flow of a moderately good conductor is here extended to the more realistic axially symmetric case, for two reasons: to substantiate the algebraic decay of the transient motion; and to clear up an apparent contradiction which would have invalidated the perturbation analysis used in both. The magnetic field diffuses in from a solenoid wound round the circular tunnel in which potential flow past the slender body has been set up. The ultimate flow is found to be essentially Lary's steady motion when the tunnel is very wide, thus substantiating the practical relevance of his work.