The suggestion that the inner core of the Earth is liquid and is the seat of a strong magnetic field is examined. Contrary to expectations of a magneto-hydrodynamic rigidity for the inner core, it is shown that a liquid inner core with a strong magnetic field should not transmit shear waves. The absence of the phase PKJKP in seismic records is favourable to the hypothesis of a strong magnetic field in a liquid inner core. If the jump in P wave velocity at the inner core boundary is due to a magnetic field, the strength of the field must be of the order of 5 x 106 G whether the field geometry is toroidal or random. A strong toroidal field leads to an apparent ellipticity of the inner core. No such ellipticity is observed, so that if the fiel...