Two alternative methods are described for obtaining inviscid velocity components at the surface of earth's liquid core, assumed perfectly conducting, given perfect and complete measurements of the geomagnetic main field and secular variation at earth's surface. The mantle is treated as a spherically-symmetric insulator for purposes of extrapolation to the core. Both methods utilize the vertical component of the induction equation and require one-dimensional interpolation along special curves on the core surface as the initial step. For the next step, the first method then utilizes the two horizontal components of the induction equation, whereas the second method relies on the horizontal components of Ohm's law. Both methods work within the confines of the ambiguity elucidated by Backus (1968) but nonetheless can still yield results of value, because the two horizontal velocity components are determined separately and at distinct locations. A brief comparison of the two methods suggests that the one, based in part on Ohm's law, should be superior from a practical viewpoint.