Summary: The magnetic field associated with a static current distribution can be expanded in terms of complete sets of functions. Using a particular definition of ’best fit’, this paper discusses how, from measurements made on the field, to estimate the relative multipliers, or moments, for such expansions, and also seeks the ’best’ choice of origin. A wide variety of pick-up coil sizes and geometries is catered for. Three simple, but not trivial, cases are discussed briefly.