  We present a method for implementing the constraints that are implied by
Maxwell's equations in fits to measurements of the magnetic field in the muon
storage ring of the $g-2$ experiment. The method that we use makes use of
toroidal-harmonic solutions of Laplace's equation. We point out that the
fitting problem can be approximated well as a linear-algebra problem. We have
devised an efficient algorithm for the linear-algebra problem that makes it
possible to find a solution for $10^5$ data points and $10^4$ harmonics in less
than an hour on a present-day desktop computer. We illustrate our method by
applying it to some preliminary measurements of the magnetic field in the $g-2$
storage ring.

Instrumentation and Detectors;High Energy Physics - Experiment;High Energy Physics - Phenomenology