A biophysical hypothesis to explain the powerful ameliorating effects of weak (nanoTesla range) magnetic fields on melatonin-related diseases is presented. The effects are dependent upon the molarity of the melatonin within specific organ spaces. The optimal ameliorating effects upon experimental allergic encephalomyelitis for both the derived intensities (about 35 and 70 nT) and the frequency (7 Hz) were congruent with the empirical observations from previously published and unpublished experiments with rats involving about 1-5000 nT strengths of either 0.5, 7, 40, or 60 Hz magnetic fields. The hypothesis predicts that weaker magnetic fields within the nanoTesla to picoTesla range would optimally affect concentrations of melatonin (in this situation) within the micromolar range and that neurological states (epilepsy) or conditions (ethanol, antidepressants, sleep deprivation) that affect nocturnal melatonin levels in human beings would determine the optimal effective intensity within the 7 Hz range. The resonance solution also suggests that mitochondrial proton gradients may be critical to the process. The model offers an alternative explanation to the variations of Faraday's Law and the Boltzmann constant that have been employed to explain and to dismiss biological effects from weak magnetic fields.