Altshuler et al discovered that dI CO /d ln t, the rate of increase of the critical current I C with time in polycrystalline high T C samples, traced a peak when measured versus H M , the amplitude of the sweep of the flux trapping magnetic field. We show that the sharp peak in dI CO /d ln t which their model generates arises from a special feature of the formulae they use to describe I C versus H M . Pursuing an extension of these formulae, and exploiting a Brandt-Indenbom formula for the return field of the magnetized grains, we (i) reproduce observations of Altshuler et al, Batista-Leyva et al and a family of curves of dI CO /d ln t reported by Cobas et al, and (ii) estimate the return fields. We also explore the peak structure of dI CO /d ln t versus H M generated by using two well known empirical expressions for I C (H), and the Brandt-Indenbom formula.