Isothermal M-H curves, coupled with the critical state model, are routinely
used to extract critical current density J(c)(B); and the limitations and
validity are well understood. These hysteretic M-H curves can also be used
to estimate the equilibrium magnetization M-eq(H), and this paper discusses
the validity of such a procedure using analytically tractable models for J
(c)(H). We put special emphasis on the case where the M-H curve shows a fis
h tail or peal; effect, and an experimental procedure to estimate errors in
the inferred M-eq(H) is presented. The need to infer M-eq(H) is underscore
d by recent experimental works speculating on thermodynamic phase transitio
ns between vortex phases having intrinsic pinning. [S0163-1829(99)01413-7].