  In the high-temperature superconductor BSCCO, local measurements of magnetic
field at the surface of a crystal in the mixed state show sharp changes as a
function of applied field or temperature. We show that if `intermediate state'
effects are accounted for, a first-order transition leads to a sharp jump in
the global magnetisation only in the case of samples that are significantly
non-ellipsoidal in shape. We also investigate the relationship between a jump
in magnetisation, M, and the associated change in the B-field immediately above
the crystal surface and show that deltaM is expected to be twice deltaB/muo. In
addition, we emphasise that the Clausius-Clapeyron relationship between
magnetisation jump and entropy jump should involve the local H-field, not the
B-field or the applied H-field. Re-interpreting some published experimental
data leads to the conclusion that the entropy change can be as much as 4.0 kB
per flux line per layer, compared with less than 2 kB previously reported. We
present and analyse new experimental data on local field jumps and global
magnetisation measurements and find that they agree with the above. We also
show that these data are consistent with the boundary region between the liquid
and solid phases having a width of around 20 flux-line spacings at a field of
10 mT.
