  A comparison of the history effects in weakly pinned single crystals of a
high $T_c$ YBa$_2$Cu$_3$O$_{7 - \delta}$ (for H $\parallel$ c) and a low $T_c$
Ca$_3$Rh$_4$Sn$_{13}$, which show anomalous variations in critical current
density $J_c(H)$ are presented via tracings of the minor magnetization
hysteresis loops using a vibrating sample magnetometer. The sample histories
focussed are, (i) the field cooled (FC), (ii) the zero field cooled (ZFC) and
(iii) an isothermal reversal of field from the normal state. An understanding
of the results in terms of the modulation in the plastic deformation of the
elastic vortex solid and supercooling across order-disorder transition is
sought.
