High-resolution heat-capacity, tilt-angle, and polarization measurements have been carried out in the vicinity of the smectic-A (SmA) chiral-smectic-C (SmC*) phase transition of p-(n-decyloxybenzylidene)-p-amino-(2- methylbutyl)cinnamate (DOBAMBC). Heat-capacity studies were done on two different samples obtained from two laboratories. Different results were obtained. Almost simultaneous measurements of the tilt angle (theta) and polarization (P) on one of the samples allow us to reveal one surprising temperature dependence of the ratio P/theta. The anomaly in the ratio P/theta seems to be closely related to the anomaly in the helical pitch just below the SmA-SmC* transition.