Precise heat-capacity measurements have been made around the smectic-C * -smectic-C * α phase transition in the R-S mixture of liquid crystal MHPOBC ([1,1 -biphenyl]-4-carboxylic acid, 4 -(octyloxy)-, 4-[[(1-methylheptyl)oxy]carbonyl]phenyl ester) which exhibits ferro-and antiferroelectric phases. Ultra-low frequency ac calorimeter and high-sensitivity differential scanning calorimeter have been used. The measurements revealed the existence of quite slow relaxation near the transition. The heat-capacity anomaly accompanying the transition showed a significant increase as decreasing heat frequency in the ac method. The excess heat capacity observed for a mixture that is closest to the critical point has been analysed quantitatively.