We briefly review the isothermal-isobaric ensemble partition function correctly derived by Corti and Soto-Campos [J. Chem. Phys. 108, 7959 (1998)] from the view point of usual simulations in which the external bath of a system is appropriately approximated. We show that, for the homogeneous system, the partition function can be reduced to the result of Attard [J. Chem. Phys. 103, 9884 (1995)] which was criticized by Corti and Soto-Campos. We conclude that the volume scale cannot be defined in general but in some particular cases and the recently controverted volume scales are those of the cases. We also confirm the validity of Brown's [Mol. Phys. 1, 68 (1958)] partition function which has never been used in simulations before, by demonstrating that it is equivalent to the one of Corti and Soto-Campos.