The equations of the most general type of solar calendar and sundial, which were derived in Vandyck M (2000 A unified and general framework for sundials and solar calendars Eur. J. Phys. 22 79), are extended here to take into account the three main systems of time-reckoning employed by the Ancients: Babylonian hours, Roman hours, and Italian (or Bohemian) hours. The results provide insight into the notions of `temporary' and `equal' hours, which are related to the concept of `uniformity' of the flow of time.