http://en.wikipedia.org/wiki/Water_clock These could be rigged to make an audible signal when the water reached a certain level.
Not to derail, but my question is, how in the world did they care for babies?? From the whole birthing process, to diapers, etc? Even with the technology we have, hospitals, and disposable diapers, it's still a B! Can't even imagine every birth being natural with no drugs to ease the pain, or washing a cloth everyday (or more) soaked with pee and crap. What a weak people we have become.
