Outflow water clock, ca 1350 BCE

The obvious limitation of sundials is that they cannot tell the time during the night or when the sun is overcast. Timekeeping with reference to the night sky is one very ancient alternative. Another is to develop mechanical devices capable of counting off the hours. The most ancient and widely-disseminated device for this purpose is the water clock or clepsydra (‘water stealer’).

There were two basic kinds of water clock: outflow and inflow.

Outflow water clocks, the simplest form, were already know in ancient Egypt, c. 1500 BC. These clocks consisted simply of a vessel with a narrow outflow spot made to discharge water slowly and at a steady pace. The inside of a container was marked with lines of measurement. Observers were able to tell time by measuring the change in water level against the lines marked on the interior of the vessel. Operators could adjust them to the changing seasons by varying the amount of liquid in the container. A video representation of an ancient Greek device of this very simple kind can be found here. 

The basic difficulty of the outflow water clock was that, as the level of the water dropped, so did the water pressure and the rate of flow one of the spigot. In other words, water flowed out of these devices more quickly when filled than when nearly empty.

An approximate solution to this problem was the proportional water clock pictured above. In these devices, the time intervals were spaced equally on the inside, but the truncated conical shape meant that more water flowed out during a given interval when the basin was full (and the water pressure high) than when it was nearly empty. An animation of this type is provided below. 

A more mathematically accurate solution was the parabolic water clock. These used a graduated parabolic scale, which placed markings for the hours further apart at the top (when the water pressure and rate of flow were higher) and closer together at the bottom (where the pressure and flow rate declined). An animation of this solution is found in the second video below. 

Outflow water clocks were mostly used for marking short periods of time, for instance, to ensure that the prosecution and the defence had equal time to make their case in a court of law. 

Commentary. Howard Hotson (May 2021)