There are two obvious methods by which clocks might be used for determining the shortest day of the year. The first might be to simply measure the time between sunrise and sunset. The second might seem to be to just determine when the sun starts to come up earlier.
This latter method would be in error for the sun does not start coming up earlier until early in January, by which time the days are already longer since the sun sets a greater amount later than it comes up later. Thus, this latter method might lead to the conclusion that the winter solstice occurs in early January.
Of course early man did not possess accurate time pieces such as we know today.
Perhaps the oldest clock involved letting water drip from an upper container to a lower container at a constant drip rate, telling the time by the water level rise in the lower container.
Unfortunately, the laws of physics cause a problem with this device since as the water level in the upper container drops so does the pressure at the bottom of the container drop - and the drip rate decreases.
One of the earliest methods to circumvent this problem was used by the Chinese who stacked up to four buckets above each other, each slowly dripping into the next lower bucket. By doing so they were able to keep the water level in the next to the bottom bucket nearly constant - and keep a constant drip rate into the bottom time measurement bucket.
|Chinese Water Clock
Museum in Nanning, China.
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From the above it is likely that water clocks were of no significance to the earliest determination of the solstices.