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In a museum in Lviv, I saw a pocket cellular clock. I don't have a photo, but it was a small disc that had 2 or 3 filaments in it which were pointed at the stars (one of them was Andromeda, I think). Through analyzing the position of the stars it was possible to determine the time of the night. I'm not sure if knowing the day of the year was promised.

I couldn't find the information about the way the clock was used. Does anyone know how such device was used?

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The device that you saw is called a nocturnal. It calculates the local time based on the month of the year and the position of Polaris and one or more other stars.

Since stars change position throughout the night, they can be used to determine time; but the positions of stars change throughout the year, so the input of the month of the year is needed. Polaris is used as a relatively fixed reference point.

More information:

Nocturnal (instrument) - Wikipedia

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