How Galileo Thermometers Work
A Galileo thermometer has inside a number of weights Suspended in a liquid. Usually those internal weights are themselves sealed glass bulbs containing colored liquid for an attractive effect.
As the liquid in the galileo thermometer changes temperature its density changes and those bulbs which are free to move, rise or fall to reach a position where their density is either equal to that of the surrounding liquid or where they are brought to a halt by other bulbs. If the bulbs differ in density by a very small amount and are ordered such that the least dense is at the top and most dense at the bottom, they can form a temperature scale.
The temperature is typically read from an engraved metal disc on each bulb. Usually a gap would separate the top bulbs from the bottom bulbs and then the temperature would be between the tag readings on either side of the gap. If a bulb is free-floating in the gap, then its tag reading would be closest to the ambient temperature. To achieve this requires manufacturing the weights to a tolerance of less than 1/1000 of a gram