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As the name implies, the wet bulb hygrometer takes advantage of evaporation as the driving force behind its function.
With a wet-dry bulb hygrometer, you have a regular hi-grade thermometer in the atmosphere you are sampling, and mounted with it is a second one, but with a
cotton wick encasing the bulb.
The wick is dampened and as the water evaporates from it into the air, it cools the bulb. Therefore, the thermometer with the wick will read lower then the dry air temp bulb.
("Swamp," or evaporative coolers, like you see in arid climates work on the same principle.)
Evaporation occurs at a constant rate for a given temperature and water vapor saturation point. This creates a known gradient, or difference, between the two bulb temperatures that can be referenced on a common wet-bulb chart.
Since the ability of air to retain water vapor is dependent on temperature, as hinted at above, this measurement is actually the water vapor saturation point of a given air mass,
relative to the given temperature. That's why we call it relative humidity, symbolized as "Rh."
As with any hygrometer, placement in the bator is best arranged in in an area that is not directly impacted by moving air. Instead, you want air exchange movement around the hygrometer, but not direct drafts which skew the results.
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(Theoretically, you can do all this with two common medical bulb thermometers and a cotton shoelace for a wick. Since there are variables involved in this "homebrew" hygrometer, it is best to rely on a known good instrument until you get your experiment sorted out.)
I hope all this helps
