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The Sling Psychrometer determines %Relative Humidity by measuring the evaporation of water into the surrounding air.
Two thermometers are placed in flowing air, one thermometer bulb being covered by a wet wick.
Evaporation from the wetted bulb causes its temperature to be depressed relative to that of the dry bulb.
In dry air evaporation will be rapid and the depression will be greater, giving a low %RH reading.
In humid air there will be little evaporation and the depression will be small, giving a high %RH reading.
If the air is completely saturated no evaporation can take place so both the wet and dry bulb thermometers will give the same reading. This equates to 100%RH.

The %RH can be read off the Slide rule calculator integrated into the psychrometer. Standard Humidity Tables can also be used.