The correct answer is option 3: wet and dry bulb thermometer.

First, let`s understand what humidity is. Humidity refers to the amount of water vapor present in the air. It is a measure of how much moisture is in the air.

Option 1, wind vane, is used to measure wind direction, not humidity. It shows which direction the wind is coming from.

Option 2, aneroid barometer, measures atmospheric pressure and is used to forecast weather changes. It does not directly measure humidity.

Option 3, wet and dry bulb thermometer, is specifically designed to measure humidity. It consists of two thermometers placed side by side, one with a wet cloth wrapped around its bulb and the other with a dry bulb. As the water evaporates from the wet bulb, it cools the bulb and causes a temperature difference between the two thermometers. This temperature difference is used to calculate the relative humidity.

Option 4, maximum and minimum thermometer, is used to measure the maximum and minimum temperature during a specific time period, not humidity.

In conclusion, the instrument used for measuring humidity of the air is the wet and dry bulb thermometer.