How would the presence of air in the tube above the mercury affect the readings of the mercury barometer?

Negatively. The readings would be distorted, such data cannot be trusted.

The structure of the Barometer is provided in this way; so that the resistance of air molecules (which should in no case be in the tube) could not affect the mercury, that is, to minimize its influence (ideally, to completely exclude it).
Since air affects the accuracy of readings, and Mercury is a very toxic substance, the device is also made completely sealed and closed.
It is also recommended to even avoid direct sunlight, as they can distort the received data from heating.



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