No. Personal barometers containing mercury and must not be taken on a plane. Aneroid barometers do not contain mercury and are allowed
Government employees may travel with specialised equipment that contain hazardous substances, including barometers containing mercury. If this applies to you please contact your airline before you travel as their approval will be required and in most cases the pilot is required to be informed.
Mercury is a poison and if taken on board a plane present as a significant risk to passengers and crew.
You will be asked to relinquish all dangerous or prohibited items found in your carry-on luggage. If you refuse:
AvSec x-ray bags going onto aircraft to ensure there is nothing dangerous in them. If something comes up on the x-ray that needs checking, the bag will be opened, searched and any dangerous good or prohibited item will be removed, with a bag search notification form left within the bag.