Air in antique or new barometers has always been a problem. In the antique wheel barometers fitted with "j" tubes it's not that critical, and the instruments will still function indicating whether the air pressure is rising or falling, which is all you really need to know anyway. But in a stick barometer, especially the scientific fortin style or kew pattern instruments, a little air in the tube kills any chance of an accurate reading.
Most of the antique Welch barometers had "air locks" in them to prevent any air to enter the upper section of the tube in case the instrument was carelessly handled or laid flat without preparing first.
Here is an air lock I made the other day. It's basically a smaller tube in a larger tube. Any air would be trapped in the large area, and the mercury would go up in the upper section of the tube thru the smaller piece of glass.
I just finished making this one for a scientific barometer for a customer.