You've seen these barometers, known as a banjo barometer. These are the same as any other decorative barometer but it does have its origins back to the 1800's. The reason for the long stem is to make it look more like a Fortin's Barometer. Its a marketing ploy. The large mercury barometers were cumbersome but also fashionable 100 years ago when aneroid barometers were plentiful builders wanted them to LOOK like a the more expensive Fortin's.
Barographs keep a running tendency of the air pressure.
These are aneroid barometers. You can see the mechanisms in the above picture. The silvery plate looking device in the middle are the bellows. This is the capsule that senses the changes in pressure. The drum on the left rotates as time passes enabling the pen to trace the pressure.