- Measure the height of the barometer. Scale the side of the building, measuring its height in barometer-units.
- Drop the barometer from the top of the building. Measure the time until it hits the street. Correcting for the mass/surface ratio of the instrument, use basic acceleration equation to find the height.
- Tie string to top of barometer. Lower from roof to almost ground. Swing. Period of pendulum can be used to find distance from barometer's Centre of Gravity to top of building.
- Place a cat on top of a building. Prod it with the barometer so that it falls off the roof. See whether the cat dies when it hits the ground. Repeat n times. Refer to Dr Karl Kruszelnickis paper on the probability of a cat dying when falling from a certain height.
- Take the barometer outside on a sunny day, measure its shadow and the buildings shadow.
- Smash the barometer on the roof of the building and time how long it takes for the mercury to drip down the wall of the building to the ground, use the known viscosity of mercury to find the velocity.
- Sell the barometer. Purchase a tape measure long enough to measure the height of the building.
- Find someone who knows how tall the building is, and trade him the barometer for the information.
Obviously I don't recommend them!
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