How could you measure the height of a building using a barometer? I set a similar guided problem in the recent Physics exam that involves the boring method. This is an urban legend ages old among us Physics majors but it is a relatively new and difficult problem for secondary students. I knew I just got to set this problem at least once in my career as a teacher.

Here's the whole story behind this problem, at least one version of it.

The following is a question on a physics exam at the University of Copenhagen:

"Describe how to determine the height of a skyscraper with a barometer."

One student replied: "You tie a long piece of string to the neck of the barometer, then lower the barometer from the roof of the skyscraper to the ground. The length of the string plus the length of the barometer will equal the height of the building."

This highly original answer so incensed the examiner that he failed the student who immediately appealed on the grounds that his answer was indisputably correct.

The university appointed an independent arbiter to decide the case.

The arbiter ruled that the answer was indeed correct, but did not display any noticeable knowledge of physics. It was decided to call the student in and allow him six minutes in which to provide a verbal answer which showed at least a minimal familiarity with the basic principles of physics.

For five minutes the student sat in silence, forehead creased in thought. The arbiter reminded him that time was running out, to which the student replied that he had several extremely relevant answers, but couldn't make up his mind which to use.

On being advised to hurry up the student replied: "First, you could take the barometer up to the roof of the skyscraper, drop it over the edge, and measure the time it takes to reach the ground. The height of the building can then be worked out from this formula I have worked out for you on my text paper here."

Then the student added, "But, Sir, I wouldn't recommend it. Bad luck on the barometer."

"Another alternative", offered the student, "is this: If the sun is shining you could measure the height of the barometer,then set it on end and measure the length of its shadow. Then you measure the length of the skyscraper's shadow, and thereafter it is a simple matter of proportional geometry to work out the height of the skyscraper. On the paper is the formula for that as well."

"But, Sir, if you wanted to be highly scientific about it, you could tie a short piece of string to the barometer and swing it like a pendulum, first at ground level and then on the roof of the skyscraper. The height is worked out by the difference in a gravitational formula, which I have determined here this time on a long sheet of paper with a very long and complicated calculation."

"Or, Sir, here's another way, and not a bad one at all. If the skyscraper has an outside emergency staircase, it would be easier to walk up it and mark off the height of the skyscraper in barometer lengths, then add them up."

"But if you merely wanted to be very boring and very orthodox about the answer you seem to seek, of course, you could use the barometer to measure the air pressure on the roof, and on the ground, and then convert the difference in millibars into feet to give the height of the building."

"But since we are constantly being exhorted to exercise independence of mind and apply scientific methods, undoubtedly the best way would be to knock on the janitor's door and say to him 'If you would like a nice new barometer, I will give you this one if you tell me the height of this skyscraper'."

The student was Niels Bohr, the only Dane ever to win the Nobel Prize in physics.