The Barometer Problem

Students devise clever ways to measure height of building using a barometer.

Claim:   A physics professor gives a final examination that requires his students to explain how to measure the height of a tall building using a barometer. Instead of the expected answer (i.e., measure the barometric pressure at the top and bottom of the building, then use those readings to calculate the altitude), one student provides several unique but technically correct alternative solutions to the problem.



[Chicago Tribune, 1988]

The best question has many answers. I am reminded of the story about a student who protested when his answer was marked wrong on a physics test.

In answer to the question, "How could you measure the height of a tall building, using a barometer?" he was expected to explain that the barometric pressures at the top and the bottom of the building are different, and by calculating, he could determine the building's height. Instead, he answered, "I would tie the barometer to a string, lower it to the ground and measure the length of the string."

His instructor admitted that the answer was technically correct but did not demonstrate a knowledge of physics.

The student then rattled off a whole series of answers involving physics — but not one using the principle in question: He would drop the barometer and time its fall. He would make a pendulum and time its frequency at the top and the bottom of the building. He would walk down the stairs marking "barometer units" on the wall.

When the instructor finally demanded the "simplest" answer to the question, the student replied, "I would go to the building superintendent and offer him a brand-new barometer if he will tell me the height of the building!"

[Collected on the Internet, 1999]

The following concerns a question in a physics degree 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 the student was failed immediately. The student appealed on the grounds that his answer was indisputably correct, and the university appointed an independent arbiter to decide the case.

The arbiter judged that the answer was indeed correct, but did not display any noticeable knowledge of physics. To resolve the problem it was decided to call the student in and allow him six minutes in which to provide a verbal answer that 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 as follows:

"Firstly, 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 the formula H = 0.5g x t squared. But bad luck on the barometer."

"Or 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 arithmetic to work out the height of the skyscraper."

"But 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 the gravitational restoring force T =2 pi sqr root (l /g)."

"Or 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."

"If you merely wanted to be boring and orthodox about it, of course, you could use the barometer to measure the air pressure on the roof of the skyscraper and on the ground, and 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 to win the Nobel Prize for physics.

[Reader's Digest, 1958]

"What steps would you take," a question in a college exam read, "in determining the height of a building, using an aneroid barometer?"

One student, short on knowledge but long on ingenuity, replied, "I would lower the barometer on a string and measure the string."


  • Another commonly mentioned method of solving the barometer problem is to measure the length of the shadows cast by both the barometer and the building and calculate the height of the building from their proportion.
  • Recent (1999) versions identify the barometer problem as "a question in a physics degree exam at the University of Copenhagen" and the imaginative student who answers it as "Niels Bohr, the only Dane to win the Nobel Prize for Physics." (This is not accurate, as two Danes, Benjamin R. Mottelson and Aage Niels Bohr, shared the Nobel Prize for physics in 1975.)

Origins:   The earliest account of the "barometer" legend we've found so far comes from a 1958 Reader's Digest collection, and the tale is usually identified as being the invention of Dr. Alexander Calandra, who included a first-person account of it in a 1961 textbook (The Teaching of Elementary Science of Mathematics) and published it as an article in Saturday Review in 1968. The various responses mentioned in the legend have also been included in lists of supposedly "real" answers given by physics students when confronted by this same question. (One such list was submitted to the periodical Current Science by Dr. Calandra himself.) Whether a real incident was the basis for Dr. Calandra's creation of this parable is Cartoon of the legend unknown.

The obvious moral here is that education should not consist merely of stuffing students' heads full of information and formulae to be memorized by rote and regurgitated upon demand, but of teaching students how to think and solve problems using whatever tools are available. In the mangled words of a familiar phrase, students should be educated in a way that enables them to figure out their own ways of catching fish, not simply taught a specific method of fishing.

True or not, this anecdote incorporates a feature common to academic legends, the notion that an instructor must give credit to a student who provides a technically correct answer to an exam question, even when it is clearly not the answer the instructor expected (see the Prime Choice legend, for example), although in this case the instructor rejects the initial answer(s) and demands one that at least demonstrates a knowledge of the subject matter at hand.

Additional information:
    Saturday Review' article   Angels on a Pin
  (Saturday Review)
Last updated:   22 June 2011


    Brunvand, Jan Harold.   The Baby Train.
    New York: W. W. Norton, 1993.   ISBN 0-393-31208-9   (pp. 294-295).

    Calandra, Alexander.   The Teaching of Elementary Science and Mathematics.
    St. Louis: Washington University Press, 1961.

    Calandra, Alexander.   "Angels on a Pin."
    Saturday Review.   21 December 1968.

    Hooson, Christopher and Linda Paresky.   "Tough Times Ahead for Traditional Minded."
    Travel Weekly.   6 December 1990   (p. 36).

    McWilliams, Brendan.   "Lateral Thinking."
    The Irish Times.   18 March 1995   (Weather; p.2).

    Chicago Tribune.   "Scientifically Speaking."
    18 September 1988   (Sunday Magazine; p. 22).

    Reader's Digest Treasury of Wit And Humor.
    Pleasantville, NY: The Reader's Digest Association, 1958   (p. 303).

Also told in:

    Canfield, Jack.   Chicken Soup for the College Soul.
    Health Communications, 1999.   ISBN 1-558-74702-8.

    van der Linden, Peter.   Expert C Programming.
    Englewood Cliffs, NJ: Prentice Hall, 1994.   ISBN 0-13-177429-8   (pp. 344-6).

    The Big Book of Urban Legends.
    New York: Paradox Press, 1994.   ISBN 1-56389-165-4   (p. 212).

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