## The Barometer Fable (142 ways)

By Robolab Technologies In More InfoIt’s just an old joke/scientific creativity test: how to measure a tower’s height using barometer

**MEASURE THE HEIGHT OF A BUILDING WITH HELP OF A BAROMETER**

For every problem, there are probably a thousand solutions. The trick is to find one you can use. So, if you ever need to measure the height of a building with a barometer, here are some methods you can try.

**THE BAROMETER FABLE**

(This seems to be the original story. If you wish to see many solutions, you can go to the next item.)

The following essay is frequently referred to, and often reprinted in textbooks on writing. I recall it was also reprinted in one of the Project Physics supplementary readers. Few people recall its source, or its author. As a bit of humor it is nicely constructed. As a parable with a moral, it falls flat. What is the author’s point, one wonders? Is it an argument against a particular kind of pedantry in teaching? Is it a demonstration that exam questions can be subject to multiple interpretations? Is it an example of how a clever student can find ingenious ways to answer a question? Just what is the difference between exploring `the deep inner logic of the subject’ and teaching `the structure of the subject’. Calandra doesn’t make that difference clear, yet his student seems not to like the first, but would rather have the second.

The title (which most people forget) is a clue. Medieval scholastics were fond of debating such meaningless questions as “How many angels can dance on the point of a pin,” “Did Adam have a navel,” and “Do angels defecate.” The emerging sciences replaced such `scholarly’ debates with experimentation and appeals to observable fact. Calandra seems to be suggesting that “exploring the deep inner logic of a subject in a pedantic way” is akin to the empty arguments of scholasticism. He compares this to the `new math’, so much in the news in the 60s, which attempted to replace rote memorization of math with a deeper understanding of the logic and principles of mathematics, and he seems to be deriding that effort also. So it still seems to me that we get no clear and useful message from this essay.

On almost every level, this essay falls apart on critical analysis. I wonder why it has become such a legend in the physics community?

[The equation, S equals 1/2 a times t-squared, may not come out properly on your browser or newsreader.]

**Angels on a Pin**

A Modern Parable by Alexander Calandra Saturday Review, Dec 21, 1968. The article is by Alexander Calandra and appeared first in “The Saturday Review” (December 21, 1968, p 60). It is also in the collection “More Random Walks in Science” by R.L.Weber, The Institute of Physics, 1982. Calandra was born in 1911, started at Washington University (St. Louis) in 1950 as Associate Prof. of Physics. B.S. from Brooklin College and Ph.D. in statistics from New York Univ. Consultant, tv teacher and has been AIP regional counselor for Missouri.

Some time ago I received a call from a colleague who asked if I would be the referee on the grading of an examination question. He was about to give a student a zero for his answer to a physics question, while the student claimed he should receive a perfect score and would if the system were not set up against the student: The instructor and the student agreed to submit this to an impartial arbiter, and I was selected.

I went to my colleague’s office and read the examination question: “Show how it is possible to determine the height of a tall building with the aid of a barometer.” The student had answered: “Take a barometer to the top of the building, attach a long rope to it, lower the barometer to the street and then bring it up, measuring the length of the rope. The length of the rope is the height of the building.”

I pointed out that the student really had a strong case for full credit since he had answered the question completely and correctly. On the other hand, if full credit was given, it could well contribute to a high grade for the student in his physics course. A high grade is supposed to certify competence in physics, but the answer did not confirm this. I suggested that the student have another try at answering the question I was not surprised that my colleague agreed, but I was surprised that the student did.

I gave the student six minutes to answer the question with the warning that the answer should show some knowledge of physics. At the end of five minutes, he had not written anything. I asked if he wished to give up, but he said no. He had many answers to this problem; he was just thinking of the best one. I excused myself for interrupting him and asked him to please go on. In the next minute he dashed off his answer which read: “Take the barometer to the top of the building and lean over the edge of the roof. Drop that barometer, timing its fall with a stopwatch. Then using the formula S = ЅatІ, calculate the height of the building. At this point I asked my colleague if he would give up. He conceded, and I gave the student almost full credit.

In leaving my colleague’s office, I recalled that the student had said he had many other answers to the problem, so I asked him what they were. “Oh yes,” said the student. “There are a great many ways of getting the height of a tall building with a barometer. For example, you could take the barometer out on a sunny day and measure the height of the barometer and the length of its shadow, and the length of the shadow of the building and by the use of a simple proportion, determine the height of the building.” “Fine,” I asked. “And the others?” “Yes,” said the student. “There is a very basic measurement method that you will like. In this method you take the barometer and begin to walk up the stairs. As you climb the stairs, you mark off the length of the barometer along the wa]l. You then count the number of marks, and this will give you the height of the building in barometer units. A very direct method.”

“Of course, if you want a more sophisticated method, you can tie the barometer to the end of a string, swing it as a pendulum, and determine the value of `g’ at the street level and at the top of the building. From the difference of the two values of `g’ the height of the building can be calculated.”

Finally, he concluded, there are many other ways of solving the problem. “Probably the best,” he said, “is to take the barometer to the basement and knock on the superintendent’s door. When the superintendent answers, you speak to him as follows: “Mr. Superintendent, here I have a fine barometer. If you tell me the height of this building, I will give you this barometer.”

At this point I asked the student if he really did know the conventional answer to this question. He admitted that he did, said that he was fed up with high school and college instructors trying to teach him how to think, using the “scientific method,” and to explore the deep inner logic of the subject in a pedantic way, as is often done in the new mathematics, rather than teaching him the structure of the subject. With this in mind, he decided to revive scholasticism as an academic lark to challenge the Sputnik-panicked classrooms of America.

Bob Pease (Nat.Semi.) records the story of the Physics student who got the following question in an exam: “You are given an accurate barometer, how would you use it to determine the height of a skyscraper ?”

1: He answered: “Go to the top floor, tie a long piece of string to the barometer, let it down ’till it touches the ground and measure the length of the string”. The examiner wasn’t satisfied, so they decided to interview the guy: “Can you give us another method, one which demonstrates your knowledge of Physics ?”

2: “Sure, go to the top floor, drop the barometer off, and measure how long before it hits the ground……”

“Not, quite what we wanted, care to try again ?”

3: “Make a pendulum of the barometer, measure its period at the bottom, then measure its period at the top……””..another try ?….”

4: “Measure the length of the barometer, then mount it vertically on the ground on a sunny day and measure its shadow, measure the shadow of the skyscraper…..”

“….and again ?….”

5: “walk up the stairs and use the barometer as a ruler to measure the height of the walls in the stairwells.”

“…One more try ?”

6: “Find where the janitor lives, knock on his door and say ‘Please, Mr Janitor, if I give you this nice Barometer, will you tell me the height of this building ?”

There are many more ways, for instance:

7: To which the less polite alternative is to threaten to wallop the caretaker with the barometer unless they tell you how high the building is.

8: Use the barometer as a paperweight while examining the building plans.

9: Sell the barometer and buy a tape measure.

10: Use a barometer to reflect a laser beam from the top and measure the travel time.

11: Track the shadow of the building positioning a barometer on the ground every hour.

12: Create an explosion on the top and measure the time for the pressure depression indicated on the barometer.

13: For fun, how about using sound; fire a starting pistol at the bottom, time the difference of arrival at the top. About a second for the Empire State building, and of course it’d have to be a damn great gun to carry over the howl and screech of downtown Gotham. Also, the detonation might get confused with the sounds of routine crack dealing below.

14: Here’s one no-one seems to have thought of :

– Build a sandpit (full of sand, OK?) at the bottom of the building.

– Rake the sand flat.

– Drop the barometer from the top of the building into the sand.

– Measure the average diameter of the crater thus created.

– From the answer to (4), the mass of the barometer and the properties of the sand (viscosity?) calculate its impact speed and thus the height from which it was dropped.

Also has the advantage that you may get your barometer back intact if:

a) The building is small.

b) The sand is soft.

c) The barometer is light and strong.

15:Borrow one of those fancy two channel digital oscilloscopes from somebody’s lab when they aren’t looking. Connect a microphone to each channel. Place one microphone on ground level. Call it “A”.

Place other microphone “B” at top of building, directly over the first microphone. Note that you may need a lot of cable. Place barometer as close to A as possible. Set scope to trigger on channel A. Whack barometer once with hammer or suitable object. The purpose of this is to make a nice, sharp impulse. Measure the difference in arrival time of the impulse in each channel. This is how long it took the sound to travel to the top of the building. The speed of sound is approximately 1 foot per millisecond under most conditions, so we can find the distance travelled by the pulse and thus the height of the building. Now don’t even get me started about using a microphone, an oscilloscope and audible “clicks” to make an acoustical motion detector. : ) Except for the trivial method (2), there are other ways to use dropping the barometer:

16: Drop the barometer off the building onto someones head, killing them outright. Wait for the next day’s papers and read the part where is says “A man (39) was killed yesterday when a scientist (26) dropped a barometer from the top of an [x] foot building”.

17: If it’s a _tall_ building, one could drop the barometer, measure how much its length had changed when it reached the bottom, work out the speed from the relativistic dilation, and form that nd knwon gravitational acceleration calculate the height..

18: Actually, you don’t have to drop it to use relativity.just hold it parallel to your speed vector (as you rotate with the world) and measure the length. do this at the top and at the bottom of the building; at the top, being further from the centre of the world, the speed is greater and can be determined by the dilatation of the length of the barometer. from there, it’s easy to find out just how much further from the centre you are; this figure being the height of the building.

19: Make sure your barometer contains alcohol[1].

Spill the alcohol over a heap of wood, paper and other inflammable stuff in the cellar of the building in question. Ignite. Get out. Listen to a local station on your radio. If all works fine, you will hear a message like “A fire broke out in the <actual height of building> feet tall <insert building name> in <insert address of building> …”

There you are. “And now the police asks for your cooperation in connection with the fire in the <insert building name> today: A young man carrying a broken barometer has been seen leaving the building right before the fire was detected. Description as follows: …”

**DISCLAIMER: Don’t try this at home. It’s far too obvious.**

20:Measure the length of the barometer.

Borrow the scaffolding from the window washers.

Place the bottom of the barometer on the ground and make a pencil mark on the building at the top of the barometer.

Raise the scaffolding a bit to facilitate barometer and pencil manipulation.

Place the bottom of the barometer at the pencil mark on the building from step 3 and make a mark on the building at the top of the barometer.

Repeat steps 4 and 5 until you reach the top of the building. Be sure to count the pencil marks as you go. If at the top of the building, you end up with the barometer sticking up above the building then you must follow the special steps noted later and add that to your answer.

Multiply the number of barometer lengths by the length of the barometer to get the building height.

*******SPECIAL STEPS NOTED HERE*******

**s1) Holding the end of the barometer at the top of the last full barometer length mark, rotate the other end of the barometer until it is in line with the top of the building. s2) Measure the angle between verticle and the barometer. s3) Take the cosine of that angle. s4) Take the answer to s4 and add that to the number of full barometer lengths measured and multiply by the length of the barometer.**

**************************************

**Note: For best results, always hold the barometer vertically.**

21: (Aneroid barometers only) Lie the barometer on its back on the ground. Bounce a laser off the glass front and time how long that takes. Subtract the thickness of the barometer.

22: (Mercury barometers only) Drain the mercury out and put it in a bowl. Bounce a laser off the surface of the mercury, etc. etc. etc. Again, subtract the height of the surface.

23:Take the glass tube out of the barometer.

Attach one end of the glass tube to the top of the building, so that the other end points directly downwards. Measure the time difference between step 2. and the other end of the glass tube touching the ground with a high-precision timing device. Calculate the height of the building using the known viscosity of glass.

24: Run a transparent tube up the side of the building. Fill it with water, seal the top and open the bottom inside a reservoir of water. I.e. effectively make a water barometer – just like a mercury barometer, but with water instead of the mercury. Wait for a day when the water level matches the height of the building, and read off the atmospheric pressure on your original barometer. Calculate the height of water that this atmospheric pressure can support. Unless your building is pretty close to 10 meters high, you may have to wait a long time.

25 : Alternatively you could use fluids with different densities until you found one which was the height of the building. Remember you have to seal the top of the tube, and remove all air from it for an accurate reading.

26:Beat on the foundation o the building, using the barometer, until the building comes crashing down.

Any sizeable pieces should be pulverized into pebbles and dust. The height of the building should be zero. If not, repeat step 2. This method may require more than one barometer. Make sure that you buy the same kind, for a more scientific study.

27: Remove the glass pipe from the barometer. Attach one end to an arrow and the other to the top of the building. Evenly heat up the middle of the tube to red heat and fire the arrow at the ground with a bow. Measure the width of the extended glass tube at several points and average. Knowing the original width, work out the distance travelled by the arrow. Measure the distance of the arrow from the base of the building. Use trigonometry to calculate the height of the building.

28: As a quick check, using the mercury you removed from the barometer: Measure the temperature of the mercury at the top of the building, and put it in a perfectly insulating container. Drop it off the building and measure the temperature of the mercury after it has landed. Calculate the energy gained and therefore the height of the building.

29: Sellotape a tuning fork to the barometer and whack it just before you throw the barometer off the building. Measure the doppler shift at the moment of impact to get its velocity and, hence, the height of the building.

30: Wait until Hell freezes over. Extrude the mercury into a wire. Use wire to measure the building.

31:Set the barometer a measured distance from the building, ensuring a clear line-of-sight exists between it and both the top and base of the building. Buy, borrow or steal a theodolite. Measure the angles (from horizontal) from the base and the top of the building to the barometer. Diagram the distances and angles at a 1: 1 scale on a really big piece of paper. Lay out the diagram on a convenient empty parking lot. Pace off the distance in question.

32: Tie a copper barometer to a copper wire of known diameter. Lower barometer from roof until it just rests on the ground. Apply a known voltage between the barometer and the end of the wire at root level. Measure current flowing between these two points and divide this number into the voltage, giving you the resistance of the barometer/wire combination. Subtract the barometer’s resistance and use the resistance of the wire to determine its length. Add back in the height of the barometer. Also, I’d like to see some answers formulated using a bungee jumping barometer. Possibly using the thickness of the bungee cord with the barometer at ground level, maybe using the barometer weight necessary to stretch the bungee cord all the way to the ground, etc… Every meteorological observation site should have at least one bungee jumping barometer. At least.

33: Read the inscription on the plaque on the back of the barometer, which says, “This barometer is the property of the <number> metres high <name> building. Please do not remove.” [1]

34: Okay, one more idea which was given to me by my graduate research advisor. Suspend the barometer from the top of the building with a wire. Remove the barometer and measure the change in length of the wire. With the weight of the barometer and Young’s modulus for the wire, one can calculate the length.

35:Look for Godzilla.

Wait until he stand before the building.

Poke him with the barometer in the,eh,backside.

YEOWCH!SLAM!PLOFF!

Now that the house is overturned (I think you call it a “flat” : -) , the task has turned into measuring the length, which is much more convenient.And then there is trigonometry, gravity force differentials, laser rangefinding…..and the list goes on.

36: Heres my silly [1] attempt at answering the question of how tall a building is, using a barometer. One can easily find the height of a building, simply by finding its top, and working from there.

Find a person with vertigo. (fear of heights)

Give them the barometer.

Tell them to put it on top of the building.

we have several measurements, which can then be cross referenced to determine the height of the building.

Measure the volume of the sound caused by the persons knees knocking together. The taller the building, the louder the knocking. This should be standardised first, by testing the sound produced for buildings of known height.

attach electrodes to your subject. measure the EEG reading at the moment immediately after placing the barometer on top of the building. (ie, the moment they look down) amplitude of waves indicates anxiety. Again, standardisation should be done to ensure accuracy. [2]
Measure the depth of the crater created when they land, after having seen how high they were when they put the barometer on top of the building.

Silky…in an attempt to be as perverse as possible. [3] [1] well everyone else has. [2] a flat line is the exception to the rule here. [3] no, not pervert.

37: Take the barometer to the top of the building. At the base of the building put a trigger that when the barometer is dropped onto it, it emits a loud, high frequency noise. Start stopwatch once the trigger is activated. Put an audiometer at the top of the building to stop the stopwatch when the audiometer is activated (at least activated higher than the backround noise already present). Determine from there the speed of sound (for that particular day) and therefore determine the top of the building.

38: I think the best procedure must be:

a) Locate a university where a physics exam or test is about to begin.

b) Locate a student waiting for this test.

c) Impose as a physics professor (wear silly clothes, talk funny, mess up your hair, etc) and lure the student into a separate room.

d) Show the barameter you brought with you to the student and ask him the following question: “You are given an accurate barometer, how would you use it to determine the height of a skyscraper?”. Try to squeeze as many answer out of him as possible.

If you didn’t get any useful answers from c), then try to post the question on Internet, preferably in a news group or on a web-page.

39: Find a barometer with heights of local buildings on it Go to all the local gift shops. Look for a fancy souvenir barometer, the kind which shows important local landmarks. Find one which shows the heights of local buildings and considers this building important enough to be listed. Use this barometer.

40: Drop the barometer on the roof and on the ground Hold the barometer straight in front of you and drop it. Measure, very carefully, how long it takes to hit the ground. Go up on the roof and hold the barometer in the same position. Drop it and measure, again very carefully, how long it takes to hit the roof. Since gravity falls off as the square of the distance from the centre of the planet, you can use the difference in times to calculate the height of the building relative to the distance from the base of the building to the centre of the planet. The local library can provide you with the distance to the centre of the planet in the required units.

Note: The ratio of the times is the same as the ratio of the distances from the drop points to the centre of the planet.

41: Drop (and shatter) the mercury barometer at the base of the buidling on a windless day. Measure the increase in the mercury vapour concentration at the top of the building. Solve the diffusion equation to determine the distance from the shattered barometer to the top of the building.

42: Place the barometer on the ground floor of the building. Seal all the building’s doors and windows. Fill the building with water. Read the pressure measurement from the barometer. This gives the weight of a column of water the same height as the building. Use this and the ratio of the density of mercury to the density of water to calculate the height of the building.

Note: It is common courtesy to evacuate the building before using this technique.

43: If you have access to an airless world, take the building there. Throw the barometer horizontally off the building. If the barometer hits the ground, retrieve it and try again, throwing harder. The objective is to throw it hard enough to achieve a circular orbit. Once the barometer is in orbit around the planet, you can measure the period of the orbit. Compare this with the period of the orbit when you throw the barometer from the base of the building. Use this ratio and Kepler’s laws to determine the height of the building (relative to the radius of the planet).

44: (1) Get a barometer that uses a dial for the reading. (2) Open the barometer and remove the mechanisim to allow the hand to swing freely. (3) Dig a hole and climb in, hold the barometer at ground level and point it at the top of the building. (4) Use the barometer as a sextant and measure the angle of inclination, then pace off the distance to the building and use trig to calculate the height of the building.

45: (1) Get an assistant, two synchronized clocks, some gas and a match. (2) Assistant remains at the base of the building and you go to the top. (3) Assistant covers barometer with gas and at a predetermined time, lights barometer with match. (4) You time when you see the flash, and calculate the distance given the speed of light.

46: (1) Go to the top of the building. (2) Drop barometer off building and start timer. (3) Stop timer when you hear barometer hit the ground (4) Solve for height taking into account gravatational acceleration and the speed of sound.

47: Go to the barometers manufacturer and tell him you want a barometer as high as the building in question. the manufacturer will say something like: “what the fuck do you need a XXX feet long barometer for”

48: Tie barometer to a yardstick. Stack many yardsticks together(head to head). Measure inches.

49: Assume that the barometer has a rectangular shape. It therefore must have a corner. If we also assume that we are finding the height of the building for a professor on a test, then we must also assume that he has an answer already prepared to compare to the students answers. Since the entire class has to solve this question, every student has a barometer. Steal some other students barometers, sell them for a ski mask. Wear the ski mask to the professor’s house, and threaten him with the pointy corner of the barometer. Force him to give the correct answer, then use the correct answer.

50:

Weigh the barometer at the ground floor of the building (W).

Take the elevator to the roof and weigh the barometer a second time (w).

The height of the building H is given by H=R*(sqrt(W/w) -1) R~=6378140 m.

51: Take barometer & hammer very flat & thin. Construct large box from barometer & place over building. From Schroedingers principle, we can now say that the state of the is unknown (so any answer will be correct!)

52: 1)Find mass of the barometer 2)weigh the barometer on the ground 3)weigh the barometer on the roof 4)use F/M=g to find two different gs 5)use g=GMm/r^2 to find two radii 6)subtract 53: Drink the Mercury. When you die you’ll go to heaven where all things are revealed including the height of the building.

54: Gather 100 friends. Have each of them guess at the height of the building 100 times. This gives a sample size of 10000. Calculate your sample mean Xn and sample variance s^2. Since the sample size is large, s^2 approximates the true variance. Use Xn -Z(s^2)/100 < height < Xn + Z(s^2)/100 to construct a 1-alpha probability interval for the height of the building. Alternatively, have your 100 friends guess at the height n times. Calculate the sample mean each time. As n goes to infinity, the various sample means follow a normal distribution with mu = true height of building. Either way, use the beat your 100 friends over the head with the barometer so your professor cannot claim you had outside help.

55: A rather advanced solution would be attaching a medium powered transmitter within the barometer. Now measure the received power in a dipole antenna with a micro-voltmeter, when the barometer is on the top of building. Now take the barometer to ground level and then measure the received power. The difference in receiving power will indicate the loss due to attenuation which is proportional to height of the building.

56: Take the barometer to the wizard of Oz. He will put some courage into it as well as some brains. Now ask the barometer to jump from the top of building. If you give a stop-watch to that barometer it will easity find the height of building.

57: This solution works in zero gravity conditions, and assuming that the barometer and the building have equal weight. First perform pirouette like action as a ballet dancer without holding anything for 10 sec. and note the number of rotations. Next try it while holding a barometer with outstreched arms, note the rotations in 10 sec. Finally hold the building and perform the same thing. The moment of inertia depends on the radius. I think this much clue is enough, you can solve the rest!

58: Go to top of building without barometer and with accurate weighing scales. Weigh self. Then place barometer at the base of the building, go back to the top and weigh self again. The increase in weight due to the gravitational attraction of the barometer can be used (knowing the mass of the barometer) to calculate the height of the building.

59: Mass the barometer. Ideally, the building has an elevator. If not, you can use the stairs, but it becomes more difficult to be accurate. Use the barometer in a lewd street comedy show, so that you can earn a few dollars to buy a scale, and a video camera. (Or, if you are very good, a stop watch, and just paper and pencil.) Go to the ground floor of the building, and get in the evelator. Start recording the scale with the video camera. If the scale does not read 0, you can use this as a clibration factor. Put the barometer on the scale. Take the elevator to the top floor (stopping at each along the way). (If the top floor is not directly accessible, go outside, look at the building, and determine which floor is half way up to the top. Multiply final answer by two) Since we stopped at each floor along the way, we have a pretty good idea what acceleration due to gravity is at various points along the elevator ride We can interpolate the spaces between sample points. Now, since initial velocity was zero, and we know the acceleration at every point in the trip (displayed weight = m*(acceleration due to gravity + acceleration due to elevator)), we can go frame by frame along the recorded video tape, and numerically integrate the acceleration to get velocity, and then position at each point in time. The resulting position at the end of the tape is the height of the building. Return scale to store to get money back. (Which I actually did for a physics project one time… We kept the scale in the packaging for the entire experiment. My two female lab partners and I then went back to the store, and said it didn’t match our bathroom.)

60: Extract the mercury from the barometer. Take an accurate mass measurement of the mercury sample. Take it to your neighborhood atomic pile. Bombard the mercury with neutrons in the highest flux region of the core for, oh, about a week. The mercury is now quite radioactive. Determine exactly how radioactive using the common activation equation. Remove the mercury from the core, and mount the mercury sample at the top of the building. (You may wish to do this remotely…..) Now use a well-calibrated radiation detector to determine the gamma ray dose rate at the bottom of the building. Use the normal radiation dose equations (with appropriate buildup factors for building material and surroundings) to determine the height of the building. (As we all know, radiation dose from a point source falls off as the inverse square of the distance.) Do not forget to correct for the decay of the radiomercury atoms during the time it takes to perform the experiment.

61: Tie a long piece of string to the barometer. Hold one end of the string from the top of the building, so that the end of the barometer barely clears the ground. Give the barometer a small displacement and time its period as a compound pendulum.

62: 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.

63: Throw the barometer horizontally off the building with a known velocity (calibrate your throwing ability by timing and measuring barometer throws on the ground). Use projectile motion to find the height of the building once the distance the barometer lands from the building is found.

64: Find a small, very efficient, very light electric motor. Weigh the barometer. Use the motor to carry the barometer up the building. Using a voltmeter and ammeter, calculate the work done by the motor, and thus the gravitational potential difference between the top and bottom of the building. Knowing g, find the height.

65: Go to the basement. Find a part of the basement such that directly above you is solid brick until you reach the roof. Throw the barometer at the ceiling of the basement, which is the floor of the building. The barometer will most likely bounce off the floor. Repeat n times, where n is a very large number. In a few trials, the barometer will tunnel through the potential field of the bricks, and appear on the top of the building. Calculate the percentage of trials for which the barometer tunnels. Use the quantum tunneling equation to calculate the length of the barrier, and thus the height of the building. Note: this effect can be calibrated properly by finding the likelyhood of the barometer tunneling through one brick.

66: Attach a copper wire to the top of the building, and attach the other end to the ground. Smash the barometer and use one of the shards of glass to cut the wire halfway up the building and place an ammeter in series with the wire. Knowing the current through the wire and the resistivity of copper, the potential difference between the top of the building and the bottom of the building can be found. This will be a gravitational potential difference, not an electrical one, but the electrons don’t know that. Thus, since g is known, the height of the building can be found.

67: Find a large wooden rod a bit longer than the building is high. Wrap an insulated copper wire around this rod at a uniform turn density. Make the coil stop at the top and bottom of the building. Run alternating current through the coil, measure current and voltage, and determine the inductance of the coil. Place the barometer in series with the coil so the resistance of the circuit is enough to stop the wires from melting. With the inductance of the coil and its turns per unit length and radius, the length of the coil, and thus the height of the building, can be found.

68: Drop the barometer off the top of the building and measure the radius of the resulting puddle of mercury.

69: Using a device that can propel an object at a known velocity (such as a baseball pitching machine or a rail gun), find the escape velocity of the barometer from the ground, after first having tied a string to the barometer so it can be retrieved from deep space. Repeat on the top of the building. The difference in escape velocity energies gives the gravitational potential difference between the ground and the roof, thus yielding the height.

70: Using the aforementioned pitching machine or rail gun, find the velocity at which the barometer needs to be projected to reach the roof from the ground.

71: Make a small hole in the barometer through which mercury drips at a constant rate. Time this rate at the ground. Place the barometer on the roof and observe the drip rate from the ground with binoculars. The drip rate will be dilated, by general relativity, by a factor which will give the difference in the curvature of space at the bottom and top of the building. Knowing the mass and radius of the earth and so on, the height of the building can be found.

**Vahha**:

72: THIS METHOD USES MORE THAN ONE BAROMETER: Pack as many barometers as possible into the building until it undergoes gravitational collapse and becomes a black hole. Knowing the number of barometers used, the mass of this hole can be calculated, and the Schwarzchild radius of the hole is thus half the height of the building.

73: Find a barometer that uses a liquid with no surface tension whatsoever (superfluid helium?). Break the barometer and spread the liquid evenly over the surface of the building. Measure the depth of the resulting liquid film. Knowing the volume of the barometer, this gives the surface area of the building, which will give its height, if its width and depth are known.

74: Stand on the roof of the building. Throw the barometer to a point exactly on the horizon. Measure the distance from the bottom of the building to the barometer. This gives the horizon distance at the top of the building, thus giving its height above the ground.

75: Make a small hole in the barometer so mercury drips out at a constant rate. Place the barometer so that it is dripping off the roof onto the ground. Measure the time between a drop being released from the barometer and the drop hitting the ground. Repeat the measurement when moving towards the ground at a known velocity. The time between a drop being released and a drop hitting the ground will change. Using the Lorentz transformation equations and taking the top of the tower as x = 0, the position of the ground can be found. This will yield the height of the tower.

76: Find a steel cable. Attach it to the barometer and use the barometer as a physical pendulum to measure g. Then attach the building to the cable (after having remove it from its foundations and attaching the cable to a crane of some sort), and using the building as a physical pendulum, and knowing g, measure its moment of inertia. This will give the dimensions of the building and so on.

77: Use a barometer containing sulfuric acid. Break the barometer on the roof of the building and time how long it takes the acid to eat its way down to the ground.

78: Measure the volume of the barometer at the bottom and top of the building. By knowing the coefficient of thermal expansion of glass, the temperature difference between the top and bottom can be calculated. Refer this to known data of atmospheric temperature as a function of height.

79: Every time somebody walks into or out of the building, stab them with the sharpened end of the barometer (after having sharpened it, of course). Word of the ‘Barometer Murderer’ will eventually reach the building’s owner, who will of course be forced to sell the building. The real estate advertisement should give the height of the building.

80: Knowing the density, width and length of the building, rip the building from its foundations and place it on top of the barometer, giving it a pressure equal to the building’s weight divided by the measurement area of the barometer. Thus the weight, and so the height, of the building can be found.

81: Find the architect who designed the building, crack the (mercury) barometer over his coffee, watch him die when he drinks it, then steal the building’s specifications, including height.

82: THIS ALSO REQUIRES MORE THAN ONE BAROMETER: knowing Young’s Modulus for brick, place barometers on the roof until the roof is lowered by one barometer length. This change in the height of the building under a known stress and Young’s Modulus will give the height of the building.

83: Place a cat on top of the 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, where n>>{a large number}. Refer to Dr Karl Kruszelnicki’s paper on the probability of a cat dying when falling from a certain height.

84: AGAIN, MORE THAN ONE BAROMETER: place as many barometers in the building as will fit. This gives the volume, thus the height, if other dimensions are known.

85: Use a machine (such as the aforementioned baseball pitching machine or rail gun) that can hurl the barometer down from the ground into a hole in the ground at a velocity that is only known to within a certain tolerance. Find the smallest uncertainty in velocity, and thus momentum, such that the barometer appears on top of the building. Use Heisenburg’s position-momentum uncertainty relationship to find the height of the building.

86: Tie a string to the barometer and hang it as a plumb bob. The string will be slightly deflected from the vertical by the gravitational effect of the building. This gives the mass of the building, etc.

87: Find at what velocity you must move upwards or downwards past the building such that the building is contracted to the same length as the barometer. Find gamma for this velocity, multiply by the length of the barometer.

88: Measure the color of the barometer. Drop the barometer off the building. Measure color doppler at the moment of impact. From there extrapolate the velocity at impact. Finally use the gravity exuation to figure the height of the building.

89: Drop barometer Measure radius of the debris field This should be a function of velocity hence the height of the building.

90: Place barometer in such a way that a rock will roll out and push whoever grabs the barometer off the building. Wait for newspaper reports about the buildings height.

91: Mount the barometer to top edge of building. Use a projectile weapon from a fixed location to shoot it. Using ballistic curve and weapon specs, calculate height of building.

92: Using barometer as a pointer, count the number of floors in building, and calculate the total height using the standard height of a storey of that type of building. Or count bricks if you need to.

93: Measure the base of the building in barometer lengths. Measure the angle to the base corner to the diagonally opposite top corner. Use Trig to calculate unknown height of triangle.

94: Sell the barometer, put the money in an fee-free long term account. Put yourself in suspended annimation until the compound-interest on your money makes you the richest man on earth, then use this money to capitalize your plans for world domination. Then when you are the Almighty Supreme Master of the Entire Universe, order one of your lackeys to report back you with the height of that building. Or you could have the stupid thing knocked down if you wanted to …

95: Get some electronic parts, and a block of plasticine, stick the parts, and some coiled wires into the plasticine, and mount the barometer to this. Put a sticker on the plasticine, that has, “C4”, or “SEMTEX”, written in clear, signal yellow lettering.

Go to your local airport and highjack an aircraft, explaining that you will detonate this device unless the pilot does exactly as told, (you can embroider this performance any way you wish … eg. Wear a towel on your head and see if you can start a Middle-Eastern war. Or maybe you could have some more selfish demands like $50 000 000 in small unmarked bills, or maybe demand that Roseanne Barr, be forced to give up acting, you know – whatever you like).

Anyway, where was I? So you instruct the pilot to fly directly past the building at roof level, and as you pass it, simply look at the altimeter. Ask the pilot if there are any calibration ajustments and then work out the building height.

After this you can tell everybody the truth about the barometer and the bomb, and you can have a jolly good laugh about it and maybe get together afterwards for a social drink, or something.

96: Comedian Ask a comedian. apparently comedians are the worlds foremost experts on using barometers to measure heights. Actually I would really like to know how to measure the height of a building with a rectal thermometer.

97: Businessman Create a small company selling barometers. Sell stock in the company. Advertise the many benefits of barometers on daytime TV. Everybody needs a barometer. They are the best thing since sliced bread. They chop. They slice. They dice. Get the ginsu barometer. Now only $19.99. You get the added bumper sticker that says “my parents went to Florida and all I got was this lousy barometer”. Diversify your product by producing a full line of models, the economy barometer, the standard barometer and the super-duper-extra-deluxe barometer with vernier caliper and laser scope for high precision measurements. Initiate a telemarketing program that calls people late at night asking them to buy barometers. Bribe all the physics professors at the university to ask their students this stupid question on their exams. When the stock goes up for sale make a million dollars profit. Hire a lobbyist. Bribe the governor to put questions about barometers on high school regents exams. Then create a contest to see who can find the height of a building using a barometer. The winner gets a million bucks. Of course no one really wins, but you get the answer for free. Or you could conduct a market survey to measure the demand for barometers, and use this to measure the approximate height subject to market fluctuations.

98: Physicist Get some poor forlorn overworked repressed suffering graduate student to solve this problem for you. If he gets the wrong answer threaten to fire him. Of course you already know the answer. This was just for fun. Then ask your undergraduates the question on an exam. Somehow none of them get the right answer. Initiate a program to measure the height of the building from outer space somehow mysteriously using the barometer. Send the experiment on a space-shuttle research mission. Put it on your web-site and resume.

99: Engineer It is perfectly obvious. Measure the height of the barometer. Get a surveying telescope. Form a triangle such that the top of the building and the top of the barometer line up as seen in the telescope. Then measure the distances along the base of the triangle and compute the ratio. (Of course this doesn’t work but then ……. back to the drawing board).

100: Anthropologist Move to a prehistoric jungle society of pygmies who live in grass huts. They are so short that you can measure the height of their “scyscraper” directly. Barometers did not exist in prehistoric times.

101: Psychiatrist Thinks to himself: This patient is extremely frustrated. I will charge him extra. Says to patient: How long have you been having this recurring fantasy about the barometer. I believe you are obsessed with it.

102: Anarchist Dye your hair blue and throw the barometer at the building. how the fuck can an anarchist measure anything?

103: Doctor Doctors use manometers all the time. Find a patient with fear of heights. Use the barometer to measure the patient’s blood pressure at the bottom of the building. Stick his head out of the window at the top of the building and measure his blood pressure again. Compute the height from the ratio of blood pressures.

104: Dry method a) buy a lot of dry sand (e.g. the whole Southern Lybia, oil wells excluded) b) use the barometer as a shovel c) cover the building with a perfect cone of sand, avoiding windy days d) measure the area covered by the sand, obtaining diameter of the cone base e) knowing the natural slope of the sand you can easily obtain the height of the building

105: Wet method (requires a lot of barometers of many types) a) use the barometer as a shovel b) dig a big hole (bigger than the bulding) c) use a barometer (better the type mounted on a wood tablet) as a trowel and cover hole walls with concrete until you have a waterproof basin d) buy as many water barometers as you can e) remove water from water barometers and put it into the basin f) seal all doors and windows of the building with duct tape g) carefully put the building into the basin h) measure the volume of water moved by the building

106: Amazon (not the bookshop!) method a) remove the glass pipe from a barometer and open both ends b) tie a light rope to the tail of an arrow c) put the arrow into the glass pipe d) go on the top of building e) blow the arrow into the nearest tree f) measure the rope g) solve the triangle formed by the rope and the building

106b) Another Amazon method – don’t require rope but a stopwatch a) remove the glass pipe from a barometer and open both ends b) put an arrow into the glass pipe c) hit a pedestrian d) start the stopwatch e) stop the stopwatch when you hear the howl f) multiply time x sound speed This must be repeated many times because reaction time of subjects may vary. In any case the last method has the advantage that you can verify your results in a easy way: if a M-16 bullet shooted by the police has x energy when launched, and y energy when it hit you, you can (well, ballistic experts can) know the distance between the gun and the hole in your head, thus measures can be compared.

107: Internet method a) ask everybody on the Net to submit you a solution b) print every message (remember to number the pages!) c) put the pile of paper aside the building until you reach the top d) use the barometer as paperweight e) multiply the number of pages for the thickness of the paper

108: Remove mercury from barometer. Place drop of mercury so it closes a circuit between two parallel non-mercury-wettable conductors at a known potential difference. Measure speed & direction of motion of droplet due to JxB forces. Rotate setup about a vertical axis until maximum speed is found. This gives the direction & magnitude of the vertical component of the local geomagnetic field.

Repeat at top of building.

Compare differences to know characteristics of the geomagnetic field. This will give height of building.

109 : Well, if one drilled a small hole in a the bottom of the barometer, one could establish the rate at which the mercury drips out of the barometer. Then one could attach a small electric motor to the top of the building. It could raise the barometer at a known rate. Using the amount of missing mercury, one could calculate the time it took to raise the barometer to the roof. Ergo, the height of the building is now known_

110. Drink the mercury. If there’s an afterlife, ask God how tall the building was. If there isn’t an afterlife, who cares that you don’t know the height of the building?

111. Set the barometer in the middle of the building. Don’t look at it as its wave function expands. When its wave function encompasses the entire building, solve Schroedinger’s equations.

112. Find a flammable barometer. Burn it and measure the time it takes for the smoke to reach the top of the building.

113. Give it to an MIT student and tell him to transform it into a robotic barometer specially designed to measure the height of buildings.

114. Tie the barometer to a string. Swing it in front of the architect of the building while muttering, “You are getting very sleepy. When I snap my fingers, you will tell me the height of the building.”

115. Find a spot on the ground with a known value for hardness. From the top of the building, throw the barometer down to this spot. (You could also throw from the ground, but you would have to throw harder.) Repeat until the barometer bounces up to the top of the building. Measure the force of your throw and calculate the height of the building.

116. Find a barometer the size of the building. Measure the barometer.

117. Weld barometers to the top of the building until they reach the moon. The building is approximately a quarter of a million miles tall.

118. Take the current air pressure and divide by zero. Your barometer (and your test paper) will burst into flames to prevent a violation of mathematical law. As the professor finds another copy of the test to give you, sneak into his desk and find the answer key.

119. Heisenberg’s Principle of Aesthetics: Measure the color of the building so precisely that you cannot measure its size. With that done, any guess is as good as the real answer.

120. Set the building on the barometer. Knowing the density, length, and width of the building as well as Young’s Modulus for the barometer, calculate the height.

121. Take the volume of the building and divide by its width and length. When you’re done, hold the barometer in the air to signal to the professor that you are finished with your test.

122. Create your own system of measurement. The unit of length will be the “building.” The building in question is precisely one building tall. When asked what the barometer was used for, state that it was around for moral support.

123. Hold the barometer between the index finger and thumb on your left hand. Hop twice on each foot before breaking out into disco. This is the rain dance for a certain Native American tribe. When the rain falls, choose a drop and measure its velocity at the top of the building and its velocity when it reaches the bottom of the building. Subtract the former value from the latter, then apply this into the gravity/acceleration formula.

124. Set a tape measure at the bottom of the building. Tie a rope to one end, string it (the rope) up around a pulley on the top of the building. At the other end of the rope, affix the barometer as a counterweight. Let it loose as the weight of the barometer pulls the tape measure to the top of the building. Go to the bottom and read the tape measure.

125. Set a laser at the top of the building. Fire the laser to the ground and have it reflect off the barometer. Then, suddenly rotate the barometer such that the laser is firing at the building. When the building vaporizes, its height should be zero. You may wish to set the laser on the ground, though, so you can use it again when you measure the next building.

126. Briskly rub the barometer with a silk handkerchief. Hammer an iron spike into the ground at the base of the building. Hold the barometer directly over the spike for one minute, recording any electric sparks. Repeat many times, and then use the probability of an electric arc to calculate the distance between the barometer and the grounding wire, which is also the height of the building.

127. (Works only for underwater buildings). Find a barometer that uses a liquid lighter than water. Hold it at the base of the building and let go. Time it as it floats past the top of the building. Calculate the height.

128. (Only works for buildings in environments with negligible air and gravity, i.e. space). Move the barometer at a steady speed along the height of the building while timing it. As every good student knows, d=rt.

129. Use the barometer to measure the density of a pool of liquid. Weigh the building and drop it into the liquid. Time the building as it sinks into the liquid. Calculate the height.

130. Hit the barometer onto a piece of flint. Start a small fire. When the fire alarms ring, the building is evacuated. Extinguish the fire, pull out a tape measure, and measure the building without anybody standing around to see that you didn’t really use the barometer.

131. Give the barometer to your younger sibling, who will run outside to play with it. Now that you have peace and quiet, do some internet research to find the height of the building.

132. (Omega must be greater than one and the cosmological constant must be less than one for this next suggestion to work) Allow the barometer to come into contact with an anti-barometer. The explosion should rip the building off its foundation and send it into deep space. Wait until the gravity of the universe causes it to collapse on itself. Since the cosmological constant is less than one, the universe should curl in on itself. When the universe’s diameter is small enough for the building’s top and bottom to meet, measure the universe’s diameter and multiply by pi, assuming that the space-time continuum is perfectly spherical.

133: Walk to a comfortable distance from the building. Place the barometer on the ground and sit on it to rest your feet. Now count the number of stories in the building and multiply it by about 3 meters (10 feet).

134: Take a barometer to the top of the building, attach a long rope to it, lower the barometer to the street and then mark the point where it is. Bring it up and drop it. Due to the Coriolis force, the barometer will not fall in the same point as before, but in another one, in westward direction. The distance between these two points is univocally determined by the height of the building (and vice versa). That’s it!

135: Here’s another way: Tie a string to the barometer. Take the barometer to the four corners of the building’s roof, and use it as a plumb bob. Use the difference in angles at the corners to find the distance from the roof to the center of the Earth, based on the Earth’s curvature. Subtract the known radius of the Earth to get the building’s height.

136: Instruments: A barometer, an anemometer, a a lead mass >=40kg(pointed) and a stop watch, a set of flaps Just drop this lead mass and mark where this falls. Draw a circle of infinite radius around this spot. Get a lab-view program and do real time data acquisition of wind-speed readings from top and bottom of this building. Drop the Barometer with the set of flaps attached to it to induce drag and when this barometer falls just measure the deviation form the the spot. If you tun into problems, remember your lab-view program? A resolution of a least 0.05mS is fine then you can compute temporally how much the wind contributes to the deviation. This does not solve the problem does it? We are just getting warmed up. Remember statistical mechanics? You will need it now… you will need to standardize the deviation from a known distance call this quantity x and then we can sum x as a unit of measure of the building height or alternatively you can measure this with actual numbers!

137:

Bring the barometer in such a linear motion, that it passes the building both at ground level and at it’s uppermost level.

Be sure not to know anything about the speed of the barometer at ground level, you know it’s exact location now.

Be sure not to know anything about the speed of the barometer at it’s uppermost level, you now know the exact location of this level as well.

The height of the building is given by Height = 3) – 2)

138: Postulate 1) Assume the building is spherical. Postulate 2) Assume the building is in a vacuum Postulate 3) Assume \hbar = 1 Postulate 4) Assume the height of the building is 100 meters.

**The height of the building is 100 meters**

proof:

1) Write the height H as H = 0.5H + 0.5H

2) According to postulate 4 the height of the building is 100 meters -> 0.5H = 50 meters 3) Combining 1) and 2) we get: H = 50 + 50 = 100, so the height of the building is 100 meters Q.E.D.

139: Put a glass cap at the open end of the barometer and turn it over so that it acts like a mirror. Place the barometer facing down from the room. Now with a laser pointer direct the beam at an angle from the ground and see where you get the light dot reflected from the barometer. You know the angle and know the horizontal distance between two dots. Its simple trigonometry after this.

140: Attach two copper cables to the metal case of the barometer. Position the barometer at the edge of the roof, so it can be seen from the sidewalk below. Tap into the electrical system to get enough current to heat the case to incandescence. Measure the flux one meter from the barometer, and again from the sidewalk. The height of the building in meters is the square root of the ratio of the one meter measurement and the sidewalk measurement.

141: Alternatively, you could fashion a cavity radiator from the case. This saves you the trouble of hauling your measuring equipment up and down the stairs (in case you knocked out power to the elevators while hacking into the building power), as you just need to measure the flux at several wavelengths. Knowing the radiating area, you can now calculate the luminosity, and from that and the apparent brightness, the distance to the roof.

142: Detonate a charge of TNT on the roof of the building. Measure the pressure of the shockwave on the ground using the barometer. Knowing the amount of tnt detonated one can work out the shockwave strength and knowing the decay rate of the shockwave one can work out the distance from the blast knowing the pressure.

Of course, you could use the barometer to measurethe pressure at the top and the bottom of the building and use the air density…

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