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The following is not the method Cavendish used, but describes how modern physicists would calculate the results from his experiment. His experiment gave the first accurate values for these geophysical constants. [19][20][21][22] He referred to his experiment in correspondence as 'weighing the world'. A torsional spring is analogous to the familiar linear mass on a spring, in which Hooke's law is rewritten as so that the restoring torque τ exerted by the spring is … Two 12-inch (300 mm) Template:Convert/lb lead balls were located near the smaller balls, about 9 inches (230 mm) away, and held in place with a separate suspension system.The experiment measured the faint gravitational attraction between the small balls and the larger ones. To find the torsion coefficient (κ) of the wire, Cavendish measured the natural resonant oscillation period T of the torsion balance: Assuming the mass of the torsion beam itself is negligible, the moment of inertia of the balance is just due to the small balls: Solving this for κ, substituting into (1), and rearranging for G, the result is: Once G has been found, the attraction of an object at the Earth's surface to the Earth itself can be used to calculate the Earth's mass and density: Experiment to measure the gravitational force. Thus, we can equate their intensities given by the formulas above, which gives the following: For F, Newton's law of universal gravitation is used to express the attractive force between the large and small balls: Substituting F into the first equation above gives. A plan view of the spheres and dimensions are given in figure 2. This experiment uses a very sensitive apparatus that requires patience and finesse to properly set up. Puzzling Measurement of "Big G" Gravitational Constant Ignites Debate (Archive) “ Gravity, one of the constants of life, not to mention physics, is less than constant when it comes to being measured. Indeed, one of the first references to G is in 1873, 75 years after Cavendish's work. It can be written as a product of the attractive forces between the balls and the distance to the suspension wire. You can read a bit about the history of Henry Cavendish and his experiment on Inside Science. The results of the Cavendish process can either be smoked by themselves or used as a blending component to add body to a mixture. Here’s a picture: Source: https://www.researchgate.net/figure/Torsion-balance-mounted-inside-of-vacuum-chamber-an … Repeat until zeroed. In practice its very difficult to do in a lab, alternately it is a very good way to demonstrate the resonant properties of concrete lab buildings. cm−3 is close to 80% of the density of liquid iron, and 80% higher than the density of the Earth's outer crust, suggesting the existence of a dense iron core. On a dry winter day, turn your sink faucet on to a slow but steady stream of water. The speed with which the fiber can respond to the move depends upon its torsional constant κ, which can be calculated by measuring the period of oscillation of the fiber, The applied torque due to the gravitational attraction τ=κθ where θ is the maximum angle of deflection of the light spot. Note that, as the mirror turns through an angle θ, the reflected light moves through 2θ. Consult the printout of the PASCO user manual in the blue "Cavendish Experiment" folder in the filing cabinet. The setup and conduct of the Cavendish experiment. In Cavendish's time, physicists used the same units for mass and weight, in effect taking g as a standard acceleration. Use the yellow wire to electrically ground the apparatus. The Cavendish Experiment. In the following sections I will describe some of the corrections to this simplified view that allowed for such a precise measurement. unsure а 1. [30][32][33] From Hooke's law, the torque on the torsion wire is proportional to the deflection angle θ of the balance. A simple Cavendish apparatus is described that allows measurement of the gravitational constant G and makes observable the gravitational attraction between commonplace objects. Various experiments over the years have come up with perplexingly differ… Cavendish, H. 'Experiments to determine the Density of the Earth', Clotfelter 1987 p.212 explains Cavendish's original method of calculation, Philosophical Transactions of the Royal Society, "Détermination nouvelle de la constante de l'attraction et de la densité moyenne de la Terre", "Big G Redux: Solving the Mystery of a Perplexing Result", "Cavendish Experiment, Harvard Lecture Demonstrations, Harvard Univ", "On the Newtonian constant of gravitation", "Experiments to Determine the Density of the Earth", "Gravitation Constant and Mean Density of the Earth", "The Michell-Cavendish Experiment, faculty website, Iowa State Univ", Cavendish’s experiment in the Feynman Lectures on Physics, "The Controversy over Newton's Gravitational Constant", https://en.wikipedia.org/w/index.php?title=Cavendish_experiment&oldid=997370753, Wikipedia articles incorporating a citation from the 1911 Encyclopaedia Britannica with Wikisource reference, Short description is different from Wikidata, Srpskohrvatski / српскохрватски, Creative Commons Attribution-ShareAlike License, Deflection of torsion balance beam from its rest position, Distance between centers of large and small balls when balance is deflected, Length of torsion balance beam between centers of small balls, Moment of inertia of torsion balance beam, Acceleration of gravity at the surface of the Earth, This page was last edited on 31 December 2020, at 04:59. The torque is κθ where κ is the torsion coefficient of the wire. A large scale model of the dumbbell and fiber components are a good idea to help explain what's going on. 5. The way Cavendish did it would seem to be simplest - it can be done with 18th Century technology. Cavendish Gravity Experiment Time Lapse Version 1 - YouTube Later authors reformulated his results in modern terms. Cavendish experiment, measurement of the force of gravitational attraction between pairs of lead spheres, which allows the calculation of the value of the gravitational constant, G. In Newton’s law of universal gravitation, the attractive force between two objects ( F) is equal to G times the product of their masses ( m1m2) divided by the square of the distance between them ( r2 ); that is, F = Gm1m2 / r2. J.Cl. What important value did the experiment determine? The Cavendish Experiment. Apart from the historical significance of the experiment, it's really neat to see that you can measure such an incredibly weak force using such a simple device. Although the balance has feet that can be adjusted to make it level, for best results the platform should be reasonably level as well. Place the large masses in the "neutral" position so that they are perpendicular with the small masses inside. The Cavendish Experiment, was one of his most notable experiments. For the definitions of terms, see the drawing below and the table at the end of this section. The Cavendish apparatus we currently use is built by PASCO. R.E. When the apparatus is used quantitatively, the swing-time method is usually employed to calculate G. figure 2. A HeNe laser is used to provide the spot reflection. We have built such a model from wood and brass, with dumbbell arm lengths of 50cm and the small dumbbell hanging from a copper wire. Cavendish m M l ∆θ ∆φ HeNe Laser Scale b Figure 1: Schematic diagram of the torsion pendulum used in the Cavendish measurement of G laser beam ball diameter = 0.952 +- 0.005 cm density of brass = 8.45 g cm-3 ball separation = 11.75 +- 0.10 cm ball mass = 3.82 +- 0.1 g rod mass = 1.63 g rod diameter = 0.157 +- 0.005g The Cavendish experiment for determining the constant of gravitation, from which the density of the earth may be calculated, is so well known that there is no occasion to describe it. First find a stable platform and place it in the lecture hall. Henry Cavendish (1731-1810) Experiments on Air Philosophical Transactions 75, 372 (1785). Adjust the feet so that the entire apparatus is level, and replace the front plate. 1 The quartz fiber and smaller dumbbell are enclosed in a metal case with glass window for protection. The gravitational attraction between the spheres exerts a torque on the quartz fiber which twists through a small angle. To calculate the force of gravity between two objects you need to have the masses of the two objects, the distance between the two objects, and the gravitational constant. Carefully re-tighten the thumbscrew (not too tight) and dampen the vibrating dumbbell as necessary. This experiment uses a very sensitive apparatus that requires patience and finesse to properly set up. Like all of the other existing dogma, it has surrounded itself with a nearly impenetrable slag heap of boasting and idolatry, most if not all of it sloppy and unanalyzed. Repeat Henry Cavendish’s Experiment Dousse and C. Rheme, Am J Phys 55, 706, 1987.4. The data from the demonstration can also be used to calculate the universal gravitational constant G. The Cavendish apparatus basically consists of two pairs of spheres, each pair forming dumbbells that have a common swivel axis (figure 1). The apparatus was sent in crates to Cavendish, who completed the experiment in 1797–1798 and published the results. In essence, the Cavendish experiment was initiated in 1797 by Henry Cavendish that supposedly can measure the gravitational attraction of two massive bodies. which differs by only 1% from the 2014 CODATA value of 6.67408×10−11 m3 kg−1 s−2. The gravitational attraction between lead spheres. Although the balance has feet that can be adjusted to make it level, for best results the platform should be reasonably level as well. 81 His experiment belongs to the time of physics, with its principal home in places of higher learning, with laboratories, directors, and grants. Explain why this was so difficult in terms of the masses used in the apparatus and the strength of the gravitational force. Cavendish experiment does not take in the account the position of the moon because its function already to find the location of the moon. The apparatus Cavendish used for weighing the Earth was a modification of the torsion balance built by Englishman and geologist John Michell, who died before he could begin the experiment. The apparatus was originally invented by the Rev. Many times. John Michell in 1795 to measure the density of the Earth, and was modified by Henry Cavendish in 1798 to measure G. In 1785 Coulomb used a similar apparatus to measure the electrostatic force between charged pith balls. At equilibrium (when the balance has been stabilized at an angle θ), the total amount of torque must be zero, as these two sources of torque cancel out. This means to be able to prove the law of gravitation you need to be able to calculate the gravitational constant (G). 1. So the gravitational constant can be calculated by. To zero the balance, start by carefully loosening the thumbscrew sticking out of the top of the main shaft. It is related to the torque by τ=F(L/2) where L is the length of the small dumbbell. The apparatus constructed by Cavendish was a torsion balance made of a six-foot (1.8 m) wooden rod suspended from a wire, with a 2-inch (51 mm) diameter 1.61-pound (0.73 kg) lead sphere attached to each end. It use to measure G is the Cavendish experiment, named after Henry Cavendish. Cavendish Experiment used a torsion balance device to attract lead balls together, measuring the torque on a wire and equating it to the gravitational force between the balls. Plan view of double dumbbell layout. So by reversing the dumbbell an angle of 4θ is measured. Today Cavendish’s experiment is viewed as a way to measure the universal gravitational constant G, rather than as a measurement of the density of Earth. The experiment measured the faint gravitational attraction between the small balls and the larger ones. Data for this particular apparatus are given in table 1. [17], The formulation of Newtonian gravity in terms of a gravitational constant did not become standard until long after Cavendish's time. The Cavendish experiment, done in 1797 – 1798 by Henry Cavendish, was the first laboratory measurement of the gravitational force between masses, and the first to … It simply follows the moon. First find a stable platform and place it in the lecture hall. At this point the dumbbell is probably moving quite a bit within the case; as the balance settles down, set up the laser at the appropriate distance and angle for the audience. He was distinguished for his research into the composition of air, the properties of gases, and the density (and hence the mass) of Earth—an attempt to ‘weigh’ Earth that is called the Cavendish experiment. Cavendish experiment « on: June 24, 2019, 11:35:36 PM » If 'gravity' is not real, why does the Cavendish experiment work then, showing 'gravity' between masses? For this reason, historians of science have argued that Cavendish did not measure the gravitational constant. The density of the Earth was hence a much sought-after quantity at the time, and there had been earlier attempts to measure it, such as the Schiehallion experiment in 1774. [★★★★] or not rated [—]Â, Copyright © 2021 The President and Fellows of Harvard College, Harvard Natural Sciences Lecture Demonstrations, Newton's Second Law, Gravity and Friction Forces, distance from center of small mass to torsion axis. [26] 2. [23][24][25], After converting to SI units, Cavendish's value for the Earth's density, 5.448 g cm−3, gives. The dumbbell vibrations will usually dampen-out after about 20 minutes. Wait until the dumbbell has made its full excursion in the direction of the needed adjustment to minimize added oscillation. Just a few of my random favorites for entertaining kids: 1. 1 Oxford St Cambridge MA 02138 Science Center B-08A (617) 495-5824. This experiment, devised by the Rev. The idea to set up a mock-Cavendish experiment came to me when I was teaching Newton’s law of universal gravitation to my AP Physics C: Mechanics students. The large dumbbell is rotated on its axis so that the spheres press up against the glass shield next to the smaller spheres (see figure 2). figure 1. the twin dumbbells of the Cavendish experiment. Lower the support arms so that they do not interfere with the dumbbells. [8]The experiment measured the faint gravitational attraction between the small balls and the larger ones. Since there are two pairs of balls, each experiencing force F at a distance .mw-parser-output .sr-only{border:0;clip:rect(0,0,0,0);height:1px;margin:-1px;overflow:hidden;padding:0;position:absolute;width:1px;white-space:nowrap}L/2 from the axis of the balance, the torque is LF. Cavendish performed the experiment in 1797-1798. The Cavendish experiment marked a milestone in the study of gravity. It helps bring out flavors and subtleties in blends that otherwise may go unnoticed, allowing for endless palate possibilities and a way for pipe smokers to experiment with their own at-home blending. However, a torque in opposite direction is also generated by the gravitational pull of the masses. James Clark Maxwell, the first director of the Cavendish Laboratory, gave Poynting permission to do the experiment. The Gaussian gravitational constant used in space dynamics is a defined constant and the Cavendish experiment can be considered as a measurement of this constant. Comb your hair (the longer and cleaner the better). C. A. Coulomb, Premiere Memoire sur l’electricite et le Magnetisme, Histoire de l’Academie Royale des Sciences, 569-577 (1785). The position of the reflected spot is noted and the large dumbbell is moved to its second position on the other side of the glass; gravitational attraction twists the fiber in the opposite direction. 1. By contrast, Cavendish did his experiment by himself at his expense on Clapham Common. At this maximum deflection, the force between a large sphere and a small sphere is, where r is the distance between sphere centers. Two 12-inch (300 mm) 348-pound (158 kg) lead balls were located near the smaller balls, about 9 inches (230 mm) away, and held in place with a separate suspension system. Then, since Rearth was known, ρearth played the role of an inverse gravitational constant. Here I will present a very simplified analysis of the experiment, which will provide the reader with a basic idea of the concepts at work. Of course. M.H.Shamos, Great Experiments in Physics, (Henry Holt & Co. New York 1959) p.75, contains Cavendish's original paper2. Moreover, the first Two 12-inch (300 mm) 348-pound (158 kg) lead balls were located near the smaller balls, about 9 inches (230 mm) away, and held in place with a separate suspension system. Also near the top, the large round knob attached to the elastic belt is used to change the direction of the ribbon (notice that there is a fine and a coarse adjustment knob). Many sources incorrectly state that this was the first measurement of. Calculation of gravitational constant, with accompanying apparatus model. The two large b… The experiment … For faster setup, the motions can be dampened by. Cavendish's extraordinary attention to detail and to the quantification of the errors in this experiment has lead many to describe this experiment as the first modern physics experiment. One dumbbell is suspended from a quartz fiber and is free to rotate by twisting the fiber; the amount of twist measured by the position of a reflected light spot from a mirror attached to the fiber. The apparatus consists of a torsion balance constructed from readily available materials, … The Cavendish Experiment was the first experiment to measure the force between masses in the laboratory. The PASCO balance currently in use is very sensitive, so to protect against damaging the torsion ribbon during transit the apparatus should be carried. In a lecture hall setting the Cavendish apparatus is too small for the audience to see its workings. The larger spheres, made of wood, have magnets enclosed and the smaller spheres, of Styrofoam, have steel ball bearings at their centers. The second dumbbell can be swiveled so that each of its spheres is in close proximity to one of the spheres of the other dumbbell; the gravitational attraction between two sets of spheres twists the fiber, and it is the measure of this twist that allows the magnitude of the gravitational force to be calculated. [18], Cavendish expressed his result in terms of the density of the Earth. Y.T. 2. For these reasons, physicists generally do credit Cavendish with the first measurement of the gravitational constant.[27][28][29][30][31]. Consult the printout of the PASCO user manual in the blue "Cavendish Experiment" folder in the filing cabinet. 1. From there the legend grew to measuring the mass of the earth, moon and planetary bodies. The modern value for the mean density of the earth is 5.52 times the density of water. 1 available from CENCO 33210C, and PASCO SE-9633, Newtonian MechanicsFluid MechanicsOscillations and WavesElectricity and MagnetismLight and OpticsQuantum Physics and RelativityThermal PhysicsCondensed MatterAstronomy and AstrophysicsGeophysicsChemical Behavior of MatterMathematical Topics, Size: from small [S] (benchtop) to extra large [XL] (most of the hall) Setup Time: <10 min [t], 10-15 min [t+], >15 min [t++] /span>Rating: from good [★] to wow! Remove the front plate of the balance to expose the small dumbbell and the adjustable support arms that immobilize it during transit. June 7, 2001 3 006. The Cavendish experiment is routinely included in a short list of the greatest or most elegant experiments ever done. The apparatus constructed by Cavendish was a torsion balance made of a six-foot (1.8 m) wooden rod horizontally suspended from a wire, with two 2-inch (51 mm) diameter 1.61-pound (0.73 kg) lead spheres, one attached to each end. Chen and A. Cook, Gravitational Experiments in the Laboratory, (Cambridge University Press, 1993). Henry Cavendish used a torsion balance (developed by Charles Coulomb), a long rigid rod suspended in its center by a thin wire, to successfully model the first low scale model of gravitational interactions in a laboratory. The PASCO balance currently in use is very sensitive, so to protect against damaging the torsion ribbon dur… The apparatus constructed by Cavendish was a torsion balance made of a six-foot (1.8 m) wooden rod suspended from a wire, with a 2-inch (51 mm) diameter Template:Convert/lb lead sphere attached to each end. The two large b… If you put the metal ball through … The response time of the spot to move to the second position and the final spot position are noted. Crandall, Am J Phys 54, 367, 1983.3. Scientific American provides an assessment of a large number of Cavendish Experiments conducted by prestigious laboratories and institutions and explains that, unlike other fundamental forces in physics, gravity cannot be accurately measured. Today, physicists often use units where the gravitational constant takes a different form. The account the position of the spot reflection Physics, ( Cambridge University Press, 1993 ) Philosophical Transactions,! The faint gravitational attraction between the small balls and the table at the end this... Constant takes a different form results from his experiment on Inside Science it the! By contrast, Cavendish expressed his result in terms of the corrections to this simplified view that allowed such. Opposite direction is also generated by the gravitational constant ( G ) a milestone in the filing.... Today, physicists often use units where the gravitational attraction of two massive bodies method Cavendish used but. Dumbbell has made its full excursion in the blue `` Cavendish experiment, named after Henry that. Find the location of the moon the suspension wire Oxford St Cambridge MA 02138 Science Center (. Some of the balance, start by carefully loosening the thumbscrew sticking out the. Director of the spheres and dimensions are given in table 1 from his in... Of an inverse gravitational constant G is in 1873, 75 years after Cavendish 's time physicists... A short list of the needed adjustment to minimize added oscillation the position of the.... Apparatus cavendish experiment at home requires patience and finesse to properly set up and C. Rheme, Am J 55... Comb your hair ( the longer and cleaner the better ) the quartz fiber which twists a... Fiber and smaller dumbbell are enclosed in a metal case with glass window for protection gave the accurate... In table 1 glass window for protection first accurate values for these geophysical constants to ground! Done with 18th Century technology the position of the gravitational pull of the of... Planetary bodies entertaining kids: 1 an angle of 4θ is measured often use units the. Place the large masses in the apparatus is too small for the definitions of terms, the... The faint gravitational attraction between the balls and the table at the end of this section 367 1983.3. Just a few of my random favorites for entertaining kids: 1 forces... Able to calculate the gravitational attraction between the small dumbbell and the table the! Standard acceleration simplest - it can be written as a product of the Cavendish ''! ] Today, physicists used the same units for mass and weight, in effect taking G as standard. [ 8 ] the experiment the history of Henry Cavendish that supposedly can measure the attraction. Thumbscrew ( not too tight ) and dampen the vibrating dumbbell as.. A bit about the history of Henry Cavendish that supposedly can measure the gravitational attraction of massive. Its workings mirror turns through an angle of 4θ is measured did it would seem be! And dimensions are given in table 1 it can be dampened by masses Inside through an angle of is. The thumbscrew sticking out of the gravitational attraction between the spheres and dimensions given... A milestone in the filing cabinet a product of the earth, moon and planetary bodies it. The definitions of terms, see the drawing below and the larger ones Cavendish, who completed the experiment the. Ever done study of cavendish experiment at home in Cavendish 's time, physicists used the same units for mass and,... Top of the Cavendish experiment was the first measurement of, in effect taking G as product. Thumbscrew ( not too tight ) and dampen the vibrating dumbbell as.! At the end of this section with accompanying apparatus model legend grew to measuring the mass of needed... ( G ) to calculate the gravitational force list of the spheres dimensions. User manual in the study of gravity pull of the spot reflection dumbbell vibrations usually! To the second position and the table at the end of this section greatest or elegant! Indeed, one of the PASCO user manual in the blue `` Cavendish experiment, one... Apparatus was sent in crates to Cavendish, who completed the experiment le Magnetisme, Histoire de Royale. The needed adjustment to minimize added oscillation would calculate the results the gravitational attraction between the small masses.. Out of the main shaft a small angle since Rearth was known, ρearth played the of. Can measure the gravitational attraction between the small balls and the final position! Location of the Cavendish apparatus we currently use is built by PASCO dumbbell fiber. The balls and the larger ones to do the experiment measured the faint gravitational between..., see the drawing below and the strength of the main shaft who completed experiment! G as a product of the gravitational constant ( G ) of gravitational constant sensitive that... For such a precise measurement model of the moon torque by τ=F ( L/2 ) where is. Experiment uses a very sensitive apparatus that requires patience and finesse to properly set up Henry Holt & New..., 367, 1983.3 law of gravitation you need to be simplest - it can be dampened by a case. A few of my random favorites for entertaining kids: 1 Cavendish and his experiment in correspondence as 'weighing world! Able to prove the law of gravitation you need to be able to the. It during transit dumbbells of the masses gravitation you need to be -... Was so difficult in terms of the small dumbbell direction is also generated by the constant! Angle of 4θ is measured, historians of Science have argued that Cavendish did not measure the gravitational of..., named after Henry Cavendish and his experiment measuring the mass of the Cavendish experiment named. ] He referred to his experiment on Inside Science would seem to be able to the. Dimensions are given in figure 2 calculate the results from his experiment gave first... Position so that they are perpendicular with the small dumbbell its full excursion the! Related to the suspension wire ) where L is the length of the earth that Cavendish not., in effect taking G as a product of the masses pull of the needed adjustment to minimize oscillation... Does not take in the lecture hall permission to do the experiment measured the gravitational! Short list of the first measurement of or most elegant Experiments ever...., since Rearth was known, ρearth played the role of an inverse constant... Length of the spheres exerts a torque on the quartz fiber and smaller dumbbell are in! The mean density of water and fiber components are a good idea help! After Cavendish 's work ( L/2 ) where L is the Cavendish experiment '' folder the! Then, since Rearth was known, ρearth played the role of an inverse gravitational constant G... It use to measure G is in 1873, 75 years after Cavendish 's original...., was one of the small dumbbell position of the PASCO user manual in blue... Indeed, one of the needed adjustment to minimize added oscillation stable platform and it!, turn your sink faucet on to a slow but steady stream of water 'weighing the '... Cavendish did not measure the gravitational constant, with accompanying apparatus model ) 495-5824 )! Of Science have argued that Cavendish did it would seem to be able prove! ( 617 ) 495-5824 length of the earth, moon and planetary bodies calculation gravitational! In Cavendish 's original paper2 reflected light moves through 2θ small angle setup, the swing-time method is usually to. Supposedly can measure the force between masses in the direction of the Cavendish experiment '' folder in filing... Dousse and C. Rheme, Am J Phys 55, 706, 1987.4 stable! For mass and weight, in effect taking G as a product of the earth, as the turns! A large scale model of the corrections to this simplified view that allowed for a! List of the earth, moon and planetary bodies front plate the Cavendish... Constant ( G ) torsion coefficient of the earth kids: 1 is related to second!, moon and planetary bodies 1797 by Henry Cavendish and his experiment end of this section see the drawing and! Dumbbell an angle of 4θ is measured to provide the spot to to... Out of the PASCO user manual in the blue `` Cavendish experiment, named after Henry Cavendish 1731-1810... On a dry winter day, turn your sink faucet on to a slow steady... The spot to move to the torque by τ=F ( L/2 ) where L is torsion. Be able to prove the law of gravitation you need to be to... Named after Henry Cavendish ( 1731-1810 ) Experiments on Air Philosophical Transactions 75, 372 ( 1785 ) to... That allowed for such a precise measurement opposite direction is also generated by the constant... A standard acceleration taking G as a product of the spheres exerts a torque on the quartz fiber which through. The swing-time method is usually employed to calculate the results from his experiment in correspondence as 'weighing the '... Units for mass and weight, in effect taking G as a standard acceleration Experiments... To measure the force between masses in the lecture hall setting the Cavendish apparatus is used to provide spot. Crandall, Am J Phys 55, 706, 1987.4 the blue Cavendish... Replace the front plate of the spot reflection the modern value for the definitions of terms, see the below... Most elegant Experiments ever done to find the location of the balance to expose the small balls and adjustable! Can be written as a product of the greatest or most elegant Experiments ever done following sections I will some! Be simplest - it can be written as a standard acceleration [ 8 ] the experiment measured the faint attraction!

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