henry cavendish experiment explained

Now for a few details that are particular to the experimental set-up. Table 1 gives an account of all masses and distances that entered the calculations and (non-negligible) corrections.

All of these values were found in Cavendish's paper. He describes how he determined the effective masses in great detail, and I will not repeat those calculations - it suffices to say that many integrals were done. It is interesting that the effective mass of the supporting rod differs depending on whether we are considering its inertial mass or its gravitational mass. I haven't thought about that very much, but I should.

Method of Analysis

The ivory slips and verniers, which allowed for a measurement of the vernier's displacement to within 1/100" (1/20" per division on the slip divided by 5 additional divisions on the vernier), were placed so that an angular displacement of the system produced a division displacement of the same sign on both ends of the rod. The pulley system suspending the large balls could be rotated, so that bringing the large balls close to the small ones from one direction would produce a positive division displacement (+), whereas bringing them close from the opposite direction would produce a negative displacement(-). See Fig. 3.

To determine the angular displacement of the torsional system, Cavendish found that the most effective method was to start with the large balls in either extreme position, (+) or (-), allow the vibrations to decay until the system was more-or-less at rest, and then move the large balls to the opposite extreme position. In this manner the torsional system would begin at its equilibrium angular displacement ± θ eq with a potential energy proportional to θ eq 2 ; upon arrival of the large balls at the opposite extreme position, the system would begin to oscillate, having been given an extra initial amount of stored potential energy. The final equilibrium position, called the "point of rest", was determined by first taking the average of the first and third extremities of the vibration, and then taking the average of that value and the second extremity. The time of vibration was determined by choosing a fixed point and measuring the time between successive returns to that point, divided by the number of vibrations during that interval. (It seems to me that what was actually being measured was a half-period.)

Each trial thus provides a value for the time of vibration (in seconds) N of the suspension wire (which corresponds to the period of oscillation) and the number of divisions B by which the ivory verniers at the supporting rod's ends has been displaced (which corresponds to the angular displacement of the torsional system). Cavendish then used each pair of results not to calculate the gravitational constant G (as described in part I of this report) but rather to find the density of the earth. How did he go about doing this?

where F θ = k θ is the force required for an angular displacement of θ. Cavendish found the period of oscillation by comparing this pendulum with a pendulum whose period was known to be 1 second, whose length was 39.14 in; then the period N of our torsional system is simply

where we've just multiplied the right side by 1 = (( L /2)/39.14)/ N 2 . We want θ in terms of the division displacement B , remembering that each division corresponds to 1/20". But we can approximate &theta = sin -1 ((B/20)/(L/2)) ≈ (B/20)/(L/2) at small angles. Plugging in for L (in inches so all units cancel out), we finally get

The final step gets us the density of the earth ρ E which is given in units of water density. The large balls each have mass equal to that of 10.66 spheres of water with diameter 1 foot each, which one can check easily. Cavendish knew the mean diameter of the Earth to be 41800000 feet as the method for calculating this value via trigonometry had been known since Eratosthenes. Then we take the ratio of the gravitational forces on each small ball due to (1) each large ball, which is 8.85 inches away, vs. (2) the Earth at its surface, will be

(the last factor comes from the fact that the large balls are actually 8.85 inches away from the small balls (center-to-center), rather than 6 inches as they would be if they were spheres of water with diameter 1 foot). We must include one extra small factor which accounts for the fact that the large balls are not directly perpendicular, center-to-center, to the supporting rod, which is 0.9779. We set F θ equal to F W and use the fact that F Earth = mg to find, finally, that

I have left out just one more correction that was used in reaching this final result, the gravitational attraction between the opposite large/small pairs, which opposes the dominant force and reduces the actual attraction by a factor of .9983. The calculation of this factor is described in detail by Cavendish.

Cavendish's Final Results

Table 2 and Fig. 4 present the results of this year-long endeavor. The first is a tabulation of results from selected experiments. The second is a graph of these results along with the calculated average alongside today's accepted value for the density of the Earth.

Today's standard value for the density of the earth (5.5153 g/cm 3 ) is well within one standard deviation of Cavendish's average of 5.48 g/cm 3 .

© Victoria Chang. The author grants permission to copy, distribute and display this work in unaltered form, with attributation to the author, for noncommercial purposes only. All other rights, including commercial rights, are reserved to the author.

June 1798: Cavendish weighs the world

In June 1798 Henry Cavendish reported his famous measurement of Earth’s density. A great chemist and physicist, Henry Cavendish (1731-1810) was obsessive, extremely shy, and eccentric. He was known for wearing clothes that were 50 years out of style. He avoided company, especially fearing women. He took walks at night to avoid beings seen by neighbors, and even had an extra staircase installed in his house to avoid meeting his servants on the stairs. Elements of this odd personality undoubtedly made him a great scientist, capable of dedicating himself to making extremely precise measurements where others would lose patience. He liked to build and rebuild scientific instruments, always trying to improve them. He was extremely methodical, systematically ruling out various sources of error, never satisfied that the work was complete. Like many scientists at the time, Henry Cavendish was an aristocrat, and had inherited enough money to finance his chemistry and physics experiments. He turned much of his house into a laboratory, dedicating only a small portion of the house to living space. Among his many experiments, he is most famous for what is now called the Cavendish experiment, which he used to determine the density of Earth. Newton had published his law of gravitation in 1687, but he hadn’t made any attempt to determine the constant G or the mass of Earth. By the 1700s, astronomers wanted to know the density of Earth, as it would make it possible to determine density of the other planets. In addition, as the New World was being explored and territory being claimed, surveyors needed to know the density of Earth. In 1763 Mason and Dixon set out to settle a boundary dispute between Maryland and Pennsylvania. Cavendish wondered how precise their measurements could be. He realized that the Allegheny Mountains would exert a slight pull on their surveying equipment, possibly affecting their measurement, but he didn’t know how large the effect would be. This led him and others to wonder about the averaged density of Earth itself. In 1772 the Royal Society set up a “Committee of Attraction” to determine the density of Earth. Some people had proposed measuring this by finding a very uniformly shaped mountain and measuring how much it deflected a plumb bob. Since gravity is so weak, this would be a tiny effect, but the committee, including Cavendish, nonetheless tried it, using a large mountain in Scotland. They came up with a value for the density of Earth of about 4.5 times the density of water. But they had made assumptions that Cavendish thought unfounded. He considered the problem for years, until in 1797, at age 67, he began his own experiments. He started with a torsion balance apparatus given to him by his friend, the geologist Reverend John Michell, who had been interested in doing the experiment himself but wasn’t able to carry it out before he died. Realizing that Michell’s equipment was inadequate to measure the tiny gravitational force between two small metal spheres, Cavendish set about tinkering until he had a more precise setup. He built a large dumbbell, with two-inch lead spheres stuck to the ends of a six-foot long wooden rod. The rod was suspended from a wire held at the center, and was free to rotate. A second dumbbell with two twelve-inch lead spheres weighing 350 pounds each was then brought near the first so that the large spheres would attract the smaller ones, exerting a slight torque on the suspended rod. Cavendish would then painstakingly watch for hours to observe the rod’s oscillations. This would provide a measure of the gravitational force of the larger spheres on the smaller ones. And since the density of the spheres was known and the gravitational attraction between Earth and the spheres could be measured by weighing the spheres, the ratio the two forces could be used to determine Earth’s density. Since the gravitational force between the spheres is so weak, the tiniest air current could ruin the delicate experiment. Cavendish placed the apparatus in a closed room to keep out extraneous air currents. He used a telescope to observe the experiments through a window, and set up a pulley system that made it possible to move the weights from outside. The room was kept dark to avoid temperature differences in different parts of the room affecting the experiment. Cavendish relentlessly tracked down potential sources of error. He rotated the spheres in case they had picked up some magnetization. He observed the attraction of the rods without the spheres on the ends. He tried different types of wire to support the apparatus. After agonizing over every possible complicating factor, Cavendish finally reported his results in June 1798 in a 57-page paper in the Transactions of the Royal Society entitled “Experiments to Determine the Density of the Earth.” He reported that the density of Earth was 5.48 times the density of water. (The currently accepted value is 5.52). Others later repeated the experiment, using similar apparatus, and for almost a century no one achieved any improvement over Cavendish’s original measurement. 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. Using updated measuring apparatus but the same basic setup, physics students and scientists today often perform Cavendish’s experiment, which is still recognized as one of the most elegant physics experiments of all time.

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February 9, 2015

How a Wire Was Used to Measure a Tiny Force of Gravity

The crowning achievement of the 18th-century researcher was the design of the first experiment to measure the force of gravity between masses in a lab

By Sara Rennekamp & Inside Science News Service

This story was originally published by Inside Science News Service .

Henry Cavendish was an odd man. He never addressed strangers directly and was petrified of women. He had a staircase built into the back of his house to avoid any encounter with the ladies he employed. When it came time for his final oral exams to complete his natural philosophy degree at Cambridge University—that's what they called a science degree before the advent of modern science and specialized degrees—he dropped out of school all together rather than talk in public.

But, beneath these eccentricities, Henry Cavendish was among the most brilliant minds of the 18th century. He was an accomplished chemist and physicist and made major contributions to electrical research.

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But his crowning achievement, and for what he is perhaps best known, was his design of the first experiment to measure the tiny force of gravity between masses in a laboratory.

Gravity is the weakest of the  four fundamental forces in the universe . In 1687, Sir Isaac Newton came up with his universal law of gravitation, which posits that all objects that have mass pull each other by an amount that depends on their mass and distance from one another. This pull is pretty evident when we consider the moon’s tendency to stay in orbit around Earth or Earth’s convenient attraction to the sun. But Newton is also saying that smaller objects, like a chair or a pencil, have a gravitational pull. I have a gravitational pull. You have a gravitational pull. Your computer screen has a gravitational pull. Your significant other has a gravitational pull (maybe that’s why you’re so attracted to him or her).

Cavendish demonstrated this using a torsion balance, a horizontally suspended wooden rod with a small lead sphere at each end. Two large lead spheres were fixed in place, 9 inches from each of the smaller spheres. When the torsion balance was released and allowed to move freely, the lead balls would be attracted by the gravitational force.

Check out a group of AP Physics students at Bishop O’Connell High School, in Arlington County, Virginia, recreating a simplified version of the experiment more than 200 years later using slightly different materials:

After more than a year of observation, Cavendish confirmed that the suspended lead balls would always tend to accelerate toward the large lead masses. He reasoned that this acceleration was caused by the force of gravity on a small scale.

Of course, this marvelous demonstration of gravitational force was only a preamble to Cavendish’s ultimate goal to measure the density of Earth, which he succeeded in doing by using the measurements taken from his experiment and applying them to Newton’s law of gravitation. In fact, the figure he came up with for Earth’s density using his wooden rods and lead spheres is within 1 percent of the figure agreed upon today—a figure obtained using much more sophisticated equipment than what Cavendish had on hand in his day.

Cavendish published his findings in 1798 in the  Philosophical Transaction of the Royal Society  journal.

So, if I have a gravitational force and you have a gravitational force, then why don’t we all have our own little solar system surrounding us at all times? Because, we live on a gravity trump card. Any gravitational force that we exude is tiny compared to the massive force of the Earth, which has a significantly larger mass than any of the objects that live upon it.

Cavendish’s experiment is a splendid demonstration of the force of gravity on any object with mass from the perspective of Newtonian physics. Einstein’s  general theory of relativity , the modern theory of gravity, usually comes into play for much larger masses (think black holes) and size scales (think two stars orbiting each other). But for most situations that you and I encounter every day, Newton’s and Cavendish’s observations are more than enough fodder for wonder. 

The Cavendish Experiment - weighing the earth

Prerequisite.

• Newton's Universal gravitation

Testing universal gravitation

In 1797, British scientist Henry Cavendish set up a precise experiment to measure gravity. Conceptually, the experiment looked like the figure at the right.

The two large gray balls were lead spheres about a foot in diameter. Lead is very dense; these balls weighed 348 pounds each and were fixed in place.

The smaller red balls were also lead, but just 2 inches across. They weighed 1.61 pounds each. The balls were balanced on a wooden rod hanging from a wire. If you were to rotate the rod a bit, it would twist the wire, and the wire would exert a force to twist the balls back. Almost anything hanging from a string will behave this way. For example, plug your phone into its charger and hold the charging cable a foot or so above the phone, with the phone dangling underneath. Twist your phone a bit and let go. The phone will twist right back to where it was. The experiment was like that, but with heavy lead balls. The more force you put on those small red balls, the more the wire would twist.

Cavendish found that the wire would twist even when he didn't put any force on it at all via pushing or pulling. The only unbalanced force on the red balls was the gravity from the big gray balls. Cavendish's experiment was sensitive enough that could measure the strength of the force by seeing just how much the rod and red balls twisted. Since he had measured all the masses and the distances, Cavendish was able to infer the value of $G$. It's quite small!

$G = \frac{2}{3} \times 10^{-10}$ N-m 2 /kg 2 .  (to better than 1%)

When Cavendish moved the gray balls further away, the force got smaller and the rod twisted less. When he moved the gray balls closer, the opposite occurred. So he learned that the closer something is, the more the gravitational force. The gravitational forces in this experiment were very small - tenths of a microNewton, so Cavendish had to control lots of sources of error to get good results. But eventually, he confirmed an equation for gravity that goes back to Isaac Newton. This says that the force between an object of mass $m_1$ and an object of mass $m_2$ is

$$\overrightarrow{F}^{grav}_{1 \rightarrow 2} = \frac{Gm_1m_2}{r_{12}^2} \hat{r}_{2 \rightarrow 1}$$

This equation says that the gravitational force of any object 1 on any other object 2 is some constant $G$ times the two masses of the objects divided by the square of the distance between them. This is called an "inverse square law", and it means that if Cavendish were to move his big gray spheres three times as far out as before, the gravitational force on the small spheres would be only one ninth as much.

The $\hat{r}_{2 \rightarrow 1}$ part is a unit vector pointing from 2 to 1. That is, an arrow that points in the direction of 1 from the point of view of 2, and that has unit magnitude and no units. This says that the force that a exerts on 2  points back towards 1 . Gravity attracts. This image from Wikipedia illustrates the gravitational force between two spheres, which could be spheres from the Cavendish experiment, or a planet and a star, or any other two objects.

$$F_1 = F_2 = \frac{Gm_1m_2}{r^2}$$

Newton's third law is built in to the universal gravitational law. If you switch the roles of a  and b , the magnitude of the force comes out the same, but you get  $\hat{r}_{1 \rightarrow 2}$ instead of $\hat{r}_{2 \rightarrow 1}$. These vectors point opposite directions, just like Newton's third law says.

In everyday life, the gravitational force between most objects is too small to notice. It becomes important when at least one of the objects is really big, like an entire planet. Newton used universal gravity to explain the orbits of planets in the solar system, and since then it has also explained things like the motion and formation of galaxies or the collapse of dust clouds into stars.

Measuring the mass of the earth

Cavendish actually thought of his experiment as a way of measuring the mass of the Earth for the first time.

Why? Try setting object 1   to be Earth and object 2 to be an apple. Because he knew how much force the Earth would exert on an apple and he knew the size of the Earth (which is $r$ in this equation — for spheres you have to measure to the center of the sphere, not the edge), Cavendish had most of the variables in the gravitational law pinned down. Once he measured $G$ with his experiment, the only variable left in the equation was $m_1$, the mass of the earth. So he could solve for it and find the mass of the Earth for the first time.

Let's see how we can do it. We know that the weight of an object of mass $m$ on the surface of the earth is $mg$ where $g \tilde 10$ N/kg. If we equate this to Newton's universal gravitation we get

$$mg = \frac{GmM_E}{R_E^2}$$

where $M_E$ is the mass of the earth and $R_E$ is the radius of the earth. In this equation we easily know $m$, $g$, and $R_E$. What's missing is $G$ and $M_E$. So if we measure $G$, we can solve for the mass of the earth:

$$M_E = \frac{gR_E^2}{G}$$

In meters, kg, and seconds, g is about 10 N/kg, the radius of the earth is about 10 7 m ($2/\pi \times 10^7$m), and G is about 10 -10 N-m 2 /kg 2 , we get about 10 25 kg! Rather difficult to weigh by putting on a scale!

Note that although both Newton and Cavendish understood universal gravitation mathematically, neither of them wrote their equations in the same form we do today. In fact, Cavendish didn't think about the constant $G$ at all. His analysis was equivalent to what we just said, but the actual details were different in terms of algebra. There are lots of ways to use math to express the same fundamental knowledge!

Mark Eichenlaub 9/11/17 and Joe Redish 2/4/19

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The Cavendish Experiment

Project Archivist Erinna Cave discovers documentation relating to Henry Cavendish's most famous experiment.

Chatsworth's Archive and Library team is cataloguing the papers of Henry Cavendish (1731-1810), an experimental scientist and philosopher credited with discovering hydrogen and calculating the earth's mass.

In this second blog in the series , project archivist Erinna Cave shares her most recent discoveries.

I have now catalogued much of Henry’s scientific papers. One glaring discovery is the absence of any notes or observations written by Henry about his most famous experiment, now named after him as “the Cavendish experiment” and involved 'weighing the world'. 

However, in the correspondence in the archive, we can see the genesis of the idea behind this experiment. In 1783, John Michell (1724-1793), rector of Thornhill, Yorkshire, F.R.S, started a correspondence with Henry Cavendish. They had previously met at the Royal Society dinners. Michell had a keen interest in geology and astronomy, being one of the first to propose the existence of black holes. The two scientists exchanged ideas and comments on their respective work.

In their letters, the topic of the “experiment” arises: Michell’s idea to use a torsion balance to calculate the mean density of the earth. Henry asks about Michell’s plans for experiments, commenting "if your health does not allow you to go on with that [Michell’s work on a large telescope] I hope it may at least permit the easier and less laborious employment of weighing the world".

Despite Henry’s hope, Michell’s health did prevent him from conducting the experiment. He only managed to build the torsion balance apparatus before he died in 1793. The instrument made its way to Henry after Michell’s death and so Henry set about completing their discussed experiment in 1797-1798. 

Image of the torsion balance devised by Michell and Henry Cavendish (1798)

That is the extent of the records in the archive about this great experiment: a few letters exchanged with Michell. I wonder where Henry’s experimental notes could be: with another family member? In another box in the archive waiting for me to find them? 

Michell’s friendship with Henry led to another significant event in Henry’s life. Michell encouraged him and Sir Charles Blagden, his secretary, to visit him in Yorkshire. In 1786, Henry set out from London, touring the Lake District, Yorkshire, Whitby Sands, Sheffield, Rotherham and Chesterfield.

In the journals that we have of this trip, Henry avoids the usual comments on the beauty of the lakes and the mountains. While Blagden writes about the “magnificent & beautiful” scenes around Windermere, Henry limits himself to writing about the strata: “the prevailing stone was slate but with limestone in places”, “Between Windermeer & Kendal rock limestone begins & starts all the way to Settle”.

For him, the point of the journey was scientific observation and research. Along the way, he takes readings with his travelling barometer and other instruments, some of which can be seen in the third image below. 

Perhaps some of you are currently contemplating a similar trip over the holidays to enjoy the beautiful sights of the Lake District: take a tip from Henry’s travels, and try to notice the details of the landscape you travel through. And remember to take your scientific instruments!

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Henry Cavendish

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Henry Cavendish (born October 10, 1731, Nice , France—died February 24, 1810, London , England) was a natural philosopher, the greatest experimental and theoretical English chemist and physicist of his age. Cavendish was distinguished for great accuracy and precision in research into the composition of atmospheric air, the properties of different gases, the synthesis of water, the law governing electrical attraction and repulsion, a mechanical theory of heat, and calculations of the density (and hence the weight) of Earth . His experiment to weigh Earth has come to be known as the Cavendish experiment .

Cavendish, often referred to as “the Honourable Henry Cavendish,” had no title, although his father was the third son of the duke of Devonshire, and his mother (née Ann Grey) was the fourth daughter of the duke of Kent. His mother died in 1733, three months after the birth of her second son, Frederick, and shortly before Henry’s second birthday, leaving Lord Charles Cavendish to bring up his two sons. Henry went to the Hackney Academy, a private school near London, and in 1748 entered Peterhouse College, Cambridge, where he remained for three years before he left without taking a degree (a common practice). He then lived with his father in London, where he soon had his own laboratory.

Lord Charles Cavendish lived a life of service, first in politics and then increasingly in science , especially in the Royal Society of London . In 1758 he took Henry to meetings of the Royal Society and also to dinners of the Royal Society Club. In 1760 Henry Cavendish was elected to both these groups, and he was assiduous in his attendance thereafter. He took virtually no part in politics, but, like his father, he lived a life of service to science, both through his researches and through his participation in scientific organizations. He was active in the Council of the Royal Society of London (to which he was elected in 1765); his interest and expertise in the use of scientific instruments led him to head a committee to review the Royal Society’s meteorological instruments and to help assess the instruments of the Royal Greenwich Observatory . Other committees on which he served included the committee of papers, which chose the papers for publication in the Philosophical Transactions , and the committees for the transit of Venus (1769), for the gravitational attraction of mountains (1774), and for the scientific instructions for Constantine Phipps’s expedition (1773) in search of the North Pole and the Northwest Passage . In 1773 Henry joined his father as an elected trustee of the British Museum , to which he devoted a good deal of time and effort. Soon after the Royal Institution of Great Britain was established, Cavendish became a manager (1800) and took an active interest, especially in the laboratory, where he observed and helped in Humphry Davy ’s chemical experiments.

Cavendish was a shy man who was uncomfortable in society and avoided it when he could. He conversed little, always dressed in an old-fashioned suit, and developed no known deep personal attachments outside his family.

About the time of his father’s death, Cavendish began to work closely with Charles Blagden, an association that helped Blagden enter fully into London’s scientific society. In return, Blagden helped to keep the world at a distance from Cavendish. Cavendish published no books and few papers, but he achieved much. Several areas of research, including mechanics , optics , and magnetism , feature extensively in his manuscripts, but they scarcely feature in his published work.

His first publication (1766) was a combination of three short chemistry papers on “factitious airs,” or gases produced in the laboratory. He produced “inflammable air” ( hydrogen ) by dissolving metals in acids and “fixed air” ( carbon dioxide ) by dissolving alkalis in acids, and he collected these and other gases in bottles inverted over water or mercury . He then measured their solubility in water and their specific gravity and noted their combustibility. Cavendish was awarded the Royal Society’s Copley Medal for this paper. Gas chemistry was of increasing importance in the latter half of the 18th century and became crucial for Frenchman Antoine-Laurent Lavoisier ’s reform of chemistry, generally known as the chemical revolution.

In 1783 Cavendish published a paper on eudiometry (the measurement of the goodness of gases for breathing). He described a new eudiometer of his own invention, with which he achieved the best results to date, using what in other hands had been the inexact method of measuring gases by weighing them. He next published a paper on the production of water by burning inflammable air (that is, hydrogen) in dephlogisticated air (now known to be oxygen ), the latter a constituent of atmospheric air. ( See phlogiston .) Cavendish concluded that dephlogisticated air was dephlogisticated water and that hydrogen was either pure phlogiston or phlogisticated water. He reported these findings to Joseph Priestley , an English clergyman and scientist, no later than March 1783, but did not publish them until the following year. The Scottish inventor James Watt published a paper on the composition of water in 1783; Cavendish had performed the experiments first but published second. Controversy about priority ensued. In 1785 Cavendish carried out an investigation of the composition of common (i.e., atmospheric) air , obtaining, as usual, impressively accurate results. He observed that, when he had determined the amounts of phlogisticated air ( nitrogen ) and dephlogisticated air (oxygen), there remained a volume of gas amounting to 1 / 120 of the volume of the nitrogen.

In the 1890s, two British physicists, William Ramsay and Lord Rayleigh , realized that their newly discovered inert gas , argon , was responsible for Cavendish’s problematic residue; he had not made an error. What he had done was perform rigorous quantitative experiments, using standardized instruments and methods, aimed at reproducible results; taken the mean of the result of several experiments; and identified and allowed for sources of error. The balance that he used, made by a craftsman named Harrison, was the first of the splendid precision balances of the 18th century, and as good as Lavoisier’s (which has been estimated to measure one part in 400,000). Cavendish worked with his instrument makers, generally improving existing instruments rather than inventing wholly new ones.

Cavendish, as indicated above, used the language of the old phlogiston theory in chemistry. In 1787 he became one of the earliest outside France to convert to the new antiphlogistic theory of Lavoisier, though he remained skeptical about the nomenclature of the new theory. He also objected to Lavoisier’s identification of heat as having a material or elementary basis. Working within the framework of Newtonian mechanism , Cavendish had tackled the problem of the nature of heat in the 1760s, explaining heat as the result of the motion of matter. In 1783 he published a paper on the temperature at which mercury freezes and in that paper made use of the idea of latent heat , although he did not use the term because he believed that it implied acceptance of a material theory of heat. He made his objections explicit in his 1784 paper on air. He went on to develop a general theory of heat, and the manuscript of that theory has been persuasively dated to the late 1780s. His theory was at once mathematical and mechanical; it contained the principle of the conservation of heat (later understood as an instance of conservation of energy ) and even contained the concept (although not the label) of the mechanical equivalent of heat.

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Cavendish experiment explained

The Cavendish experiment , performed in 1797–1798 by English scientist Henry Cavendish , was the first experiment to measure the force of gravity between mass es in the laboratory [1] and the first to yield accurate values for the gravitational constant . [2] [3] Because of the unit conventions then in use, the gravitational constant does not appear explicitly in Cavendish's work. Instead, the result was originally expressed as the relative density of Earth , [4] or equivalently the mass of Earth . His experiment gave the first accurate values for these geophysical constants.

The experiment was devised sometime before 1783 by geologist John Michell , [5] [6] who constructed a torsion balance apparatus for it. However, Michell died in 1793 without completing the work. After his death the apparatus passed to Francis John Hyde Wollaston and then to Cavendish, who rebuilt the apparatus but kept close to Michell's original plan. Cavendish then carried out a series of measurements with the equipment and reported his results in the Philosophical Transactions of the Royal Society in 1798. [7]

The experiment

The apparatus consisted of a torsion balance made of a 6feet wooden rod horizontally suspended from a wire, with two 2adj=mid0adj=mid, 1.61lb lead spheres, one attached to each end. Two massive 12inches, 348lb lead balls, suspended separately, could be positioned away from or to either side of the smaller balls, away. [8] The experiment measured the faint gravitational attraction between the small and large balls, which deflected the torsion balance rod by about 0.16" (or only 0.03" with a stiffer suspending wire).

The two large balls could be positioned either away from or to either side of the torsion balance rod. Their mutual attraction to the small balls caused the arm to rotate, twisting the suspension wire. The arm rotated until it reached an angle where the twisting force of the wire balanced the combined gravitational force of attraction between the large and small lead spheres. By measuring the angle of the rod and knowing the twisting force ( torque ) of the wire for a given angle, Cavendish was able to determine the force between the pairs of masses. Since the gravitational force of the Earth on the small ball could be measured directly by weighing it, the ratio of the two forces allowed the relative density of the Earth to be calculated, using Newton's law of gravitation .

Cavendish found that the Earth's density was times that of water (due to a simple arithmetic error, found in 1821 by Francis Baily , the erroneous value appears in his paper). [9] [10] The current accepted value is 5.514 g/cm 3 .

To find the wire's torsion coefficient, the torque exerted by the wire for a given angle of twist, Cavendish timed the natural oscillation period of the balance rod as it rotated slowly clockwise and counterclockwise against the twisting of the wire. For the first 3 experiments the period was about 15 minutes and for the next 14 experiments the period was half of that, about 7.5 minutes. The period changed because after the third experiment Cavendish put in a stiffer wire. The torsion coefficient could be calculated from this and the mass and dimensions of the balance. Actually, the rod was never at rest; Cavendish had to measure the deflection angle of the rod while it was oscillating. [11]

Cavendish's equipment was remarkably sensitive for its time. [9] The force involved in twisting the torsion balance was very small,, [12] (the weight of only 0.0177 milligrams) or about of the weight of the small balls. [13] To prevent air currents and temperature changes from interfering with the measurements, Cavendish placed the entire apparatus in a mahogany box about 1.98 meters wide, 1.27 meters tall, and 14 cm thick, http://cavendish-deneyi.com/pdf/Cavendish-c%CC%A7izim-03.pdf all in a closed shed on his estate. Through two holes in the walls of the shed, Cavendish used telescopes to observe the movement of the torsion balance's horizontal rod. The key observable was of course the deflection of the torsion balance rod, which Cavendish measured to be about 0.16" (or only 0.03" for the stiffer wire used mostly). [14] Cavendish was able to measure this small deflection to an accuracy of better than using vernier scale s on the ends of the rod. [15] The accuracy of Cavendish's result was not exceeded until C. V. Boys ' experiment in 1895. In time, Michell's torsion balance became the dominant technique for measuring the gravitational constant ( G ) and most contemporary measurements still use variations of it. [16]

Cavendish's result provided additional evidence for a planetary core made of metal, an idea first proposed by Charles Hutton based on his analysis of the 1774 Schiehallion experiment . [17] Cavendish's result of 5.4 g·cm -3 , 23% bigger than Hutton's, 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. [18]

Reformulation of Cavendish's result to G

The formulation of Newtonian gravity in terms of a gravitational constant did not become standard until long after Cavendish's time. Indeed, one of the first references to G is in 1873, 75 years after Cavendish's work. [19]

Cavendish expressed his result in terms of the density of the Earth. He referred to his experiment in correspondence as 'weighing the world'. Later authors reformulated his results in modern terms. [20] [21] [22]

2 earth 3 4 G =, [23] which differs by only 1% from the 2014 CODATA value of . [24] Today, physicists often use units where the gravitational constant takes a different form. 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.In Cavendish's time, physicists used the same units for mass and weight, in effect taking g as a standard acceleration. Then, since R was known, ρ played the role of an inverse 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. Derivation of G and the Earth's mass The following is not the method Cavendish used, but describes how modern physicists would calculate the results from his experiment. [25] [26] [27] From Hooke's law , the torque on the torsion wire is proportional to the deflection angle \kappa\theta \kappa\theta  = LF For F , Newton 's law of universal gravitation is used to express the attractive force between a large and small ball: Substituting F into the first equation above gives \kappa\theta  = L          ( 1 ) To find the torsion coefficient ( T =2 \pi\sqrt{ Assuming the mass of the torsion beam itself is negligible, the moment of inertia of the balance is just due to the small balls. Treating them as point masses, each at L/2 from the axis, gives: I = m\left ( 2 \right ) 2 + m\left ( \right ) 2 = 2 m\left ( \right ) 2 = 2 Solving this for 2 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: 2 2 4 3 3 4 Definitions of terms Symbol Unit Definition s Deflection of torsion balance beam from its rest position Gravitational force between masses and m kg s Gravitational constant kg Mass of small lead ball kg Mass of large lead ball m Distance between centers of large and small balls when balance is deflected m Length of torsion balance beam between centers of small balls N m rad Torsion coefficient of suspending wire kg m Moment of inertia of torsion balance beam s Period of oscillation of torsion balance m s Acceleration of gravity at the surface of the Earth kg Mass of the Earth m Radius of the Earth kg m Density of the Earth Boys, C. Vernon . On the Newtonian constant of gravitation . Nature . 1894 . 50 . 1292 . 330–334 . 10.1038/050330a0 . 1894Natur..50..330. . 2013-12-30 . free . Cavendish . Henry . Experiments to Determine the Density of the Earth . 1798 . Philosophical Transactions of the Royal Society. 88 . 469–526 . 10.1098/rstl.1798.0022. free . Clotfelter, B. E. . The Cavendish experiment as Cavendish knew it . American Journal of Physics . 1987 . 55 . 3 . 210 - 213 . 10.1119/1.15214. 1987AmJPh..55..210C . Establishes that Cavendish didn't determine G. Falconer, Isobel . Henry Cavendish: the man and the measurement . Measurement Science and Technology . 1999 . 10 . 6 . 470 - 477 . 10.1088/0957-0233/10/6/310 . 1999MeScT..10..470F . 250862938 . Web site: Hodges . Laurent . 1999 . The Michell-Cavendish Experiment, faculty website, Iowa State Univ. . 2013-12-30 . https://web.archive.org/web/20170906134148/http://www.public.iastate.edu/~lhodges/Michell.htm . 2017-09-06 . dead . Discusses Michell's contributions, and whether Cavendish determined G. Book: McCormmach . Russell. Russell McCormmach . Jungnickel . Christa. Christa Jungnickel . Cavendish . Philadelphia, Pennsylvania . . 1996 . 978-0-87169-220-7 . 2013-12-30 . Lally, Sean P. . Henry Cavendish and the Density of the Earth . The Physics Teacher . 1999 . 37 . 1 . 34 - 37 . 1999PhTea..37...34L . 10.1119/1.880145. Book: Poynting, John H. . The Mean Density of the Earth: An essay to which the Adams prize was adjudged in 1893 . 1894 . C. Griffin & Co. . London . 2013-12-30 . Review of gravity measurements since 1740. Gravitation . 12 . 384–389. John Henry. Poynting. John Henry Poynting. External links Cavendish’s experiment in the Feynman Lectures on Physics Sideways Gravity in the Basement, The Citizen Scientist , July 1, 2005 . Homebrew Cavendish experiment, showing calculation of results and precautions necessary to eliminate wind and electrostatic errors. "Big 'G'", Physics Central , retrieved Dec. 8, 2013. Experiment at Univ. of Washington to measure the gravitational constant using variation of Cavendish method. Web site: The Controversy over Newton's Gravitational Constant . Eöt-Wash Group, Univ. of Washington . December 8, 2013 . 2016-03-04 . https://web.archive.org/web/20160304031910/http://www.npl.washington.edu/eotwash/bigG. . Discusses current state of measurements of G . Model of Cavendish's torsion balance , retrieved Aug. 28, 2007, at Science Museum, London. Notes and References https://books.google.com/books?id=ZrloHemOmUEC&pg=PA355 Boys 1894 'The aim [of experiments like Cavendish's] may be regarded either as the determination of the mass of the Earth,...conveniently expressed...as its "mean density", or as the determination of the "gravitation constant", G'. Cavendish's experiment is generally described today as a measurement of G .' (Clotfelter 1987 p. 210). Many sources incorrectly state that this was the first measurement of G (or Earth's density); for instance: Book: Feynman, Richard P.. California Institute of Technology. 9780465025626. Pasadena, California. mainly mechanics, radiation and heat . The Feynman lectures on physics. I. 2013. 1963. https://feynmanlectures.caltech.edu/I_07.html. 7. The Theory of Gravitation. 7–6 Cavendish’s experiment. December 9, 2013. There were previous measurements, chiefly by Bouguer (1740) and Maskelyne (1774), but they were very inaccurate ( Poynting 1894 ). Clotfelter 1987, p. 210 https://books.google.com/books?id=EUoLAAAAIAAJ&pg=PA336 Jungnickel & McCormmach 1996 https://books.google.com/books?id=O58mAAAAMAAJ&pg=PA59 Cavendish 1798 Cavendish, H. 'Experiments to determine the Density of the Earth', Philosophical Transactions of the Royal Society of London , (part II) 88 pp. 469–526 (21 June 1798), reprinted in Cavendish 1798 https://books.google.com/books?id=dg0RAAAAIAAJ&pg=PA45 Poynting 1894 Cavendish, Henry . 5 . 580–581. https://books.google.com/books?id=O58mAAAAMAAJ&pg=PA64 Cavendish 1798 https://books.google.com/books?id=ZrloHemOmUEC&pg=PA357 Boys 1894 https://books.google.com/books?id=O58mAAAAMAAJ&pg=PA60 Cavendish 1798 https://books.google.com/books?id=O58mAAAAMAAJ&pg=PA99 Cavendish 1798 https://books.google.com/books?id=O58mAAAAMAAJ&pg=PA63 Cavendish 1798 https://books.google.com/books?id=EUoLAAAAIAAJ&pg=PA341 Jungnickel & McCormmach 1996 Book: Danson, Edwin . Weighing the World . Oxford University Press. 2006. 153–154. 978-0-19-518169-2. see e.g. Hrvoje Tkalčić, The Earth's Inner Core , Cambridge University Press (2017), p. 2 . Cornu . A. . Baille . J. B. . 1873 . Détermination nouvelle de la constante de l'attraction et de la densité moyenne de la Terre . fr . New Determination of the Constant of Attraction and the Average Density of Earth . C. R. Acad. Sci. . Paris . 76 . 954–958 . https://books.google.com/books?id=ZrloHemOmUEC&pg=PA353 Boys 1894 https://books.google.com/books?id=dg0RAAAAIAAJ&pg=PA4 Poynting 1894 https://books.google.com/books?id=O58mAAAAMAAJ&pg=PA1 MacKenzie 1900 Adam . Mann . The curious case of the gravitational constant . September 6, 2016 . Proceedings of the National Academy of Sciences . Jennifer Lauren . Lee . Big G Redux: Solving the Mystery of a Perplexing Result . November 16, 2016 . NIST . Web site: Cavendish Experiment, Harvard Lecture Demonstrations, Harvard Univ . 2013-12-30. . '[the torsion balance was]...modified by Cavendish to measure G .' https://books.google.com/books?id=dg0RAAAAIAAJ&pg=PA41 Poynting 1894 Clotfelter 1987 p. 212 explains Cavendish's original method of calculation. This article is licensed under the GNU Free Documentation License . It uses material from the Wikipedia article " Cavendish experiment ". Except where otherwise indicated, Everything.Explained.Today is © Copyright 2009-2024, A B Cryer, All Rights Reserved. Cookie policy . In order to continue enjoying our site, we ask that you confirm your identity as a human. Thank you very much for your cooperation. Henry Cavendish and the Weight of the Earth Drawing of torsion balance device used by Henry Cavendish in the ‘Cavendish Experiment’ On October 10 , 1731 ,  British natural philosopher Henry Cavendish was born. A scientist as well as an important experimental and theoretical chemist and physicist , Cavendish is noted for his discovery of hydrogen or what he called “ inflammable air “. Most notably, he determined the mass and density of the Earth. Henry Cavendish Henry Cavendish (1731-1810) Cavendish Experiment References and Further Reading: [1] Henry Cavendish at Famous Scientists [2] Henry Cavendish at Chamistry Explained [3] The Cavendish Experiment [4] Modern Chemistry started with Lavoisier , SciHi Blog [5] A Life of Discoveries – the great Michael Faraday , SciHi Blog [6] Henry Cavendish at Wikidata [7]  Feynman Messenger Lecture – Cavendish’s Experiment , Richard Feynman,  Ryougi  @ youtube [8] Modern Chemistry started with Antoine Lavoisier , SciHi Blog [9] Cavendish, Henry (1921).   Scientific Papers . Vol. 1. Cambridge: Cambridge University Press.   – edited by James Clerk Maxwell and revised by Joseph Larmor [10]  Cavendish, Henry (1921).   Scientific Papers . Vol. 2. Cambridge: Cambridge University Press.   – edited by James Clerk Maxwell and revised by Joseph Larmor [11]  Cavendish, Henry (1879).   The Electrical Researches of the Honourable Henry Cavendish . Cambridge: Cambridge University Press.   cavendish henry.   – edited by   James Clerk Maxwell [12]  Cavendish, Henry (1766).  “Three Papers Containing Experiments on Factitious Air, by the Hon. Henry Cavendish” .  Philosophical Transactions of the Royal Society . The University Press.  56 : 141–184. [13]  Wilson, George (1851). “1”.  The life of the Hon. Henry Cavendish . Cavendish Society.  [14] Timeline of Discoverers of Chemical Elements via DBpedia and Wikidata Tabea Tietz Related posts, sir benjamin baker and the forth bridge, melanie klein and the psychoanalysis of children, karl pearson and mathematical statistics, william buckland’s eccentricities and the discovery of megalosaurus, one comment. Pingback: Whewell’s Gazette: Year 3, Vol. #09 | Whewell's Ghost Leave a Reply Cancel reply Your email address will not be published. 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Results and Implications Significance. Do you prefer video lectures over reading a webpage? Follow us on YouTube to stay updated with the latest video content! Want to study more? Visit our Index here ! Share this: Click to share on Twitter (Opens in new window) Click to share on Facebook (Opens in new window) Click to print (Opens in new window) Click to email a link to a friend (Opens in new window) Click to share on WhatsApp (Opens in new window) Click to share on LinkedIn (Opens in new window) Click to share on Reddit (Opens in new window) Click to share on Tumblr (Opens in new window) Click to share on Pinterest (Opens in new window) Click to share on Pocket (Opens in new window) Click to share on Telegram (Opens in new window) Click to share on Mastodon (Opens in new window) Have something to add? Leave a comment! Cancel reply Henry Cavendish - Chemistry Encyclopedia Henry Cavendish ENGLISH PHYSICIST AND CHEMIST 1731–1810 Henry Cavendish, born in Nice, France to an aristocratic English family, was an avid and excellent experimenter. At the age of forty, he inherited an immense fortune that afforded him the luxury of pursuing his scientific interests (he was described by some as the "richest of all the learned and the most learned of all the rich"). He was an extraordinarily odd man, whose extreme shyness rendered him a virtual recluse. Despite this, he is remembered as a great, albeit humble, man who devoted his life to science. Cavendish explored all areas of science, including astronomy, optics, electricity, geology, and pure mathematics. Among his accomplishments are the first calculation of Earth's mass (his results were just 10% off modern measurements) and the introduction of the concept of voltage . His principal interest nevertheless was experimental chemistry. His most famous contribution to science was the discovery and description of the properties of hydrogen and its status as a constituent element in water. Cavendish, like many before him, noticed that a gas was produced when zinc or iron was dropped into an acid. He called this gas "inflammable air" (known today as hydrogen). Using his exacting experimental skills, Cavendish was the first to distinguish this inflammable air from ordinary air and to investigate its specific properties. He presented a paper detailing his findings in 1766. The importance of inflammable air became clear about fifteen years after Cavendish presented his paper. Joseph Priestley (1733–1804) was also interested in gases, and in 1781 told Cavendish of the results of some of his own experiments. When Priestley used an electrostatic machine to spark ordinary air with inflammable air, he noticed that water was formed. Cavendish repeated this experiment, as well as others like it, but using oxygen (or, as he called it, "dephlogisticated air") in place of ordinary air. Cavendish's results were the same as Priestley's, but he did not publish or present his findings. Sometime before 1783, however, Cavendish did advise Priestley of his results. Priestley told Charles Blagden, secretary of the Royal Society in London, and Blagden in turn informed Antoine Lavoisier (1743–1794) in France. Cavendish did eventually publish his findings on the formation of water in 1784. But Lavoisier claimed that he had discovered how water was formed—in fact, it was Lavoisier who coined the name "hydrogen," which means "water former." It was not until the mid-nineteenth century, when Cavendish's notebooks were published, that he was given sole credit for discovering that water is composed of inflammable air and dephlogisticated air, or hydrogen and oxygen. As may be seen in his collaborative work with Priestley in the investigation of the composition of water, Cavendish did not allow his natural shyness to impede his work. The relationship between him and Priestley demonstrates not only Cavendish's devotion to science, but the general cooperative nature of scientific investigation. By sharing the results of their separate experiments, these two great scientists were able to discover the composition of water. For all of his scientific genius, Cavendish was a pronounced eccentric. He rarely left his house except for weekly meetings of the Royal Society, and even there, despite being one of the most famous scientists of his time, he was known to linger outside the meeting room and enter only when he thought no one would notice. He could barely tolerate the company of women; if any of his female servants happened to cross his path, she was likely to be fired. Though enormously wealthy, he was reputed to own but one suit, and an old-fashioned one at that. Cavendish lived a lonely and humble life, committed to the cultivation of science. To him, science was measurement, and he showed himself to be one of the most respected experimentalists of the time. His death was as lonely as his life; when he sensed that the end was near, he instructed his servant to leave the room and not come back until a certain time. When the servant returned, he found that Cavendish had died. SEE ALSO Hydrogen ; Lavoisier, Antoine ; Priestley, Joseph . Lydia S. Scratch Bibliography Berry, Arthur John (1960). Henry Cavendish: His Life and Scientific Work. London: Hutchinson. Jaffe, Bernard (1976). Crucibles: The Story of Chemistry from Ancient Alchemy to Nuclear Fission. New York: Dover. Jungnickel, Christa, and McCormmach, Russel (1999). Cavendish: The Experimental Life. Cranbury, NJ: Bucknell. Internet Resources "Henry Cavendish." BBC History. Available from http://www.bbc.co.uk . User Contributions: Comment about this article, ask questions, or add new information about this topic:. The Cavendish experiment, done in 1797 – 1798 by Henry Cavendish , was the first experiment to measure the force of gravity between masses in the laboratory,[1] and the first to yield accurate values for the gravitational constant and the mass of the Earth.[2][3] However, these were derived by others from Cavendish's result, which was a value for the Earth's density.[4] The experiment was devised sometime before 1783[5] by John Michell,[6] who constructed a torsion balance apparatus for it. However, Michell died in 1793 without completing the work, and after his death the apparatus passed to Francis John Hyde Wollaston and then to Henry Cavendish, who rebuilt the apparatus but kept close to Michell's original plan. Cavendish then carried out a series of measurements with the equipment, and reported his results in the Philosophical Transactions of the Royal Society in 1798.[7] The experiment The apparatus constructed by Cavendish was a torsion balance made of a six-foot wooden rod suspended from a wire, with a 2 inch diameter 1.61 pound lead sphere attached to each end. Two 12 inch 348 pound lead balls were located near the smaller balls, about 9 inches away, and held in place with a separate suspension system.[8] The experiment measured the faint gravitational attraction between the small balls and the larger ones. The two large balls were positioned on alternate sides of the horizontal wooden arm of the balance. Their mutual attraction to the small balls caused the arm to rotate, twisting the wire supporting the arm. The arm stopped rotating when it reached an angle where the twisting force of the wire balanced the combined gravitational force of attraction between the large and small lead spheres. By measuring the angle of the rod, and knowing the twisting force (torque) of the wire for a given angle, Cavendish was able to determine the force between the pairs of masses. Since the gravitational force of the Earth on the small ball could be measured directly by weighing it, the ratio of the two forces allowed the density of the earth to be calculated, using Newton's law of gravitation. Cavendish found that the Earth's density was 5.448 ± 0.033 times that of water (due to a simple arithmetic error, found in 1821 by F. Baily, the erroneous value 5.48 ± 0.038 appears in his paper).[9] To find the wire's torsion coefficient, the torque exerted by the wire for a given angle of twist, Cavendish timed the natural oscillation period of the balance rod as it rotated slowly clockwise and counterclockwise against the twisting of the wire. The period was about 7 minutes. The torsion coefficient could be calculated from this and the mass and dimensions of the balance. Actually, the rod was never at rest; Cavendish had to measure the deflection angle of the rod while it was oscillating.[10] Cavendish's equipment was remarkably sensitive for its time.[11] The force involved in twisting the torsion balance was very small, 1.47 x 10–7 N,[12] about 1/50,000,000 of the weight of the small balls[13] or roughly the weight of a large grain of sand.[14] To prevent air currents and temperature changes from interfering with the measurements, Cavendish placed the entire apparatus in a wooden box about 2 feet thick, 10 feet tall, and 10 feet wide, all in a closed shed on his estate. Through two holes in the walls of the shed, Cavendish used telescopes to observe the movement of the torsion balance's horizontal rod. The motion of the rod was only about 0.16 inch.[15] Cavendish was able to measure this small deflection to an accuracy of better than one hundredth of an inch using vernier scales on the ends of the rod.[16] Cavendish's experiment was repeated by Reich (1838), Baily (1843), Cornu & Baille (1878), and many others. Its accuracy was not exceeded for 97 years, until C. V. Boys (1895) experiment. In time, Michell's torsion balance became the dominant technique for measuring the gravitational constant (G), and most contemporary measurements still use variations of it. This is why Cavendish's experiment became the Cavendish experiment.[17] Did Cavendish determine G? It is not unusual to find books that state erroneously that Cavendish's purpose was determining the gravitational constant (G),[18][19][20][21][22] and this mistake has been pointed out by several authors.[23][24][25][26] In actuality, Cavendish's only goal was to measure the density of the Earth; he called it 'weighing the world'. The method Cavendish used to calculate the Earth's density consists in measuring the force on a small ball caused by a large ball of known mass, and comparing it with the force on the small ball caused by the Earth, so the Earth can be calculated to be N times more massive than the large ball without the need to obtain a numeric value for G.[27] The gravitational constant does not appear in Cavendish's paper, and there is no indication that he regarded it as a goal of his experiment. One of the first references to G is in 1873, 75 years after Cavendish's work.[28] In Cavendish's time, G did not have the importance among scientists that it has today; it was simply a proportionality constant in Newton's law.[29] The purpose of measuring the force of gravity was instead to determine the Earth's density. This was a much-desired quantity in 18th-century astronomy, since once the Earth's density was known, the densities of the Moon, Sun, and the other planets could be found from it.[30] A further complication is that up through the mid-nineteenth century, scientists did not use a specific unit of measurement for force.[31] This unnecessarily tied G to the mass of the Earth, as opposed to G being recognized as a universal constant. However, even though Cavendish did not report a value for G, the results of his experiment allowed it to be determined. During the late 1800s, as scientists began to recognize G as a fundamental constant of nature, they calculated it from Cavendish's accurate results, thus:[32] After converting to SI units, Cavendish's value for the Earth's density, 5.45 g cm−3, gives G = 6.74 × 10−11 m3 kg−1 sec−2, which is within 1% of the currently accepted value. Derivation of G and the Earth's mass For the definitions of terms, see the drawing below and the table at the end of this section. The following is not the method Cavendish used, but shows how modern physicists would use his results.[33][34][35] From Hooke's law, the torque on the torsion wire is proportional to the deflection θ of the balance. The torque is κθ where κ is the torsion coefficient. However, the torque can also be written as a product of the attractive forces and the distance to the wire. Since there are two pairs of balls, each experiencing force F at a distance L / 2 from the axis of the balance, the torque is LF. Equating the two formulas for torque 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 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: * Boys, C. Vernon (1894). "On the Newtonian constant of gravitation". Nature 50 (1292): 330-4. * Cavendish, Henry (1798), "Experiments to Determine the Density of the Earth", in MacKenzie, A. S., Scientific Memoirs Vol.9: The Laws of Gravitation, American Book Co., 1900, pp. p.59-105, <http://books.google.com/books?id=O58mAAAAMAAJ&pg=PA59> Online copy of Cavendish's 1798 paper, and other early measurements of gravitational constant. * Clotfelter, B. E. (1987). "The Cavendish experiment as Cavendish knew it". American Journal of Physics 55: 210 – 213. Establishes that Cavendish didn't determine G. * Falconer, Isobel (1999). "Henry Cavendish: the man and the measurement". Measurement Science and Technology 10: 470 – 477. * "Gravitation Constant and Mean Density of the Earth". Encyclopaedia Britannica, 11th Ed. 12. (1910). The Encyclopaedia Britannica Co.. * Hodges, Laurent (1999). The Michell-Cavendish Experiment, faculty website, Iowa State Univ.. Retrieved on August 28, 2007. Discusses Michell's contributions, and whether Cavendish determined G. * Lally, Sean P. (1999). "Henry Cavendish and the Density of the Earth". The Physics Teacher 37: 34 – 37. * McCormmach, Russell; Jungnickel, Christa (1996). Cavendish. Philadelphia, Pennsylvania: American Philosophical Society. ISBN 0-87169-220-1. * Poynting, John H. (1894). The Mean Density of the Earth: An essay to which the Adams prize was adjudged in 1893. London: C. Griffin & Co.. Review of gravity measurements since 1740. 1. ^ Boys 1894 p.355 2. ^ Encyclopaedia Britannica 1910 p.385 'The aim [of experiments like Cavendish's] may be regarded either as the determination of the mass of the Earth,...conveniently expressed...as its "mean density", or as the determination of the "gravitation constant", G'. Cavendish's experiment is generally described today as a measurement of G (Clotfelter 1987 p.210). 3. ^ Many sources state erroneously that this was the first measurement of G (or the Earth's density), such as Feynman, Richard P. (1963), Lectures on Physics, Vol.1, Addison-Wesley, pp. p.6-7, ISBN 0201021161, <http://books.google.com/books?id=k6MQrphL-NIC&pg=PA28>. There were previous measurements, chiefly Bouguer (1740) and Maskelyne (1774), but they were very inaccurate (Poynting 1894)(Encyclopedia Britannica 1910). 4. ^ Clotfelter 1987, p.210 5. ^ McCormmach & Jungnickel 1996, p.336: A 1783 letter from Cavendish to Michell contains '...the earliest mention of weighing the world'. Not clear whether 'earliest mention' refers to Cavendish or Michell. 6. ^ Cavendish 1798, p.59 Cavendish gives full credit to Michell for devising the experiment 7. ^ Cavendish, H. 'Experiments to determine the Density of the Earth', Philosophical Transactions of the Royal Society of London, (part II) 88 p.469-526 (21 June 1798), reprinted in Cavendish 1798 8. ^ Cavendish 1798, p.59 9. ^ Poynting 1894, p.45 10. ^ Cavendish 1798, p.64 11. ^ Poynting 1894, p.45 12. ^ Boys 1894 p.357 13. ^ Cavendish 1798 p. 60 14. ^ A 2-mm sand grain weighs ~13 mg. Theodoris, Marina (2003). Mass of a Grain of Sand. The Physics Factbook. 15. ^ Cavendish 1798, p. 99, Result table, (scale graduations = 1/20 inch) The total deflection shown in most trials was twice this since he compared the deflection with large balls on opposite sides of the balance beam. 16. ^ Cavendish 1798, p.63 17. ^ McCormmach & Jungnickel 1996, p.341 18. ^ Halliday, David & Resnick, Robert (1993), Fundamentals of Physics, John Wiley & Sons, pp. p.418, ISBN 0471147311, <http://books.google.com/books?id=-AjnmJHPiKMC&pg=PA418> 'The apparatus used in 1798 by Henry Cavendish to measure the gravitational constant' 19. ^ Feynman, Richard P. (1963), Lectures on Physics, Vol.1, Addison-Wesley, pp. p.6-7, ISBN 0201021161, <http://books.google.com/books?id=k6MQrphL-NIC&pg=PA28> 'Cavendish claimed he was weighing the Earth, but what he was measuring was the coefficient G...' 20. ^ Feynman, Richard P. (1967), The Character of Physical Law, MIT Press, pp. p.28, ISBN 0262560038, <http://books.google.com/books?id=k6MQrphL-NIC&pg=PA28> 'Cavendish was able to measure the force, the two masses, and the distance, and thus determine the gravitational constant G' 21. ^ Cavendish Experiment, Harvard Lecture Demonstrations, Harvard Univ., <http://www.fas.harvard.edu/~scdiroff/lds/NewtonianMechanics/CavendishExperiment/CavendishExperiment.html>. Retrieved on 26 August 2007. '[the torsion balance was]...modified by Cavendish to measure G.' 22. ^ Shectman, Jonathan (2003), Groundbreaking Experiments, Inventions, and Discoveries of the 18th Century, Greenwood, pp. p.xlvii, ISBN 0313320152, <http://books.google.com/books?id=SsbChdIiflsC&pg=PAxlvii> 'Cavendish calculates the gravitational constant, which in turn gives him the mass of the earth...' 23. ^ Clotfelter 1987 24. ^ McCormmach & Jungnickel 1996, p.337 25. ^ Hodges 1999 26. ^ Lally 1999 27. ^ McCormmach & Jungnickel 1996, p.337 28. ^ Cornu, A. and Baille, J. B. (1873), Mutual determination of the constant of attraction and the mean density of the earth, C. R. Acad. Sci., Paris Vol. 76, 954-958. 29. ^ Boys 1894, p.330 In this lecture before the Royal Society, Boys introduces G and argues for its acceptance 30. ^ Poynting 1894, p.4 31. ^ McCormmach & Jungnickel 1996, p.337 32. ^ MacKenzie 1900, p.vi 33. ^ Cavendish Experiment, Harvard Lecture Demonstrations, Harvard Univ. 34. ^ Poynting 1894, p.41 35. ^ Clotfelter 1987 p.212 explains Cavendish's original method of calculation * Sideways Gravity in the Basemen t, The Citizen Scientist, July 1, 2005, retrieved Aug. 9, 2007. Homebrew Cavendish experiment, showing calculation of results and precautions necessary to eliminate wind and electrostatic errors. * Measuring Big G, Physics Central, retrieved Aug. 9, 2007. Recent experiment at Univ. of Washington to measure the gravitational constant using variation of Cavendish method. * The Controversy over Newton's Gravitational Constant , Eot-Wash Group, Univ. of Washington, retrieved Aug. 9, 2007. Discusses current state of measurements of G. * Model of Cavendish's torsion balance , retrieved Aug. 28, 2007, at Science Museum, London. Retrieved from "http://en.wikipedia.org/" All text is available under the terms of the GNU Free Documentation License 203 IMAGES The Cavendish Experiment Explained The Cavendish Experiment Cavendish Experiment PPT Das Cavendish-Experiment The Cavendish Experiment And The Gravitational Constant VIDEO Henry Cavendish: Unveiling the Secrets of Matter Gravitationswaage Documental Henry Cavendish do second cavendish experiment clearer Henry Cavendish Key Experiments of Physics COMMENTS Cavendish experiment 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 (m 1 m 2) divided by the square of the distance between them (r 2); that is, F ... Cavendish experiment The Cavendish experiment, performed in 1797-1798 by English scientist Henry Cavendish, was the first experiment to measure the force of gravity between masses in the laboratory [1] and the first to yield accurate values for the gravitational constant. [2] [3] [4] Because of the unit conventions then in use, the gravitational constant does not ... Cavendish Experiment figure 1. the twin dumbbells of the Cavendish experiment. ... 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. ... A large scale model of the dumbbell and fiber components are a good idea to help explain what's going on. We have ... Cavendish and the Value of G Cavendish's measurements resulted in an experimentally determined value of 6.75 x 10 -11 N m 2 /kg 2. Today, the currently accepted value is 6.67259 x 10 -11 N m 2 /kg 2. The value of G is an extremely small numerical value. Its smallness accounts for the fact that the force of gravitational attraction is only appreciable for objects with large ... Weighing the Earth in 1798: The Cavendish Experiment Henry Cavendish's experiments determining the density of the Earth were published in the Philosophical Transactions of the Royal Society in 1798. His method, following a procedure obtained from his friend John Michell, consisted of using a torsional spring to find the gravitational force between lead spheres smaller than 1 foot in diameter. The Cavendish Experiment and the Quest to Determine the Gravitational Cavendish's experiment essentially allowed scientists to "weigh" Earth (more properly to determine its mass and density). Once the value of the gravitational constant was determined, the mass of Earth could be calculated from the experimentally determined gravitational acceleration of 9.8 m/s 2. An accurate value for the gravitational constant ... June 1798: Cavendish weighs the world June 1798: Cavendish weighs the world. A profile illustration of Henry Cavendish with his signature at the bottom. He is wearing the attire of the late 1800s. In June 1798 Henry Cavendish reported his famous measurement of Earth's density. A great chemist and physicist, Henry Cavendish (1731-1810) was obsessive, extremely shy, and eccentric. How a Wire Was Used to Measure a Tiny Force of Gravity Henry Cavendish was an odd man. He never addressed strangers directly and was petrified of women. ... Cavendish's experiment is a splendid demonstration of the force of gravity on any object ... The Cavendish Experiment In 1797, British scientist Henry Cavendish set up a precise experiment to measure gravity. Conceptually, the experiment looked like the figure at the right. ... Newton used universal gravity to explain the orbits of planets in the solar system, and since then it has also explained things like the motion and formation of galaxies or the collapse ... PDF The Cavendish Experiment the density of the earth performed by Henry Cavendish, and published in 1798.1 The purpose of this experiment is to perform a modern version of the Cavendish experiment, determine the gravitational constant, G, and compare it to its accepted value. 2 Theory The primary apparatus used to perform this experiment is the torsion balance which is The Cavendish Experiment One glaring discovery is the absence of any notes or observations written by Henry about his most famous experiment, now named after him as "the Cavendish experiment" and involved 'weighing the world'. However, in the correspondence in the archive, we can see the genesis of the idea behind this experiment. In 1783, John Michell (1724-1793 ... Henry Cavendish Henry Cavendish (born October 10, 1731, Nice, France—died February 24, 1810, London, England) was a natural philosopher, the greatest experimental and theoretical English chemist and physicist of his age.Cavendish was distinguished for great accuracy and precision in research into the composition of atmospheric air, the properties of different gases, the synthesis of water, the law governing ... The Cavendish Experiment Explained This video is for my Physics Semester 1 recovery. We walk through the cavendish experiment, which uses a torsion balance to calculate the value of G. First w... Cavendish experiment explained Cavendish experiment explained. The Cavendish experiment, performed in 1797-1798 by English scientist Henry Cavendish, was the first experiment to measure the force of gravity between mass es in the laboratory [1] and the first to yield accurate values for the gravitational constant. [2] [3] Because of the unit conventions then in use, the ... Cavendish's Experiment & the Value of G In 1797, Henry Cavendish conducted the first successful experiment to find the value of the gravitational constant. The equipment looked like the set in the section above. You have two small ... Henry Cavendish and the Weight of the Earth Cavendish Experiment. However, the famous Cavendish experiment became the scientist's best known. It was conducted in 1798 in order to determine the density of the Earth and the device used was a modification of the torsion balance built by the geologist John Michell.The device consisted of a torsion balance with a pair of lead spheres suspended from the arm of a torsion balance and two much ... Cavendish Experiment The Cavendish Experiment, conducted by British scientist Henry Cavendish in 1797-98, was the first to measure the force of gravity between masses in the laboratory, and the first to yield accurate values for the gravitational constant and the mass of the Earth. Henry Cavendish Henry Cavendish. English chemist and physicist Henry Cavendish, who discovered hydrogen. Henry Cavendish, born in Nice, France to an aristocratic English family, was an avid and excellent experimenter. At the age of forty, he inherited an immense fortune that afforded him the luxury of pursuing his scientific interests (he was described by some ... Henry Cavendish (1731-1810): hydrogen, carbon dioxide, water, and Henry Cavendish (1731-1810) was an outstanding chemist and physicist. Although he was not a major figure in the history of respiratory physiology he made important discoveries concerning hydrogen, carbon dioxide, atmospheric air, and water. Hydrogen had been prepared earlier by Boyle but its properties had not been recognized; Cavendish described these in detail, including the density of the ... Cavendish experiment The Cavendish experiment, done in 1797 - 1798 by Henry Cavendish, was the first experiment to measure the force of gravity between masses in the laboratory, [1] and the first to yield accurate values for the gravitational constant and the mass of the Earth. [2] [3] However, these were derived by others from Cavendish's result, which was a ... The Cavendish Experiment Henry Cavendish was an unusual man but also one of the first great scientists. Many of his discoveries remained hidden in his notebooks, but his name is stil... Henry Cavendish Henry Cavendish FRS (/ ˈ k æ v ən d ɪ ʃ / KAV-ən-dish; 10 October 1731 - 24 February 1810) was an English natural philosopher and scientist who was an important experimental and theoretical chemist and physicist.He is noted for his discovery of hydrogen, which he termed "inflammable air". He described the density of inflammable air, which formed water on combustion, in a 1766 paper, On ... Cavendish Experiment Description: Henry Cavendish was the first scientist to measure the gravitational force between two objects in the laboratory using a gravitational torsion balance. In this video physics teacher Andrew Bennett attempts to recreate this experiment. Reading the comments section is very interesting. Pseudoscientific flat-earthers attempt to point ... essay homework paper phd project resume review speech thesis