﻿ Henry Cavendish: Weighing the Earth

Henry Cavendish
Weighing the Earth
For the Advanced Science Hobbyist: Repeat Henry Cavendish’s Experiment

### Henry Cavendish's Experiment

 Cavendish's Torsion Balance Vertical section drawing of Cavendish's torsion balance instrument including the building in which it was housed. The large balls were hung from a frame so they could be rotated into position next to the small balls by a pulley from outside.
In 1686 Isaac Newton realized that the motion of the planets and the moon as well as that of a falling apple could be explained by his Law of Universal Gravitation, which states that any two objects attract each other with a force equal to the product of their masses divided by the square of their separation times a constant of proportionality.

Newton was not particularly concerned to evaluate the constant of proportionality, G, for two reasons. First, a consistent unit of mass was not in widespread use at the time. Second, he judged that since the gravitational attraction was so weak between any pair of objects whose mass he could sensibly measure, being so overwhelmed by the attraction each feels toward the center of the earth, any measurement of G was impractical. However, Newton estimated this constant of proportionality, called G, perhaps from the gravitational acceleration of the falling apple and an inspired guess for the average density of the Earth.

More than 100 years elapsed before G was first measured in the laboratory; in 1798 Cavendish and co-workers obtained a value accurate to about 1%. When asked why he was measuring G, Cavendish replied that he was "weighing the Earth"; once G is known the mass of the Earth can be obtained from the 9.8m/s2 gravitational acceleration on the Earth surface and the Sun's mass can be obtained from the size and period of the Earth orbit around the sun. Early in this century Albert Einstein developed his theory of gravity called General Relativity in which the gravitational attraction is explained as a result of the curvature of space-time. This curvature is proportional to G.

Naturally, the value of the fundamental constant G has interested physicists for over 300 years and, except for the speed of light, it has the longest history of measurements. Almost all measurements of G have used variations of the torsion balance technique pioneered by Cavendish. The usual torsion balance consists of a 'dumbbell' (two masses connected by a horizontal rod) suspended by a very thin fiber. When two heavy attracting bodies are placed on opposite sides of the dumbbell, the dumbbell twists by a very small amount. The attracting bodies are then moved to the other side of the dumbbell and the dumbbell twists in the opposite direction. The magnitude of these twists is used to find G.

Some history:
Spurred by his interest in the structure and composition of the interior of the earth, Henry Cavendish in a 1783 letter to his friend Rev. John Michell discussed the possibility of devising an experiment to "weigh the earth." Borrowing an idea from the French scientist Coulomb who had investigated the electrical force between small charged metal spheres, Michell suggested using a torsion balance to detect the tiny gravitational attraction between metal spheres and set about constructing an appropriate apparatus. He died in 1793, however, before conducting experiments with the apparatus.

The apparatus eventually made its way to Cavendish's home/laboratory, where he rebuilt most of it. His balance was constructed from a 6-foot wooden rod suspended by a metal fiber, with 2-inch-diameter lead spheres mounted on each end of the rod. These were attracted to 350-pound lead spheres brought close to the enclosure housing the rod. He began his experiments to "weigh the world" in 1797 at the age of 67, and published his result in 1798 that the average density of the earth is 5.48 times that of water. His work was done with such care that this value was not improved upon for over a century. The modern value for the mean density of the earth is 5.52 times the density of water. 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.

### Repeat Henry Cavendish’s Experiment

It is not unusual to find books that state erroneously that Cavendish's purpose was determining the gravitational constant (G). 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. 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.

In order to measure G we need refined and delicate laboratory apparatus (torsion balance) and experimental design, in which a multitude of subtle effects must be compensated for or canceled out. We, however, aren't going to measure anything - we're only interested in observing universal gravitation. This allows simplifying the torsion balance to something we can set up in the basement.

### John Walker's Experiment

The following experiment was suggested by John Walker, Fourmilab Switzerland. It is strongly recommended to read his full article in order to perform correctly this experiment: Bending Spacetime in the Basement

An underground room is ideal because it minimises temperature variations and vibration which might perturb the balance arm. Prevent air currents from disrupting the balance arm.

Don’t set up the balance near one of the walls, the gravitational field from all that rock and brick will mask that of the test masses, and the balance will assume a "gravity gradient" position with one of the ends of the bar pointing toward the wall, and will budge only slightly under the influence of the test masses. With the bar in the middle of the room, the tidal influence of the mass of the wall and the rock behind it is reduced to a negligible value.

### Criticism of Walker's Experiment

Norman Scheinberg, a professor of electrical engineering at The City College of the City University of New York, repeated Walker's Experiment.

Scheinberg's analysis of Walker's video revealed many problems. Timestamping of the video shows that it takes only three minutes for the pendulum to move from one side to the other. But this is too short a time for the pull of gravity to move the balls 5 inches.

In his article Scheinberg presents detailed calculations showing that the swing time must be much more longer than three minutes since Walker used too light steel balls in order to fit into the three minutes swing period. John walker used 2 lb steel balls, by contrast Cavendish used 300 lb lead weights. (http://www.sas.org...)

Scheinberg designed his own Cavandish experiment in which the pendulum moved about 1 inch with 75 lb weights in 15 minutes.

Our sound advice: repeat both experiments and maybe you'll come up with your own conclusions. We would like to be informed.

### Further Reading

Bending Spacetime in the Basement - John Walker
Tthe Michell-Cavendish Experiment - Laurent Hodges
Helping 'Big G' Get Back on Track - John Moore
Norman Scheinberg's Cavendish Experiment
Background to Boys' experiment to determine G - The Clarendon Laboratory Archive
Cavendish and G - Physics Classroom
The Weight of Expectation - C. D. Hoyle
Gravitational Torsion Balance: Instruction Manual - PASCO
Measurement of the Gravitational Constant - Rice University
The Controversy over Newton's Gravitational Constant - The UW Eot-Wash Group
Cavendish Experiment - Harvard

### Books

Follow Us On:

Privacy Policy - Site Map - About Us - Letters to the Editor

Comments and inquiries:
webmaster@julianTrubin.com

Last updated: February 2018
Copyright 2003-2018 Julian Rubin