The Man Who Weighed the Earth

lowres-picturecabinet.com.s3-eu-west-1.amazonaws.com/43/main/15/94282.jpg

In 1798, the scientist Henry Cavendish published what would become a famous experiment. His setup involved a torsion balance (consists of a rod suspended by a fiber), four lead spheres, and the planet Earth; two of the lead spheres were larger and stationary, while the other two were attached to the torsion balance. Cavendish’ goal was to measure the gravitational force between the two lead spheres to compute the density of the Earth.

The instrument used by Cavendish was fabricated by the geologist John Michell. The torsion balance, introduced by Michell, was an important progress in gravitation experiments. Unfortunately, Mitchell died before he could complete his instrument and his apparatus was handed to Cavendish who improved it further by minimizing the effects of the induced air and temperature differences.

The apparatus consists of a fine torsion metal fiber that supports a dumbbell-shaped structure consisting of a wooden arm and the two small lead spheres. The gravitational force between the two large, stationary spheres and the two small spheres can be measured from the twist of the fiber since the arm with the two smaller spheres rotates until it is in equilibrium, that is, when the torque due to the force of gravitation is equal to the elastic torque due to the fiber. Cavendish used the period of oscillation of Michell’s torsion balance to compute the gravitational attraction between the spheres, which he then applied to compute the Earth’s density to an astonishing degree of accuracy. Cavendish’s work paved way for an accurate calculation of G, the gravitational constant, and the mass of the Earth.

Cavendish’s setup was remarkable in many ways. Before Cavendish’s experiment, there were efforts to demonstrate gravitation by measuring the influence of gravitational force on a pendulum due to a mountain in order to measure the density of the Earth; this phenomenon was known as the ‘Attraction of the Mountains’ and the experiment that used this effect to find the Earth’s mean density was known as the Schiehallion experiment. However, the Cavendish experiment was much more accurate and straightforward. Also, being able to probe the world from his home laboratory rather than out in the open was probably more favorable to his shy and agoraphobic personality, an aspect that is best described by Christa Jungnickel and Russell McCormmach in their book, Cavendish:

“With it [his setup of lead spheres instead of mountains] he did not need to go out into the world to know it; he could know it and know it more precisely by staying home and manipulating his apparatus and reasoning from universal principles. The world came to Cavendish. (Another way of viewing it is that Henry Cavendish was a Cavendish, and the Cavendishes liked to stay home and let the world come to them.) Cavendish stayed at home, inside of a building, looking inside of a room and through a slit in a case inside of which was the world – his world, on his terms.

It has been noted that while there is much talk about the effect of the scientist’s personality on science, there is little of the other, perhaps more profound, effect of science on the personality. In Cavendish we see both effects, mutually reinforcing. From the beginning Cavendish turned away from what he found difficult, ordinary society, and toward nature and its understanding through science, and through science he came into a society he found, if not comfortable, to his liking.

[...]

The experiment on the density of the earth is arguably not Cavendish’s most important experiment, but if it is looked at for what it reveals about the experimenter – as if it were a diary, which he did not keep, or a formal portrait, which he did not allow – it is the most expressive of his experiments.”

Finally, it was during the time of Cavendish that precision measurement emerged as an important factor in science. Cavendish often worked with instrument makers and attempted to improve their inventions. This is what he did with Michell’s setup; he also published a paper on how to improve astronomical instruments for better accuracy. His work was celebrated for its carefulness and exactness.

Michell’s setup, for example, modified and used by Cavendish, continues to be remembered because it was able to measure the delicate force of gravity between the two lead balls, only 1/50,000,000 of their weight! He achieved it by removing all factors and sources of error that might have affected the precision of his experiment. The estimate of the Earth’s density computed by Cavendish lies within 1 percent of the value that is accepted at present!

Further Reading
Cavendish: The Experimental Life, by Christa Jungnickel and Russell McCormmach