In the summer of 1797, in a garden shed in Clapham, one of the richest and shyest men in England began measuring a force roughly ten million times weaker than the weight of a grain of sand. He worked alone, watched his apparatus through telescopes bored into the shed walls so that the heat of his own body would not disturb it, and took a year over it. The result told him what the planet he was standing on weighs.
Henry Cavendish’s torsion balance experiment is usually described as the moment we measured the gravitational constant. That is not quite what he thought he was doing, and the difference is worth getting right, because it says something about how physics actually moves forward.
What Newton Left Unfinished
Newton’s law of universal gravitation says that two masses attract each other in proportion to the product of their masses and inversely as the square of the distance between them. It is one of the most successful statements ever made about nature. It also, by itself, cannot tell you the mass of anything.
The reason is that the law gives ratios. Watching the Moon orbit the Earth tells you the strength of the Earth’s pull relative to the distance, but the mass of the Earth and the strength of gravity appear multiplied together and cannot be separated. Astronomers of the eighteenth century could state the mass of Jupiter as a fraction of the mass of the Sun with real precision, and could not say what either was in pounds.
To break the deadlock you need to measure the gravitational attraction between two objects whose masses you already know, in a laboratory, with a scale you can read. Since gravity is by far the weakest of the forces, this seemed close to impossible. Newton himself thought so, and wrote in Book III of the Principia that the attraction between ordinary bodies on Earth would be far too small to detect. He then made a shrewd guess anyway, reasoning from the rocks he knew about, that the Earth was probably five or six times denser than water.
He was right, and it took a century to prove it.
Michell’s Apparatus
The instrument was not Cavendish’s invention. It was designed by John Michell, a Yorkshire clergyman and geologist who was one of the most original scientific minds of the century, and who had also worked out that a star could be massive enough to trap its own light. Michell built the balance but died in 1793 before using it. The apparatus passed to Francis Wollaston and then to Cavendish, who rebuilt much of it.
The principle is elegant. A wooden rod about six feet long hangs horizontally from a thin wire, with a small lead sphere at each end. Twisting the rod even slightly makes the wire resist, and the strength of that resistance can be calibrated by watching how long the rod takes to swing back and forth. Now bring two large lead spheres close to the small ones, one on each side, so that their gravitational pull tugs the rod around. Measure how far it turns and you have measured gravity.
The scale of the problem becomes clear from the numbers. The large spheres weighed about 158 kilograms each. The force they exerted on the small ones was in the region of a ten millionth of a newton. The rod moved a few millimetres.
The Obsessive Part
What makes the experiment a landmark is not the concept but the paranoia about error. Cavendish enclosed the whole balance in a sealed case to stop air currents. He then enclosed the case in a room he did not enter. He operated the large spheres by a pulley system from outside and read the deflection through telescopes mounted in the walls, lit by lamps positioned so their heat could not reach the apparatus.
He worried about temperature gradients causing convection inside the case, and tested for it. He worried that the lead spheres might be magnetic, and substituted them to check. He measured the period of oscillation of the rod to calibrate the wire, repeated the whole procedure seventeen times, and reported his results with a full account of the sources of uncertainty. The paper reads like modern experimental physics, which in 1798 it was not.
His answer was that the Earth is 5.48 times as dense as water. The currently accepted figure is 5.51. He was within one percent, using equipment made of wood, lead, and wire.
He Was Not Measuring G
Cavendish’s paper is titled “Experiments to Determine the Density of the Earth”. The gravitational constant does not appear in it, and the symbol G was not in use. The idea of gravity having a universal numerical constant that could be tabulated alongside the speed of light came later in the nineteenth century, largely through the work of Poynting and others who reworked Cavendish’s data.
The distinction is not pedantry. It shows how an experiment can be more general than its author’s intention. Cavendish wanted a number for the Earth because geologists and astronomers wanted it. Once you have it, though, you can run the whole argument backwards: knowing the density and size of the Earth gives you its mass, and knowing its mass unlocks the mass of the Sun, the Moon, and every planet whose orbit had been measured. A single afternoon of tiny deflections in a Clapham shed put absolute figures on the entire solar system.
It also made possible the modern treatment of gravitational problems where the masses genuinely matter, including the notorious three-body problem and the perturbation calculations that later led to the discovery of Neptune.
The Strangest Man in Science
Cavendish is one of the great oddities of scientific history. He was the grandson of two dukes and inherited a fortune he seemed barely to notice. He was so uncomfortable in company that he communicated with his housekeeper by note, had a second staircase built so he could avoid meeting her, and dismissed a maid for the offence of being visible. At Royal Society dinners, colleagues learned to address remarks to the empty air near him rather than to him directly, and to walk alongside without turning their heads.
He published very little of what he did. After his death in 1810 his papers revealed that he had, decades before the men whose names are attached to them, found the relationship now called Ohm’s law, worked out the inverse square law of electrostatic force before Coulomb, and anticipated a good deal of the theory of capacitance. None of it was known because he had not bothered to tell anyone.
It fell to James Clerk Maxwell to edit and publish the electrical papers in 1879, seventy years late. Maxwell, who repeated many of the experiments to verify them, was clearly torn between admiration for the work and exasperation at the waste. A substantial chunk of the nineteenth century unification of electricity had been sitting in a drawer.
In chemistry he did publish, and the results were similarly fundamental. He isolated hydrogen and identified it as a distinct substance, then showed that burning it with common air produces water, which demolished the ancient idea of water as an element.
From Principle to Number
There is a pattern here that recurs throughout physics. A theory arrives that is correct in form but incomplete in magnitude. It states how quantities relate without saying how large they are. Then, sometimes a century later, an experimentalist with unusual patience supplies the missing number and the theory becomes a tool for measuring the world rather than merely describing it.
Newton wrote the law in 1687. He guessed the density of the Earth in the same book and had no way to check. Cavendish checked it in 1798, and confirmed the guess to within a few percent. The Principia, presented in our edition as the three separate books Newton designed, is where the framework was set out, including the reasoning in Book III about the composition of the Earth that Cavendish would eventually settle.
A Shed, a Wire, and a Year of Patience
The Cavendish experiment is still performed in undergraduate laboratories, usually with a laser instead of a telescope and an afternoon instead of a year. Students routinely fail to reach one percent accuracy, which is a useful reminder of what the original involved.
There was no new theory in it, no mathematical breakthrough, no dramatic moment of insight. There was an idea inherited from a dead clergyman, a wire, some lead, a great deal of lead, and a wealthy recluse who was willing to spend a year eliminating every possible source of error before he trusted his own eyes. That is a large part of what experimental physics has always been, and it is how we came to know the weight of the world.
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