Give the beam an easy direction to move
Two spheres resting on a table do not visibly slide toward one another. Friction resists motion, and the Earth pulls both downward. A torsion balance hangs the small spheres from a wire. The wire carries their weight and allows the beam to rotate horizontally. As the wire twists, it pushes back with a restoring torque: the turning equivalent of the force from a soft spring.
John Michell devised the apparatus. Cavendish credited him at the start of his paper and described the roughly six-foot wooden beam that eventually came into his possession. Modern teaching balances are much smaller. They often add a mirror and laser, but retain the same physical idea: a very weak sideways pull can produce a measurable turn against a sufficiently soft suspension.
The force stays small; the spot travels farther
Attach a small mirror to the beam and aim a narrow light beam at it. The reflected light lands on a distant screen. When the mirror turns, the incoming direction stays fixed and the reflected direction turns through twice the mirror’s angle. Moving the screen farther away turns the same angle into a larger displacement.
For a simple geometric example, let the mirror turn through one milliradian, about one-seventeenth of a degree. A screen one and a half metres away receives a spot displaced by about three millimetres. The optical path has increased the readability of the motion. It has added no gravitational force to the apparatus.
The moving spot also reveals the beam’s inertia. After the source spheres move, the beam commonly overshoots its new equilibrium. The wire pulls it back, and the spot swings through successively smaller excursions. Its instantaneous position during this motion is different from the equilibrium position needed for a static measurement.
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Time the wire before assigning a force
An angle alone is not a force measurement. The same attraction produces a large turn against a soft wire and a small turn against a stiff one. The balance needs an independent way to determine its torsional stiffness: the torque required for a given rotation.
Move the source spheres away and gently release the beam into free oscillation. Its period, together with the known moving mass and geometry, determines the stiffness. A stiffer suspension brings the beam back more quickly and gives a shorter period. Damping slows the oscillation slightly, so a measurement that resolves that correction also estimates the rate at which the oscillations decay.
The spheres have finite size. Their centres travel around the suspension axis, and each sphere also turns as part of the rigid assembly. Both contributions enter the moment of inertia. Treating the mirror and beam as massless is a useful teaching approximation, provided the model says so. The geometry and inertia are what turn a measured time into a calibrated mechanical response.
Reverse the pull and read again
Even with the source spheres removed, the spot may miss the screen’s marked zero. Move the large spheres to the other side of the small ones and the gravitational torque reverses. The separation between the two settled readings helps distinguish the attraction from a shared zero offset.
Each small sphere feels both large spheres. The farther attraction partly cancels the torque from the nearest neighbour. A geometric calculation should therefore add all four source–test interactions. Keeping only the two nearest pairs overstates the torque for that geometry and changes the inferred gravitational constant.
A zero that drifts between the two measurements still biases their difference. This is why careful gravity measurements depend so much on stable conditions. Air motion, temperature changes and the properties of a suspension can shift a response that is already extremely small. Changing conditions and repeating the measurement help reveal where those shifts originate.
A small apparatus gives the Earth a scale
Cavendish’s paper was read to the Royal Society on 21 June 1798. Its title concerned the density of the Earth. The laboratory attraction supplied a gravitational scale that could be combined with the Earth’s pull to infer its average density. Today a related torsion-balance experiment is commonly framed as a measurement of the gravitational constant.
The attraction never became stronger. The apparatus chose a useful direction of motion, provided a soft restoring force and made the resulting displacement readable. A slowly travelling spot of light could then reveal the attraction between objects that otherwise seemed perfectly still.