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The experimental atlas / 1798

Cavendish

Weighing the world · A source-based reconstruction

Newtonian · SI units

Physics & provenance

01 / Source masses2 × 158.045 kg

Move the large masses around the enclosure. The suspension wire is not driven by this control.

02 / Time & motion

Display acceleration

Acceleration executes more fixed 0.5 s RK4 steps per real second; it never scales forces or angles.

Full free-oscillation period

Viscous damping ζ

Upper-clamp zero θ₀

Initial condition

Each change starts a new calibration segment. Earlier samples stay in the record, dimmed, and are excluded from fits. The balance angle is not moved. A new A / B run restores the documented calibration.

03 / View the mechanism

Component annotationsGravitational force vectorsRoom / remote observationsTelescope sight axes

Camera focus

Geometry and motion stay at 1:1. Force arrows are scaled annotations, not visible physical objects. Changing the view never changes the experiment.

04 / Virtual measurement

A controlled ring-down, approach and reversal. Reconstruct G, wire stiffness and damping from sampled angular positions.

No fit for the current calibration yet. Run the A / B measurement, or fit a record with changing source positions.

Notebook

Successful fits are kept here with their run and calibration.

Reset apparatus and a new A / B run replace the position record. Notebook fits persist until you clear them; views, the guide and the layout never clear them.

Not a modern laser balance.The two telescopes observe end scales through glazed openings. Cutaway views and digital plots are present-day teaching aids.

Keyboard shortcuts

Focus the 3D view first. Space runs or pauses · A / B source stops · M midway · X cycles enclosure views · R resets the apparatus · H home view · Esc releases the keyboard.

Longitudinal enclosure cutaway

A force smaller than a millionth of a newton.

Independent supports. A slender wire. Four lead spheres.

Drag to orbit · Scroll / pinch to zoom
Right-drag / two fingers to pan · Click a component

00:00:00

Cavendish / 1798

Assembling the torsion balance

Preparing embedded geometry, materials and the physical solver.

Balance / Live state

Angular displacement θ (ideal)

End-scale shift

Angular velocity

Nearest-pair force

Center separation

Ideal diagnostics from the accepted model state, not telescope observations.

Through the telescope

Nearest vernier division

Five-part vernier: 0.254 mm resolution. The angle below is the ideal model value; this inset is a schematic, not a ray-traced eyepiece image.

What makes the balance move?

Gravity

Wire

Damping

Net torque

I θ̈ = τ(gravity) − κ(θ − θ₀) − b θ̇

Displacement microscope: cyan motion enlarged 40×. This inset alone exaggerates angles.

Component inspector

Michell–Cavendish torsion balance

Select a component in the scene. The test balance hangs from its own wire; the much heavier source masses hang from the ceiling pivot. They interact gravitationally, not through a drive linkage.

Numerical self-checks

Open to run the deterministic checks for the 900 s calibration.

Angle against physical elapsed time

θ(t)Static equilibrium

Peak-to-peak time is a full oscillation. Dimmed traces belong to earlier calibrations.

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1798 · Physics

Cavendish Torsion Balance — Weighing the World

A source-based reconstruction of Cavendish’s torsion balance: move the lead masses, read the telescope, and fit G from recorded angles.

In 1798 Henry Cavendish hung a light wooden arm carrying two small lead spheres from a long wire inside a sealed case, and swung two heavy lead spheres close to them from a separate suspension. The attraction twisted the arm by a tiny angle, which he read from outside the room through telescopes aimed at ivory scales and verniers.

This exhibit reconstructs that apparatus from the documented dimensions and masses and computes one torsional degree of freedom with a fixed-step Runge–Kutta solver. Both source spheres act on both test spheres, and the deal arm, silver bracing and copper supports are included. Time acceleration executes more physical steps; it never enlarges forces or angles.

The A / B measurement records a midway ring-down and both source positions every two seconds of physical time, then fits G, the wire stiffness and damping from those angles alone. The simulated data are ideal and noise-free, so the result is a numerical consistency check of a Newtonian idealization, not Cavendish’s own data reduction or a historical uncertainty.

Specifications

Published: Experiments to Determine the Density of the Earth, Phil. Trans. 88 (1798)
Source masses: 2 × 2,439,000 grains (158.045 kg) of lead
Test masses: 2 × 11,262 grains (0.730 kg) on a 73.3-inch span
Torsion wire: 40 in (1.016 m); stiffness calibrated from a 450 s or 900 s period
Readout: Ivory scale with a five-part vernier, 1/100 inch resolution
Modeled: Newtonian torque, RK4 in SI units, contact stop, angle-only least-squares fit

All exhibits

Assembling the torsion balance

Angle against physical elapsed time

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