The Tide Predicter · No. 1

The Tide-Predicting Machine

In 1872 Sir William Thomson — later Lord Kelvin — devised a machine that could calculate the sea. The tide at any port is, to remarkable accuracy, a sum of simple cosines: one for the Moon’s main pull (M₂), one for the Sun’s (S₂), others for the Moon’s elliptical orbit, the bodies’ wanderings north and south of the equator, and the distortions of shallow water. Astronomy fixes each component’s speed forever; only its local amplitude and phase must be measured at the port.

Thomson’s machine embodies that sum in brass. A hand crank turns a shaft; gear trains cut to the true astronomical ratios turn one wheel per constituent. A crank pin, clamped at a radius equal to the constituent’s amplitude, drives a slotted yoke and lifts a pulley in perfect sinusoidal rhythm. A single wire, fixed at one end, passes over every moving pulley and under fixed ones; each pulley pays out or takes up twice its own displacement, so the free end of the wire — carrying the pen — moves with the sum of every motion. A drum, geared to the same shaft, turns under the pen: the coming year of tides, drawn in four hours of cranking. Successor machines with up to 62 components served until electronic computers retired them in the 1960s; among their finest hours were the secret tide tables for the Normandy landings of 1944.

Nothing in this model is faked. Each frame, the pen’s height is computed from the conserved length of the wire over the pulleys’ actual positions — the curve you see is the machine’s own mechanical output. (A live audit against the analytic harmonic sum is shown beneath the chart; they agree to a fraction of a millimetre.) Switching a constituent off slides its crank pin to zero radius, exactly as an operator would have.

• Springs & neaps — leave only M₂ and S₂ on, run at high speed, and watch the beat: when the two cranks turn in step (see the little dial), the tides swell; in opposition, they shrink. The full cycle takes 14.8 days.
• Why two tides a day? — solo M₂ draws the pure lunar tide, repeating every 12 h 25 m — which is why high water comes ~50 minutes later each day.
• Diurnal seas — choose the Hòn Dấu preset: there the daily constituents dominate and the sea breathes only once a day.
• Estuary distortion — on the Avonmouth preset, toggle M₄ and watch the curve sharpen and lean, as real shallow-water tides do.
• The slowest wheel — find Mf at the far right: geared down 55-fold, it creeps through one turn a fortnight.