In the winter of 1872, a London instrument firm did something no one had done before: it taught brass to add. The Légé-built prototype of Lord Kelvin’s tide predictor had just ten constituents, stood about chest-high, and looked — to modern eyes — more like a loom than a computer. Yet when its crank turned, a pen drew real tides. Here is how, piece by piece.
The commission
Kelvin had argued since 1867 that if tides are sums of harmonic constituents (see my harmonic analysis explainer), then a machine could perform the summation physically. The British Association funded a trial; James White’s Glasgow workshop and the Légé firm handled construction. My instruments survey suggests the builders were as important as the inventor — gear-cutting tolerances made or broke these machines.
Ten shafts, ten speeds
The heart of the prototype was a layshaft driven by a hand crank through worm gearing. From it, ten gear pairs branched off, each pair cut to make its shaft rotate at exactly one constituent’s speed: M2, S2, K1, O1, and six companions. The ratios were fearsome — approximating the moon’s 12.4206-hour period with toothed wheels demands compound trains, and the builders’ notebooks show repeated re-cutting. My gear primer explains the arithmetic with a simple 10:1 example.
Cranks, pins, and the wire
Atop each shaft sat a slotted crank arm with a sliding pin. The pin’s radius set that constituent’s amplitude: full out for a big contribution, wound home for none. Fine chains — later machines used wire — ran from each pin over guide pulleys and joined in the famous cascade: each pulley floated between its own crank’s chain and the common line, so the common line’s motion was the sum of all ten motions. The free end drove the pen carriage. The same principle, enlarged, is drawn in my pulley adder sketch — and the No. 2 machine later stretched it to 37 constituents.
The demonstration that mattered
Kelvin’s team set the ten pins from analysed constants of a test port, cranked through weeks of simulated time, and compared the pen trace against actual recorded tides. Agreement was close enough — within the few inches that mattered to Victorian harbour masters — to justify everything that followed: the India Office machine, the American giants, and ninety years of brass prediction chronicled in my history pillar.
Clearing up confusion
Why only ten constituents? Ten was what the gear budget and the analysis of the day could support. It proved the principle; later machines added shallow-water and minor constituents as analysis improved under Doodson.
Does the original survive? The prototype’s descendant — the South Kensington demonstration model — survives in London’s Science Museum collections. Check my museums guide before visiting, since displays rotate.
Could I build a working replica? A ten-component replica is the classic amateur project: model gears, slotted cranks, and fishing-line pulleys genuinely work. Start with the setup-run reconstruction to learn the calibration ritual first.
If you build the replica
Ten constituents is the sweet spot for a home build: model gears, slotted cranks from aluminium strip, fishing-line pulleys — it genuinely works, and every failure teaches what the gear primer only describes. Start with the setup ritual before you cut anything, and when your pen first draws a believable tide, compare it against Machine No. 2 to see what thirty more years of refinement bought.