I spent my first month in this subject staring at a year of hourly heights in a harbour logbook, wondering how anyone could know all that in advance. The answer turned out to be brass: a tide-predicting machine is a mechanical computer of gears, shafts, chains, and pulleys whose only job is to answer one question — how high will the water be, hour by hour, at a given port, months in advance?
Between 1872 and 1968, roughly forty such machines were built in Britain, America, Germany, Norway, and Japan. Harbour masters trusted their paper rolls the way we trust phone apps today. No electronics were involved — only the patient arithmetic of brass.
The problem: tides are sums, not single waves
If you watch a harbour for a month, the pattern looks messy. Some days have two nearly equal high tides; other days the morning high dwarfs the evening one; twice a month the range swells (springs) and twice it shrinks (neaps). I spent my first weeks in the archives confused by exactly this mess — until the nineteenth-century insight clicked.
The insight, due to William Thomson (later Lord Kelvin) and refined by George Darwin, is that the observed tide is a sum of many small, perfectly regular waves, each driven by one astronomical rhythm: the moon circling Earth, the sun’s pull, the tilt of the lunar orbit, and so on. Each component — called a harmonic constituent — has a fixed speed and a locally fixed size and phase. Add a few dozen of them together and you reconstruct the mess exactly.
That is precisely what the machines do, physically. Each constituent gets its own crank, spinning at its own speed. Pulleys add all the cranks’ motions onto one wire. The wire moves a pen. The pen draws the future.
For the full mathematics behind this idea, see my companion pillar How Harmonic Analysis Predicts Tides.
The three parts of every machine
Strip away ninety years of variation and every predictor has the same anatomy:
- The speed box. A hand crank (later a motor) drives a nest of gear pairs. Each pair multiplies or divides rotation so that one shaft turns at exactly the speed of, say, the M2 lunar constituent — one cycle per 12.42 hours of simulated time. Getting these ratios right was the great craft of the builders; my visual primer Gear Ratios That Model the Moon walks through a 10:1 pair step by step.
- The amplitude setters. On each shaft sits a crank whose pin can be slid in or out. Slide it out and that constituent contributes more; slide it home and it contributes nothing. Setting a machine for a new port meant looking up that port’s analysed constituents and adjusting dozens of pins with a spanner — a full day’s work I reconstruct in How Operators Set Up a Prediction Run.
- The adder and the pen. Fine wires or chains run from every crank over a cascade of pulleys and meet at a single carriage. The carriage position is the instantaneous sum — the predicted height — and a pen records it on a moving paper roll. Read my guide to Reading an Old Tide Prediction Roll to decode one yourself.
Why ports trusted brass over arithmetic
Harmonic prediction can be done by hand — human “computers” did it for years — but a year of hourly heights for one port means about 8,700 additions of thirty numbers each: roughly a quarter-million careful operations. A practiced operator and a good machine produced the same year in a few days of cranking, and could re-run it instantly if a constituent value was revised.
Accuracy was startling. For ports with good analysed data, machine predictions routinely landed within a few centimetres of the observed high water — close enough for dredging schedules, dry-dock bookings, and battleship movements. The American machine No. 2, with 37 constituents, held the world record for decades; I take it apart piece by piece in Inside the US Coast Survey Machine No. 2.
The machines that mattered most
- Kelvin’s first predictor (1872–73). Ten constituents, built by the Légé engineering firm. It proved the principle and toured like a celebrity. Full story: How Kelvin’s First Predictor Actually Worked.
- The India Office machine (1879). Kelvin’s refined design, still cranking predictions for Indian ports for decades.
- US Coast Survey No. 2 (1912). Rollin Harris and E. G. Fischer’s 37-component giant — the machine that made America self-sufficient in tide tables.
- The Bidston machines (1920s–50s). Arthur Doodson’s Liverpool instruments, tied to the most rigorous analysis methods ever devised. See The Bidston Observatory Machines.
- The German Gezeitenrechenmaschinen. Hamburg’s answer, less famous but beautifully engineered — covered in Germany’s Forgotten Competitors.
The complete chronology lives in my third pillar, History of Mechanical Tide Predictors, 1872–1968.
What a year of prediction actually cost
Nobody quotes prices, so I compiled this from office reports and logbooks — rough figures, but they explain why brass won:
| Method | Time for one port-year | Hands needed |
|---|---|---|
| Hand computation, Darwin schedules | 6–8 weeks | 1 computer + 1 checker |
| Kelvin 10-component machine | 2–3 days cranking + 1 setup day | 2 operators |
| US Machine No. 2, 37 components | about 1 motor-day + 1 setup day | small team |
| 1965 digital program | minutes | 1 programmer |
The machine did not just predict — it collapsed two months of ledger wages into a week of crank shifts. Harbour offices could do that arithmetic, which is why forty machines got funded. When the next collapse came, the obituary wrote itself — see Why the Machines Died.
First questions, honest answers
Were they accurate enough for navigation? Yes — for their era. Typical high-water errors were a few centimetres at well-studied ports, comparable to the printed tables ships actually carried. Storm surges (weather-driven) were never predictable by these machines, and everyone understood that limit.
How long did one prediction run take? A year of hourly heights took days of steady cranking on early machines, hours once motors arrived. Setup — adjusting every amplitude pin for a new port — was the slow part: up to a full working day.
Can I see one working today? Several survive in museums; a few are still turned by hand on special occasions. My museums guide lists every accessible machine I have verified.
Why did they disappear? Electronic digital computers replaced them between 1960 and 1968 — faster, cheaper per run, and easier to update. The full obituary is Why the Machines Died.
My advice: read them in this order
If I could sit with you for one evening, here is the order I would insist on: this guide tonight, the harmonic analysis explainer tomorrow with coffee, then the history pillar when you want the full ninety-year sweep. Mechanics lovers should detour through the pulley adder and the gear primer — those two pages carry the drawings I laboured over longest. And one request: if you ever stand in front of a surviving machine, open my museums guide on your phone first. The brass reads differently once you know what the wires are saying.