Digital computers have rounding error. Brass computers had something more tactile: drag, slack, and stretch. Understanding these three error sources explains nearly every design decision in this archive — from Fischer’s jewel bearings to Hamburg’s shortened wire runs.
1. Friction: the tax on every pulley
Each floating pulley in the adder cascade steals a little motion. With 36 pulleys in series (No. 2’s 37 constituents), the tax compounds: small constituents arrive at the pen weakened, phase-shifted, or swallowed entirely. This is the physical reason 37 was the limit — a 38th crank would have added more drag than signal. Bidston’s builders fought back with larger pulleys on finer bearings; operators diagnosed sticky ones by ear (see setup day).
2. Backlash: the slack in the teeth
Gears never mesh perfectly — a hair of play exists between tooth and gap, and it reverses with direction. In a gear train carrying a slow constituent, backlash shows up as pen wobble near turning points: the exact moments clerks most need to read (see Reading a Prediction Roll). Good builders minimised it with tight cutting and spring-loaded split wheels; good operators learned each machine’s personality — which shaft hesitated, and by how much.
3. Wire stretch: the weather in the machine
The long summing wires changed length with temperature and humidity. A warm afternoon stretched the whole cascade and shifted the pen’s zero — which is why machines lived in thermally stable rooms, wore draught-proof cases (the German specialty — see Hamburg’s machines), and were re-zeroed against a reference before every run.
How big was it all?
At well-kept machines, high-water predictions still landed within centimetres of observation — the total error budget sat below the uncertainty in the tidal constants themselves. Gears were rarely the limit; the sky-to-paper chain was. When digital computers removed all three error sources at once, brass never stood a chance.
Before you ask
Could you feel the error? Literally — veterans judged a machine by cranking it with all pins home: any pen drift meant drag somewhere. Try the cardboard version in my weekend project and feel friction eat your neaps.
Did error grow over a run? Phase error from imperfect ratios accumulated slowly over simulated months; friction error stayed roughly constant. Designers budgeted both against the required table accuracy.
Why does this matter today? Because every error budget in modern tide software inherits these categories — friction became noise modelling, backlash became quantisation. The physics changed; the accounting did not.
Feel the floor
Error budgets sound abstract until they buzz under your fingers. Crank the cardboard adder with gritty washers, then with graphited ones, and feel accuracy return — that difference, scaled down ten-thousandfold, is what separated a good predictor from a great one. When you want the full-scale version, Inside Machine No. 2 shows error-fighting at its most heroic, and the glossary names every vice you just felt.