Tide-predicting machine

William Thomson built the first in 1872–73 with Edward Roberts and the instrument maker Alexander Légé. Every tidal constituent — M2 for the moon, S2 for the sun, and a dozen more — gets a pulley of its own, driven by a gear pair cut to that constituent's period and set to the amplitude measured at the port in question. A wire runs over all the pulleys, so its total length is the sum of the sine terms. At the end of it sits a pen resting on a paper roll.

A year of tides for one harbour took a few hours of cranking, against months by hand. Kelvin's brother James Thomson had devised the ball-and-disk integrator used in the companion harmonic analyser — the same component Vannevar Bush would build the differential analyser out of sixty years later.

In 1944 Arthur Doodson at the Liverpool Tidal Institute computed the Normandy landing tides on two such machines, working from harmonic constants for a place he was told only to call Position Z. The machines were not retired until the 1960s, when computers finally became both faster and cheaper than brass.