Kelvin tide-predicting machine

Designed by Lord Kelvin (William Thomson) in 1872–73, this special-purpose mechanical analog computer performs real-time Fourier synthesis. Each tidal harmonic constituent (M2, S2, N2 …) is represented by a pulley on a crank whose radius sets the amplitude and whose rotation rate is geared to the constituent's period. A single wire threads over all pulleys in series; as a hand-crank advances time, the wire's endpoint traces the sum of all cosines, drawing the predicted tide curve on a paper roll. Kelvin's final version summed 24 harmonic components and could predict a full year of tides in about four hours. Variants were built for the US, India, and other nations and remained in operational use through World War II. Speed: a full year of tidal predictions in ~4 hours of cranking. Capacity: up to 40 harmonic components (later US machines); continuous output.