Analog computer
A machine that doesn't calculate but imitates: the quantity is a voltage or a turned shaft, and the answer is read off as a measurement.
A digital machine represents 3.7 as a pattern of digits. An analog machine represents it as 3.7 volts, or a wheel turned 3.7 revolutions. Arithmetic therefore becomes physics. An integrator is a friction wheel riding on a rotating disc. An addition is two shafts feeding a differential gear. A differential equation is solved by an apparatus whose own behaviour obeys that same equation — no instruction fetch, no clock, the answer simply appears and keeps appearing as you turn the dial.
Before 1950, essentially all serious solving of differential equations was analog: Kelvin's tide predictors, Bush's differential analyser, the fire-control computers in warship turrets and submarine control rooms. After the war the machines were built from operational amplifiers rather than gears — the component is named that precisely because it performed a mathematical operation. Flight simulators and power-station models still ran analog into the 1970s.
What killed them was not speed. Accuracy stalled at around a tenth of a percent no matter how well you built, because the error is physical and you cannot fix it by adding a digit. Reprogramming meant repatching cables by hand. And two runs of the same problem never gave quite the same answer. Digital machines were slower at first but repeatable, and repeatability won.