Digital computers can only draw a straight line. To draw a circle, a digital computer approximates it with many short straight lines, producing bumps. Those bumps cause a gun to jump when a digital computer positions it, and cause star-tracker images to blur during long photographic exposures. Analog computer outputs are smooth and continuous — which is why the world’s telescopes are still positioned by analog computers.
This paper by A. Ben Clymer traces the history of mechanical analog computers from their earliest developments through their peak in World War II and their obsolescence in the 1950s. The framework is the work of Hannibal Ford, William Newell, and the Ford Instrument Company, whose devices were central to the superb gunnery of the US Navy. Topics covered include the naval fire control problem, how analog computers solved it from 1910 onward, and their parallel application to bombsights.
See also: Fire Control Analog Computer 1953 — Two Videos