Firing table
The booklet telling a gun crew how high to point the barrel — and the arithmetic backlog that became the reason to build ENIAC.
An artillery piece does not hit where it is aimed but where ballistics takes the shell. A firing table converted the range you wanted into the elevation you needed, for every combination of shell type, charge, powder temperature, wind, air pressure and altitude. Without the pocket-sized booklet the gun was a blunt object, and every new gun and every new kind of ammunition demanded a table of its own.
The arithmetic behind it was brutal. One table rested on a couple of thousand computed trajectories, each of them thousands of multiplications in sequence. During the Second World War the Aberdeen Proving Ground in Maryland employed some two hundred human computers — almost all women, many freshly graduated mathematicians — working desk calculators, plus access to the Moore School's differential analyzer. A single trajectory took a person up to a couple of days and the analyzer about a quarter of an hour.
The queue grew faster than it was cleared, and that was the argument that got the Army to fund an electronic machine of doubtful prospects in 1943. ENIAC was finished in November 1945, after the war had ended, and computed a trajectory in roughly thirty seconds — about as long as the shell itself needed to arrive.