Ship gun fire-control system
The gyro's drift is low enough not to matter for short periods of time; when the ship resumes more typical cruising, the erecting system corrects for any error.
The Earth's rotation is fast enough to need correcting. A small adjustable weight on a threaded rod, and a latitude scale makes the gyro precess at the Earth's equivalent angular rate at the given latitude. The weight, its scale, and frame are mounted on the shaft of a synchro torque receiver fed with ship's course data from the gyro compass, and compensated by a differential synchro driven by the housing-rotator motor. The little compensator in operation is geographically oriented, so the support rod for the weight points east and west.
At the top of the gyro assembly, above the compensator, right on center, is an exciter coil fed with low-voltage AC. Above that is a shallow black-painted wooden bowl, inverted. Inlaid in its surface, in grooves, are two coils essentially like two figure 8s, but shaped more like a letter D and its mirror image, forming a circle with a diametral crossover. One coil is displaced by 90 degrees. If the bowl (called an "umbrella") is not centered above the exciter coil, either or both coils have an output that represents the offset. This voltage is phase-detected and amplified to drive two DC servo motors to position the umbrella in line with the coil.
The umbrella support gimbals rotate in bearing with the gun director, and the servo motors generate level and crosslevel stabilizing signals.
The Mark 1A's director bearing receiver servo drives the pickoff gimbal frame in the stable element through a shaft between the two devices, and the Stable Element's level and crosslevel servos feed those signals back to the computer via two more shafts.
(The sonar fire-control computer aboard some destroyers of the late 1950s required roll and pitch signals for stabilizing, so a coordinate converter containing synchros, resolvers, and servos calculated the latter from gun director bearing, level, and crosslevel.)

Fire Control Radar: The fire-control radar used on the Mark 37 GFCS has evolved. In the 1930s, the Mark 33 Director did not have a radar antenna. The Tizard Mission to the United States provided the USN with crucial data on UK and Royal Navy radar technology and fire-control radar systems. In September 1941, the first rectangular Mark 4 Fire-control radar antenna was mounted on a Mark 37 Director, and became a common feature on USN Directors by mid 1942. Soon aircraft flew faster, and in c1944 to increase speed and accuracy the Mark 4 was replaced by a combination of the Mark 12 (rectangular antenna) and Mark 22 (parabolic antenna) "orange peel" radars. (pictured) in the late 1950s, Mark 37 directors had Western Electric Mark 25 X-band conical-scan radars with round, perforated dishes. Finally, the circular SPG 25 antenna was mounted on top.

Deployment: destroyers (1 per vessel, 456 total) 
2 rebuilt Mahan-class: Downes, Cassin
several modernized Porter-class: Phelps, Selfridge, Winslow
12 Sims-class (launched ca. 1939)
30 Benson-class (1939 - 1942)
66 Gleaves-class (1940 - 1942)
175 Fletcher-class (1942 - 1944)
58 Allen M. Sumner-class (ca. 1944)
12 Robert H. Smith-class (ca. 1944)
98 Gearing-class (ca. 1945)
possibly on USS Castle (DD-720) and USS Seaman (DD-791) which were launched incomplete and never commissioned
light cruisers (63 total)
TBD: Atlanta, Fargo classes
3 Juneau-class(ca. 1945) (2 per vessel, 6 total)
27 Cleveland-class(launched ca. 1942 - 1945) (2 per vessel, 54 total)
one Mk37 removed on Oklahoma City during CLG conversion
2 Worcester-class(ca. 1947) (4 per vessel, 8 total)
1 Brooklyn-class ( Savannah, refitted as upgrade in 1944)
heavy cruisers (46 total)
14 Baltimore-class(ca. 1942 - 1945) (2 per vessel, 28 total)
3 Oregon City-class(ca. 1945) (2 per vessel, 6 total)
3 Des Moines-class(ca. 1947) (4 per vessel, 12 total)
2 Alaska-class large cruisers (ca. 1943) (2 per vessel, 4 total)
aircraft carriers (2 total)
TBD: Yorktown, Essex classes, Midway(?)
Saratoga: 2xMk37 refitted by May 1942
battleships (16 total)
TBD: North Carolina, South Dakota classes, all the old ones that were upgraded with 5in/38(?)
4 Iowa-class(launched ca. 1942 - 1943) (4 per vessel)

Mark 38 GFCS: The Mark 38 Gun Fire Control System (GFCS) controlled the large main battery guns of Iowa-class battleships. The radar systems used by the Mark 38 GFCS were far more advanced than the primitive radar sets used by the Japanese in World War II. The major components were the director, plotting room, and interconnecting data transmission equipment. The two systems, forward and aft, were complete and independent. Their plotting rooms were isolated to protect against battle damage propagating from one to the other.

Director: The forward Mark 38 Director (pictured) was situated on top of the fire control tower. The director was equipped with optical sights, optical Mark 48 Rangefinder (the long thin boxes sticking out each side), and a Mark 13 Fire Control Radar antenna (the rectangular shape sitting on top). The purpose of the director was to track the target's present bearing and range. This could be done optically with the men inside using the sights and Rangefinder, or electronically with the radar. (The fire control radar was the preferred method.) The present position of the target was called the Line-Of-Sight (LOS), and it was continuously sent down to the plotting room by synchro motors. When not using the radar's display to determine Spots, the director was the optical spotting station.

Plotting room: The Forward Main Battery Plotting Room was located below the waterline and inside the armored belt. It housed the forward system's Mark 8 Rangekeeper, Mark 41 Stable Vertical, Mark 13 FC Radar controls and displays, Parallax Correctors, Fire Control Switchboard, battle telephone switchboard, battery status indicators, assistant Gunnery Officers, and Fire Controlmen (FC's)(between 1954 and 1982, FC's were designated as Fire Control Technicians (FT's)).

The Mark 8 Rangekeeper was an electromechanical analog computer whose function was to continuously calculate the gun's bearing and elevation, Line-Of-Fire (LOF), to hit a future position of the target. It did this by automatically receiving information from the director (LOS), the FC Radar (range), the ship's gyrocompass (true ship's course), the ships Pitometer log (ship's speed), the Stable Vertical (ship's deck tilt, sensed as level and crosslevel), and the ship's anemometer (relative wind speed and direction). Also, before the surface action started, the FT's made manual inputs for the average initial velocity of the projectiles fired out of the battery's gun barrels, and air density. With all this information, the rangekeeper calculated the relative motion between its ship and the target. It then could calculate an offset angle and change of range between the target's present position (LOS) and future position at the end of the projectile's time of flight. To this bearing and range offset, it added corrections for gravity, wind, Magnus Effect of the spinning projectile, stabilizing signals originating in the Stable Vertical, Earth's curvature, and Coriolis effect. The result was the turret's bearing and elevation orders (LOF). During the surface action, range and deflection Spots and target altitude (not zero during Gun Fire Support) were manually entered.

The Mark 41 Stable Vertical was a vertical seeking gyroscope, and its function was to tell the rest of the system which-way-is-up on a rolling and pitching ship. It also held the battery's firing keys.
The Mark 13 FC Radar supplied present target range, and it showed the fall of shot around the target so the Gunnery Officer could correct the system's aim with range and deflection spots put into the rangekeeper. It could also automatically track the target by controlling the director's bearing power drive. Because of radar, Fire Control systems are able to track and fire at targets at a greater range and with increased accuracy during the day, night, or inclement weather. This was demonstrated in November 1942 when the battleship USS Washington engaged the Imperial Japanese Navy battlecruiser Kirishima at a range of 18,500 yards (16,900 m) at night. The engagement left Kirishima in flames, and she was ultimately scuttled by her crew. This gave the United States Navy a major advantage in World War II, as the Japanese did not develop radar or automated fire control to the level of the US Navy and were at a significant disadvantage.