Ship gun fire-control system
History of analogue fire control systems: Naval fire control resembles that of ground-based guns, but with no sharp distinction between direct and indirect fire. It is possible to control several same-type guns on a single platform simultaneously, while both the firing guns and the target are moving.
Though a ship rolls and pitches at a slower rate than a tank does, gyroscopic stabilization is extremely desirable. Naval gun fire control potentially involves three levels of complexity:

Local control originated with primitive gun installations aimed by the individual gun crews.
The director system of fire control was incorporated first into battleship designs by the Royal Navy in 1912. All guns on a single ship were laid from a central position placed as high as possible above the bridge. The director became a design feature of battleships, with Japanese "Pagoda-style" masts designed to maximize the view of the director over long ranges. A fire control officer who ranged the salvos transmitted elevations and angles to individual guns.
Coordinated gunfire from a formation of ships at a single target was a focus of battleship fleet operations. An officer on the flagship would signal target information to other ships in the formation. This was necessary to exploit the tactical advantage when one fleet succeeded in crossing the T of the enemy fleet, but the difficulty of distinguishing the splashes made walking the rounds in on the target more difficult.
Corrections can be made for surface wind velocity, roll and pitch of the firing ship, powder magazine temperature, drift of rifled projectiles, individual gun bore diameter adjusted for shot-to-shot enlargement, and rate-of-change of range with additional modifications to the firing solution based upon the observation of preceding shots. More sophisticated fire control systems consider more of these factors rather than relying on simple correction of observed fall of shot. Differently colored dye markers were sometimes included with large shells so individual guns, or individual ships in formation, could distinguish their shell splashes during daylight. Early "computers" were people using numerical tables.

Pre-dreadnought control system: The Royal Navy was aware of the fall of shot observation advantage of salvo firing through several experiments as early as 1870 when Commander John A. Fisher installed an electric system enabling a simultaneous firing of all the guns to HMS Ocean, the flagship of the China Station as the second in command. However, the Station or Royal Navy had not yet implemented the system fleet-wide in 1904. The Royal Navy considered Russia a potential adversary through The Great Game, and sent Lieutenant Walter Lake of the Navy Gunnery Division and Commander Walter Hugh Thring of the Coastguard and Reserves, the latter with an early example of Dumaresq, to Japan during the Russo-Japanese War. Their mission was to guide and train the Japanese naval gunnery personnel in the latest technological developments, but more importantly for the Imperial Japanese Navy (IJN), they were well aware of the experiments.

 During the 10 August 1904 Battle of the Yellow Sea against the Russian Pacific Fleet, the British-built IJN battleship Asahi and her sister ship, the fleet flagship Mikasa, were equipped with the latest Barr and Stroud range finders on the bridge, but the ships were not designed for coordinated aiming and firing. Asahi's chief gunnery officer, Hiroharu Kato (later Commander of Combined Fleet), experimented with the first director system of fire control, using speaking tube (voicepipe) and telephone communication from the spotters high on the mast to his position on the bridge where he performed the range and deflection calculations, and from his position to the 12-inch (305 mm) gun turrets forward and astern.
With the semi-synchronized salvo firing upon his voice command from the bridge, the spotters using stopwatches on the mast could identify the distant salvo of splashes created by the shells from their own ship more effectively than trying to identify a single splash among the many.  Kato gave the firing order consistently at a particular moment in the rolling and pitching cycles of the ship, simplifying firing and correction duties formerly performed independently with varying accuracy using artificial horizon gauges in each turret. Moreover, unlike in the gun turrets, he was steps away from the ship commander giving orders to change the course and the speed in response to the incoming reports on target movements.
Kato was transferred to the fleet flagship Mikasa as the Chief Gunnery Officer, and his primitive control system was in fleet-wide operation by the time the Combined Fleet destroyed the Russian Baltic Fleet (renamed the 2nd and 3rd Pacific Fleet) in the Battle of Tsushima during 27–28 May 1905.

Central fire control and World War I: Centralized naval fire control systems were first developed around the time of World War I. Local control had been used up until that time, and remained in use on smaller warships and auxiliaries through World War II. Specifications of HMS Dreadnought were finalized after the report on the Battle of Tsushima was submitted by the official observer to IJN onboard Asahi, Captain Pakenham (later Admiral), who observed how Kato's system worked first hand. From this design on, large warships had a main armament of one size of gun across a number of turrets (which made corrections simpler still), facilitating central fire control via electric triggering.
The UK built their first central system before the Great War. At the heart was an analogue computer designed by Commander (later Admiral Sir) Frederic Charles Dreyer that calculated range rate, the rate of change of range due to the relative motion between the firing and target ships. The Dreyer Table was to be improved and served into the interwar period at which point it was superseded in new and reconstructed ships by the Admiralty Fire Control Table.
The use of Director-controlled firing together with the fire control computer moved the control of the gun laying from the individual turrets to a central position (usually in a plotting room protected below armor), although individual gun mounts and multi-gun turrets could retain a local control option for use when battle damage prevented the director setting the guns. Guns could then be fired in planned salvos, with each gun giving a slightly different trajectory. Dispersion of shot caused by differences in individual guns, individual projectiles, powder ignition sequences, and transient distortion of ship structure was undesirably large at typical naval engagement ranges. Directors high on the superstructure had a better view of the enemy than a turret mounted sight, and the crew operating it were distant from the sound and shock of the guns.

Analogue computed fire control: Unmeasured and uncontrollable ballistic factors like high altitude temperature, humidity, barometric pressure, wind direction and velocity required final adjustment through observation of fall of shot. Visual range measurement (of both target and shell splashes) was difficult prior to availability of radar. The British favoured coincidence rangefinders while the Germans and the US Navy, stereoscopic type. The former were less able to range on an indistinct target but easier on the operator over a long period of use, the latter the reverse.
During the Battle of Jutland, while the British were thought by some to have the finest fire control system in the world at that time, only three percent of their shots actually struck their targets. At that time, the British primarily used a manual fire control system. This experience contributed to computing rangekeepers becoming standard issue.
The US Navy's first deployment of a rangekeeper was on USS Texas in 1916. Because of the limitations of the technology at that time, the initial rangekeepers were crude. For example, during World War I the rangekeepers would generate the necessary angles automatically but sailors had to manually follow the directions of the rangekeepers. This task was called "pointer following" but the crews tended to make inadvertent errors when they became fatigued during extended battles. During World War II, servomechanisms (called "power drives" in the US Navy) were developed that allowed the guns to automatically steer to the rangekeeper's commands with no manual intervention, though pointers still worked even if automatic control was lost. The Mark 1 and Mark 1A computers contained approximately 20 servomechanisms, mostly position servos, to minimize torque load on the computing mechanisms.

Radar and World War II: During their long service life, rangekeepers were updated often as technology advanced and by World War II they were a critical part of an integrated fire control system. The incorporation of radar into the fire control system early in World War II provided ships with the ability to conduct effective gunfire operations at long range in poor weather and at night.
In a typical World War II British ship the fire control system connected the individual gun turrets to the director tower (where the sighting instruments were) and the analogue computer in the heart of the ship. In the director tower, operators trained their telescopes on the target; one telescope measured elevation and the other bearing. Rangefinder telescopes on a separate mounting measured the distance to the target. These measurements were converted by the Fire Control Table into bearings and elevations for the guns to fire on. In the turrets, the gunlayers adjusted the elevation of their guns to match an indicator which was the elevation transmitted from the Fire Control Table—a turret layer did the same for bearing. When the guns were on target they were centrally fired.
The Aichi Clock Company first produced the Type 92 Shagekiban low angle analog computer in 1932. The US Navy Rangekeeper and the Mark 38 GFCS had an edge over Imperial Japanese Navy systems in operability and flexibility. The US system allowing the plotting room team to quickly identify target motion changes and apply appropriate corrections.