Looking up at the main armament & bridge work of the
California (BB-44) in dry dock at Hunters Point Naval Ship Yard in 1936. Note the concentration dial, or "Clock".
The practice of gunnery at the beginning of the 20th century put a lot of emphasis on shooting first. Radio communications was cumbersome, morse code, slow and visual signals, light, flaghoist or semaphore, were not much better. When an enemy was detected it also took time to train and elevate the guns to shoot at him. In poor visibility this might give him the first shot. The range clocks, and their companion, the deflection markers, were developed to shorten the time needed to get off the first salvo.
Concentration of fire was also a major consideration, and usually all ships of a division would fire on the same target. Fire control was based on mechanical analog devices that incorporated input from the optical range finders located at several places on the ship. In USN ships this included the top of the cage mast.
Long range visibility under battle conditions was often poor. The heavy black smoke from burning coal just made it worse. But individual ships could be expected to have a reasonably clear view of the next ship ahead in the division line. The flagship was almost always in the lead, and could direct concentration of fire by passing range and deflection data to the other ships. This process was made much faster by simply training the flagships own guns in the direction of the enemy and displaying the ships own average rangefinder results on a circular display. Trailing ships often did not have as good a view of the enemy as the leader, but could observe where the leaders guns were aimed (and read numbers from the range clock) in order to set initial values for aiming their own guns.
There was no CIC as we know it today, but there was a central fire control plot on each ship. This plot included a MECHANICAL device for determining and transmitting refined settings for azimuth and elevation of the guns. Initial inputs were often set manually. Communications between the plot and the gun turrets (and the range clocks) included up to 4 separate and parallel methods. First, there was a mechanical connection, usually a bicycle chain and sprocket drive to ensure equivalent movement. Second, voice tubes connected the plot with rangefinder positions and guns. Third, when they became available, there were internal communications telephones matching the above circuits. Finally, if other means failed, you could write a note and send it by messenger.
As a final note range "clocks" are numbered from 1 to 10, not 1 to 12. The figures were usually given in thousands of yards.