Wikipedia
A plotting board was a mechanical device used by the U.S. Coast Artillery to track the observed course of a target (typically a moving ship), project its future position, and derive the uncorrected data on azimuth (or direction) and range needed to direct the fire of the guns of a battery to hit that target. Plotting boards of this sort were first employed by the Coast Artillery around 1905, and were the primary means of calculating firing data until WW2.
Although several different types of plotting boards were used by the Coast Artillery over the years, the example described here is the Whistler-Hearn Plotting Board, Model of 1904 which was widely employed by the Coast Artillery between about 1905 and 1925. This description is primarily derived from two manuals of the period, each of which leaves certain aspects of the board's design and use unexplained. A 1940 manual also describes the Whistler-Hearn board.