This is a stadimeter, derived from the instrument developed in the 1890s by the innovative American naval officer, Bradley Allen Fiske (1854-1942). The United States Navy transferred it to the Smithsonian in 1921, noting that it had been used "during the war with Germany, 1917-1918." Its height scale reads from 50 to 200 feet, and its distance scale reads from 200 yards to infinity.
Ref: Instructions for the Use and Care of the Fiske Ship-Telegraphs and Stadimeter
(Published by Authority of the Bureau of Ordnance, Navy Department, 1896).
Paolo E. Coletta, Admiral Bradley A. Fiske and the American Navy (Lawrence:
University of Kansas Press, 1979), pp. 38-40.