This is a 56 hour chronometer with a later pattern Earnshaw spring detent escapement, and indications for hours, minutes, seconds, and up and down. It was made around 1910. The U.S. Navy Bureau of Ships transferred it to the Smithsonian in 1956. Edward John Dent (1790-1853) was a clock and watch maker in London from 1826 to 1851, took part in the chronometer trials at the Royal Greenwich Observatory in 1826 to 1829, partnered with John Roger Arnold from 1830 to 1840, and held several patents, including one for a liquid compass card. The firm was later known as Dent & Co.
Ref: Vaudrey Mercer, The Life and Letters of Edward John Dent, Chronometer Maker, and Some Account of His Successors (London, 1977)
Vaudrey Mercer, A Supplement to Edward John Dent and his Successors (London, 1983)