I found out the smallest instrument shown has to date between 1833 and 1851, since that's when James Green worked in Baltimore.
This is an extract from an online database of instrument makers.
GREEN, JAMES 2 England; USA., 1808-96, MIM NIM OIM PHIM Surveyor's Compass = Infantry and Cavalry School, Fort Leavenworth, Kansas (1891); Barometer = USNM; Aneroid Barometer = USNM. emigrated from London in 1833; succeeded in Baltimore by F.W. and R. King in 1851; dealt in European instruments. London (1817-23); 72 Baltimore Street (1835-36); 15 Liberty Street (1840-41); 53 South Street (1842); all in Baltimore Md.; New York, N.Y. (1849-96); 175 Grand Street, New York, N.Y. (1868). Smart 1; USNM; Middleton 1 and 4; D.J. Warner 6 and 10; RSW.
I still don't know for sure if it is gunner's quadrant or something else.