USCS Madison was a schooner

Schooner

A schooner is a type of sailing vessel characterized by the use of fore-and-aft sails on two or more masts with the forward mast being no taller than the rear masts....

 that served as a survey ship in the United States Coast Survey from 1850 to 1858.

Madisons origins are obscure, but the Coast Survey acquired her in 1850 and placed her in service along the United States East Coast, where she spent her entire Coast Survey career. She was retired in 1858.