Information from an article from the NARA entitled Leaving the Army during Mr. Madison's War: Certificates of Discharge for the War of 1812:
"Because they remained in private hands, carefully preserved (or not) by the soldier or his heirs, discharge certificates are usually difficult to locate and are seldom available for public research. One notable exception, however, is a small series of extant discharge certificates and other records relating to more than 2,200 Regular Army soldiers from 1792 to 1815."
"The discharge records have been reproduced as National Archives Microfilm Publication M1856*...".
*See PDF file (excerpted below - my links included)
A possibility for my William Hinds? He was in the Artillery.:
Hines [?], John 1813 Lists of Sick Men (Light Artillery, Capt. Thornton’s Co., 1813)
Jesse L. Morton.