Prior to 1854, both army officers and enlisted-men's uniform buttons had the initial letter of their branch of service (Infantry, Artillery, etc.) on the shield on the eagle's chest. In 1854, the regulation was changed, to only Officers having the "letter-in-shield" buttons. So, your 1860-to-65-manufactured Horstmann & Allien NY eagle-I button was worn by a US Infantry Officer, of either Lieutenant, Captain, or Major rank. (Colonels and Generals wore the 3-piece Staff Officer type buttons.)