http://www.history.army.mil/books/R&H/R&H-1Art.htm
I believe if you look in section 303 of this site you'll see the answer:
"The regiment was at first stationed at the posts in New York Harbor and on the New England coast, but after a service there of six years it was sent to the more southerly posts between Annapolis, Md., and Charleston, S. C., where it remained, though with many interchanges of station by the several companies, until January, 1836, when eight companies reached Florida, followed in October of the same year by the ninth."
There's a lot more on the site.