Here is a little on Patrick H Hamilton.
www.tngenweb.org/civilwar/rosters/inf/inf2/cok2.html#vn36
Patrick H Hamilton
Rank: Prvt
Age: 28
Enlisted: Mar 17 63 Mustered: June 5 63
www.tngenweb.org/civilwar/rosters/inf/inf2/col2.html#vn42
Patrick H Hamilton
Rank: Prvt
Age: 28
Enlisted: Mar 17 62 Mustered: June 5 63
http://home.cinci.rr.com/secondtennessee/roster.html
Hamilton, Patrick H; Private; K; Knox Co TN; 26; 17 Mar 1863 - 3 Aug 1865. Honorable discharge. Died 12 Jan 1926 at Cedar Co MO. Born in Jefferson Co TN. Married. Residence Knox Co TN. Captured at Rogersville. Confined at Belle Isle. Paroled at City Point VA 7 Mar 1864. At Camp Parole MD 9 Mar. Admitted to hospital then returned to Camp Parole in Apr. At Camp Chase OH 30 Apr. Sent back to reg 18 May 1864. Deserted 24 Dec 1864. Returned and restored 2 Jan 1865.
By the way I have some Hamiltons in my Family tree, from New England though.