Hi... Doesn't look like the same William Adams.Here is info provided by another researcher on the one who I believe is my ancestor:
WILLIAM ADAMS - born ca. 1763, died Sept. 1815 from wounds received during his service in the War of 1812. He was a Sargent. Mention of his also being in the Rev. War, but no documents have been found to prove this. He married 1788 MARY ELIZABETH HAWTHORNE. William Adams was a 2nd cousin of Pres. John Adams. He is said to have graduated from a Boys School in Edinburg, Scotland and after taught Writing in his alumni school. Mary was to have been from VA. They met while she was on a trip to Europe with her parents. After their marriage, they lived in Cumberland County, PA. After Wm.'s death, Mary migrated north with some of her children, who were then married, and lived in Counties of Allegheny, Lawrence and finally, Mercer Counties of Pennsylvania. Mary was a teacher also. She taught in a Girls Seminary School in Alexandria, VA before she was married and later in Transfer, Mercer County, PA. When Mary was quite old, she applied for a Widow's Pension at the Mercer County Courthouse, Mercer PA for her husband's service in the War of 1812. She was denied, though, as she did not know the name of the captain of his regiment.
William Adams and several of his sons (Matthew, William, etc.) were in the War of 1812. War records for Matthew Adams show he was in the 49th Regiment, Maxwell's.
MARY ELIZABETH (HAWTHORNE) ADAMS's father was: Rev. War JAMES HATHORN of Cumberland County, PA. James 2nd wife, was MARTHA (Brownfield) KERR. Martha may have been James' 2nd wife and not Mary's mother. Mary's brothers/sisters were: Alexander Hawthorne born 3/3/1776 married MARY McMURRAY and lived in Lawrence and Mercer Counties of PA, a sister who married ABRAHAM BOYD of Cumberland County, PA; James Hawthorne born 12/11/1774 married NANCY CLARK; a sister, PRUDENCE HAWTHORNE; and a sister, ANN, who married J. H. NEAL.
WILLIAM AND MARY ELIZABETH ADAMS had 11 children:
1. JAMES ADAMS - married MARY WOOLEATER, lived in South, had 20 children
2. MATTHEW ADAMS - born ca. 1801 in PA, in War of 1812, cripple, married to NANCY COLVERTSON, lived in Mercer, PA
3. WILLIAM ADAMS (JR.) - born ca. 1797 or 98, died in War of 1812, froze to death, was a drummer boy,never married
4. RICHARD ADAMS - born ca. before 1795, he and some other brothers are mentioned in their grandfather Hawthorne's Will
5. MARTHA ADAMS - married Rev. James Rodgers and lived in Wooster, Ohio and had a son… - THIS IS YOUR LINE?