This is Reverend Archibald Alexander (April 17, 1772 – October 22, 1851). He was the grandson of the Archibald Alexander who was the first sheriff of Augusta County, Virginia. He attended what is now Washington & Lee University and became a minister at the age of 21. He also served as president of Hampden-Sydney College. When the Princeton Theological Seminary was established in 1812, Archibald Alexander was appointed its first professor. There is an Alexander building on campus that was named for him.
He married Janetta Waddell, the daughter of another minister, James Waddell. Their branch of the family largely stayed in the New Jersey & New York area. He is my first cousin five times removed.