Hamilton's father was an assistant to Robert Adam, who sent William to Rome, where he studied under Zucchi. He returned in 1769 and entered the Royal Academy Schools, becoming a full Academician in 1789. He painted portraits until 1789 subsequently concentrating on subject pictures of biblical, historical or Shakespearean themes. In watercolour he executed illustrations for the poetical works of Gray, Milton and Thomson. His style is similar to Cipriani and Angelica Kauffman.
The nine muses with their domains are Calliope, epic poetry; Clio, history; Erato, love poetry; Euterpe, music; Melpomene, tragedy; Polyhymnia, sacred poetry; Terpsichore, dancing; Thalia, comedy; Urania, astrology.