According to Justice Joseph Story, "the whole audience had been wrought up to the highest excitement; many were dissolved in tears." But it was Webster's legal reasoning that most influenced the Court, which ruled that the contract clause of the Constitution protected private corporate charters. Chief Justice John Marshall's majority opinion in favor of the college closely followed the logic of Webster's brief, and the case became a landmark defense of contracts. During his later career in the Senate, Webster frequently appeared before the Supreme Court, but he considered the Dartmouth case his greatest victory.
Back at Dartmouth, students celebrated by firing a cannon. The grateful college arranged for Gilbert Stuart to paint Webster's portrait, which today hangs in Dartmouth's Webster Hall.
For further reading:
Shewmaker, Kenneth E., ed. Daniel Webster, "The Completest Man (Hanover, N.H.: University Press of New England, 1990)