Curiously enough, twenty-five years later, apparently without realizing the significance of his own statement, Burr himself confirmed that Hamilton’s bullet had hit the tree overhead. In his seventies, he returned to the dueling ground with a young friend and relived the dramatic encounter. Of Hamilton’s shot, he remembered that “he heard the ball whistle among the branches and saw the severed twig above his head.” Burr thus corroborated that Hamilton had honored his pledge and fired way off the mark. In other words, Burr knew that Hamilton had squandered his shot before he returned fire. And how did he react? He shot to kill, even though he had a clear shot at Hamilton and could have just wounded him or even stopped the duel. The most likely scenario is that Hamilton had fired first but only to show Burr that he was throwing away his shot . How else could he have shown Burr his intentions? As he had written the night before, he wanted to give Burr a chance “to pause and to reflect.” He must have assumed that, once he fired, Burr would be too proud or too protective of his own political self-interest to try to kill him.
Ron Chernow, Alexander Hamilton, 704.