To the Editor:

Alexander Hamilton's efforts to handle an attempt to expose his affair with Maria Reynolds is discussed in ''Hamilton's Troubles'' (letter, May 15). The letter says that ''Hamilton went to President James Monroe and confessed the sordid story.'' Monroe was not yet President. The year was 1792, when Hamilton was Secretary of the Treasury.

Hamilton did tell the story of his affair, but it was at his home in Philadelphia, and he told it not only to Monroe, then a United States Senator from Virginia, but also to Abraham Venable, a Virginia Representative, Oliver Wolcott, Comptroller of the Currency, and Frederick Muhlenburg, lately Speaker of the House.

The letter also says that when the story of the affair cropped up again in 1797, Hamilton ''was certain that President Monroe was responsible for the 'leak.' '' James Monroe was at the time an opponent of Hamilton, believing, with some justification, that Hamilton had been responsible for Monroe's recall as Minister to France. Again, however, Monroe was not yet President. He became President in 1813, and Hamilton was killed by Aaron Burr in 1804. The letter says, too, that Hamilton thought of challenging Monroe to a duel, but was dissuaded by friends. It was, however, Hamilton who felt he was responding to a challenge from Monroe. It was Monroe who had to try to calm things down. He did so through an intermediary, and the duel did not take place. Monroe's intermediary in 1797 was, of all people, Aaron Burr. BERNARD JOHNSTON Brooklyn, May 16, 1987