A Prince, a First Lady, and 1,300 men in blue

Prince Charles, heir to the British throne, has no direct responsibility for Great Britain's policies -- that devolves on his mother, Queen Elizabeth II, and on another woman, Prime Minister Margaret Thatcher.

But the nation's troubles nonetheless follow the Prince wherever he goes -- a reality neither he nor the New York City Police Department could help but be aware of June 17.

It was a pleasant day in the city, and Charles determinedly enjoyed it. He had lunch with First Lady Nancy Reagan and Mayor Edward I. Koch as they toured New York Harbor on a yatch lent by publisher Malcolm Forbes; attended a reception at Lincoln Center, followed by a 50th anniversary benefit performance of "The Sleeping Beauty" by the Royal Ballet; and capped the day (or night) at a ball, dancing with Mrs. Reagan.

No matter that Irish Republican Army sympathizers tried their best to spoil it: The Prince was heckled by demonstrators when he disembarked from the harbor cruise near South Street Seaport, and outside Lincoln Center. In the Metropolitan Opera House, a couple of people who shouted epithets at him were quickly removed by police.

Police guarding the Prince -- some 1,300 of them at a cost put by city officials at $300,000 -- heaved a collective sigh of relief when his 24-hour visit to Manhattan ended at 10:32 a.m. June 18. (Naturally, the city will seek reimbursement from Washington.)

"New York's finest," as the police here are sometimes called, were for the most part successful in steering demonstrators clear of the Prince's path as he moved about the city. A contingent of some 300 US State De partment personnel and Secret Service agents helped.