Suddenly, DiMaggio was confronted with logistics. He had a tuxedo at the home of his close friend, Joe Camilleri, in Miami. But he had no formal shirt, no airline reservation, no transportation, no place to stay in Washington. But, with one swing, so to speak, he solved all problems. He called another close friend, Edward Bennett Williams, the celebrated lawyer who owns the Baltimore Orioles.

''He called me back on his car phone,'' DiMaggio remembered. ''And I asked him, 'Ed, did you get an invitation to the White House dinner?' He said no. I said, 'Well, I did, and I need some help.'

''He arranged my flight to Washington. He sent his driver, Leroy, to meet me at the airport. He put me up at the Jefferson Hotel, which he owns. He even gave me one of the six overcoats he keeps in his office. And Leroy went out hunting for a formal shirt my size, and found one in Georgetown on the third try.''

By now, DiMaggio had a purpose to go with his finery. But he needed a baseball. So Leroy drove to an Orioles souvenir shop, also owned by Williams, came out with a dozen baseballs and headed for the White House.

''I took one and put it in the pocket of Ed's overcoat,'' DiMaggio said. ''But how do you get a baseball signed at the White House? It was a million-to-one shot.

''But when I checked my coat, I asked the checkroom lady to keep my coat nearby because I might want to come back and get something out of the pocket. And all during dinner, I kept thinking of it.

''On the receiving line, the greeter asks how you'd like to be introduced. I said, 'Just Joe DiMaggio.' Then the President introduced me to Mr. Gorbachev and said, 'This is one of our greatest players in the United States.' Mr. Gorbachev looked as though he knew me.