Gov. Mario M. Cuomo came this morning to the mock Democratic convention at Washington and Lee University, which over the years has compiled a remarkably accurate track record in forecasting Presidential nominees, and told a raucous group of students that "the next President of the United States should be the candidate you nominate before the Virginia sun goes down."

It was all over by 1:30 P.M. The winner on the first ballot was Gov. Bill Clinton of Arkansas.

Shortly after that the students, who have a more erratic record with Vice Presidential selections, tapped Mr. Cuomo for that job on the second ballot. Governor Cuomo, who was already on a plane back to Albany when the balloting was going on, has categorically denied any interest in ever being Vice President and repeated his stance when a reporter for the student newspaper asked him about it before the vote.

From 1952 on, the mock convention, always held for the party out of the White House, has correctly picked the eventual nominee every year except 1972, when students passed over George S. McGovern and chose Edward M. Kennedy instead.

Another Cuomo Keynote

This time around Mr. Clinton won 809 delegates on the first ballot, just four more than the number needed to win, to 563 for Paul E. Tsongas of Massachusetts, 120 for Senator Tom Harkin of Iowa, 107 for Edmund G. Brown Jr. of California and 12 for for Senator Bob Kerrey of Nebraska, who dropped out of the race earlier this week.

There was some speculation that Mr. Cuomo, who received $20,000 and transportation by private jet in return for delivering the keynote speech at the mock convention, might, with his oratory, secure the top spot on the ticket for himself.

But while many students said they were moved by the Governor's 40-minute speech, which he told them was similar to the famous keynote he delivered in 1984 to a real Democratic convention in San Francisco, they noted that their vote was supposed to be based on research of expected voting patterns, not their own preferences.

"You'd like to, but you can't do it on emotion," explained Andrew Wright, a freshman from Corvallis, Ore., who described himself as a lifelong political junkie who was a "Carter supporter in diapers." Mr. Wright, chairman of the Idaho delegation, said his mock homestate voted first for Mr. Harkin then switched to Mr. Clinton in a vote of acclamation.

The Scientific Method

The campus's mock convention has been a quadrennial tradition here in the Blue Ridge Mountains since 1904, and some of its impressive record of prognostication has been inadvertent.

In 1924, for instance, in a sentimental move, students nominated a little-known Wall Street lawyer, John W. Davis. He was not a declared candidate, but he had the advantage of being a Washington and Lee alumnus. As things turned out, however, delegates at the real Democratic convention deadlocked on 102 ballots on the major candidates then turned to Mr. Davis on the 103d.

These days, however, the decision is made far more scientifically by delegations proportionally the same size as the real ones, which helps to explain the good track record.

The chairman of the Guam delegation, Vince Keesee, who is actually from Georgia, said its seven members telephoned several politicians, journalists and professors in the South Pacific and guaged that Bill Clinton would be the island's man.

Colorful Speeches

Nearly every one of the 1,600 undergraduates participates in some way at the convention, financed in part by a Dallas philanthropist. The campus's sweltering gymnasium was packed with cheering delegates, most waving flags or placards. One, borrowing the lingo of the "Saturday Night Live" skit "Wayne's World," read: "Kerrey for President / Not!!"

And just like a real convention, individual state delegates often prefaced announcement of their votes with colorful characterizations of their states. The "great state of Virginia," its chairman announced to loud cheers, was "proud to be the home of the mother of all Presidents, George Washington."