You might imagine that Vice President Gore decided to give the commencement speech at Thomas Jefferson High School for Science and Technology next week because the Fairfax County school symbolizes his commitment to scientific research and technological advances.

The vice president likes those things, to be sure. But what really is bringing him to Jefferson are the efforts of Katie Day, basketball star and senior class co-historian.

How did Day manage to persuade Gore to come? She succeeded in the way most high-schoolers find commencement speakers: she knew somebody. In this case, the key contact was her father, McLean builder and architect Bart Day, who has been Gore's friend since high school.

That's how the game is played when Washington area high schools search for a famous person to speak at graduation. Every June, some schools get the visitor they craved while others, lacking the right connection, wind up with nothing more than some regretful replies written on celebrity stationery.

At most high schools, the senior class officers are in charge of finding a speaker, with the help of a faculty adviser. The seniors "want to have someone who they think will be worthwhile to the students, and they will put big names on their lists," said William G. Smith, a faculty adviser to the seniors at Damascus High School in Montgomery County.

School administrators often encourage that approach. A famous politician, athlete, actor or writer brings attention to the school and confers a sense of importance on all who attend the graduation.

Famous parents are usually the easiest to get. Queen Noor of Jordan spoke at her son's graduation at the Maret School in Washington this month, as did columnist George F. Will at his daughter's graduation from the National Cathedral School.

But the celebrity-hunting effort often requires some patience and savvy. Hillary Rodham Clinton agreed to speak at the Bethesda-Chevy Chase High School graduation after receiving a letter last fall from seniors Carter Beach, Jonathan Ruckman and Micah Baskir. All three have parents who know the Clintons. The letter was delivered personally to the White House by Carol Beach, Carter's mother, who writes for Hillary Clinton.

According to Carol Beach, the letter pushed every conceivable button. It mentioned the 1937 Bethesda-Chevy Chase commencement address of Eleanor Roosevelt, referred to the school's diverse student body and public service programs, and noted that the commencement would be in Constitution Hall, just a short stroll from the White House.

At some schools, the same celebrity is pursued year after year. Washington-Lee High School in Arlington has landed such speakers as Colin L. Powell and Attorney General Janet Reno, but actress and alumna Sandra Bullock still hasn't been able to find a hole in her schedule.

Principal William Sharbaugh, who is retiring this year after 24 years at the school, remembers Bullock as a pleasant student and fine cheerleader. He said she had tentatively promised to speak two years ago, but had to cancel "because she was doing one of those `Speed' movies, or whatever it was."

Bullock had to turn the school down again this year, but Sharbaugh said "she promised she would take care of us someday."

This year's Washington-Lee seniors also had hopes of getting an acceptance from Secretary of State Madeleine K. Albright, a friend of one student's parents, but Albright's spring proved to be too busy. The graduates instead will hear Lawrence R. Baca, president of the Native American Bar Association, who also has connections to a Washington-Lee student.

Some celebrities are so hot that they're worth inviting even when they have no link to anyone at the school. Famous young actors Jennifer Love Hewitt, Leonardo DiCaprio and James Van Der Beek fall into that category, several Washington area students said. If nothing else, the graduation committee will have the thrill of examining the signature on the rejection letter. The invitee might even follow the example of Frank Sinatra, who would send large checks with his regrets, telling the class to spend it on the prom.

Seniors typically write to their dream choices in the fall. Reality sinks in around Christmas and they begin to focus on a somewhat less prominent group of names.

But some schools have sworn off celebrity speakers altogether. Debby Messer, a teacher at Hammond High School in Howard County, said students and faculty began to reconsider their annual hunt for a big name after a well-known politician -- she refuses to identify him -- addressed a Hammond graduation in the early 1980s.

"It was an election year, and a political speech, and it was so blatant and so removed from what mattered to the kids," she said.

The next year, the students decided that henceforth they would have a student be the keynote speaker.

That is also the system now used at T.C. Williams High School in Alexandria. The school's last celebrity speaker was President Gerald R. Ford, who addressed his son's graduation.

Manassas Park High School students have made it their policy to invite a teacher to give the main address. "This year they came and said they wanted to have, not a teacher from the high school, but an eighth-grade teacher many of them really liked," said Principal Margaret Huckaby. Coming up from Florida, where she has been living in retirement, is Patricia Zahl, who exposed a generation of Manassas Park middle-schoolers to the wonders of science.

At Jefferson, students appear to be happily anticipating Gore's speech and have congratulated Day and the other senior officers for their hard work. After Day's father spoke to Gore, the class leaders followed up with a letter pointing out how much the vice president's frequent emphasis on the Internet and advances in technology matched the school's goals.

Day said she has heard a few students worrying that a man running for president will likely have a political message. "But," she said, "I am very, very sure that is not going to happen."

CAPTION: Hillary Rodham Clinton, who spoke at the Bethesda-Chevy Chase graduation, is hugged by senior James Finlay.