Boston — * If Adlai Stevenson III gets elected governor of Illinois in November by more than half a million votes, he will immediately become a prime candidate for the Democratic presidential nomination in 1984.
* If Edmund G. Brown Jr. becomes the junior US senator from California, his presidential star will once again be on the rise.
* If Sen. Edward Kennedy of Massachusetts fails to carry his state by more than 200,000 votes, his White House aspirations may finally come to an end.
* If Tom Bradley is elected governor of California by a substantial margin, there will be a major attempt within the Democratic Party to ''move him as the running mate'' on the 1984 ticket. He would be the first black to reach this high an office.
These assessments come from a guru of American politics, the Boston-born Theodore H. White, who has chronicled US elections for more than two decades in his best-selling books. His latest, ''America in Search of Itself: The Making of the President, 1956-1980,'' just off the presses, deals primarily with the Reagan-Carter race of 1980 and the mood of America that heavily influenced its outcome.
Although the book makes no predictions about future presidential candidates, the pixieish, whimsical, feisty, and ever-buoyant Mr. White discussed 1984 Democratic prospects in an interview with the Monitor.
He says it is impossible to speculate about Republicans, since President Reagan's 1984 hopes are uncertain. But Mr. White points out that no US chief executive has served out two full terms since Dwight D. Eisenhower (1953-1961). Richard M. Nixon was reelected in 1972 after one full term, but resigned in the face of Watergate.
The 1984 Democratic field will begin to shape up seriously after this fall's election, he says, as victory margins in Senate and governors' races can make or break a candidate. Mr. Brown, for instance, appears to have a clear path to the Democratic nomination for California senator, he says. But in the general election, a loss or even a narrow win would likely derail him from the presidential track. Also, key constituencies play a role, he notes: ''How Kennedy does in South Boston is an important factor.''
Right now, according to Mr. White, the Democratic field lines up on three levels -- with former Vice-President Walter Mondale and Senator Kennedy as the front-runners. Sens. John Glenn of Ohio and Gary Hart of Colorado, as well as Governor Brown, are in the next group. Exploring are former Gov. Reubin Askew of Florida and Gov. James B. Hunt of North Carolina.
What will be the determining factors? The economy will be first and foremost, Mr. White says. The state of the cities and US foreign affairs, particularly Soviet-American relations, also will be vital issues. The Pulitzer Prize-winning journalist-historian (he copped the prestigious award for the first book in his presidential series, ''The Making of the President 1960'') says that if President Reagan could be credited with the ratification of an arms-control treaty, his political stock would sharply rise.
Political fortunes change rapidly, however, and sometimes with little warning , Mr. White cautions. He says that in 1958, when he first embarked on presidential chronicles, the leading Democratic candidate was then Gov. W. Averell Harriman of New York. That November Mr. Harriman was unseated in Albany by Nelson Rockefeller. And the same day, John F. Kennedy enjoyed a substantial senatorial victory in Massachusetts. The latter, of course, went on to win the Democratic nomination two years later and was elected president.
Mr. White also stresses the increased role of television in choosing some candidates -- and eliminating others. ''It's a kind of curious synthetic drama invading our politics,'' he says. ''We wouldn't have had a Jimmy Carter or [1972 Democratic candidate George] McGovern without television. Ronald Reagan might have made it. But he came up through television.''
The presidential chronicler says that often the printed media ''screen out'' potential White House candidates for television. For example, he pointed out that this newspaper's regular breakfasts with politicians, led by Godfrey Sperling Jr., catches the eye of the networks. Then they decide who is marketable.