Washington — They used to poke fun at the vice-presidency. John Adams, the first American vice-president, wrote his wife Abigail that the office was ''the most insignificant office that ever the invention of man contrived.''
Thomas Jefferson, who next had a stint at the job, complained there was ''hardly enough to live on.'' The third vice-president, Aaron Burr, was indicted for murder and tried for treason.
Whether men of distinction, dullards, or scoundrels filled the second-highest position in the land, the office over the decades of American history came to be viewed with scorn. But no longer.
As Democratic presidential nominee-apparent Walter F. Mondale searches for his No. 2 man - or woman - he is making one of the most important decisions of his political life.
''It is time to take the vice-presidency seriously as a major resource for presidents and an office of great potential for its incumbents,'' says political scientist Paul C. Light of the Brookings Institution. The office can further a politician's presidential prospects. It can also heighten his or her influence on government policy.
Writing in the coming summer issue of the Brookings Review, Dr. Light cites three changes that have transformed the vice-presidency in the past decade into a significant office:
* Vice-presidents no longer are relegated to cutting ribbons, attending funerals, and other ceremonial functions. They now have solid political and policy roles as players in election campaigns, as congressional lobbyists, and as senior presidential advisers.
* Their resources and staffs have vastly increased. Vice-President Lyndon B. Johnson had a staff of fewer than 20; Vice-President George Bush has about 70 and an annual budget of $2 million. He also has an official residence and even a seal and flag. Most important, the last two vice-presidents have had offices in the West Wing of the White House - not far from the Oval Office.
* Presidents have come to realize how helpful vice-presidents can be as allies and advisers - especially given the decline of national party organizatons, the diffusion of power in Congress, and the complexity of national and global issues the president must deal with.
The emergence of a strong vice-presidency began after the Watergate scandal, Light says. Gerald Ford, as a condition for replacing Spiro T. Agnew, demanded more staff and more independence. Then when Mr. Ford succeeded to the presidency , he gave his second-in-command, Nelson A. Rockefeller, increased duties such as chairmanship of the Domestic Council.
''It remained for Walter Mondale to consolidate and build on the gains that had been made and, in so doing, to establish a powerful precedent for future vice-presidents,'' says the scholar. Mr. Mondale became a member of President Carter's inner circle and influenced Cabinet appointments, establishment of the Department of Education, decisions about the Shah of Iran and the US hostages in Tehran, and policies on electoral reform, job training, and hospital costs.
Mondale also had setbacks. But, despite them, Light says, Mondale's influence raised expectations about the office and ''made it more difficult for future presidents to turn back the clock.''
Like his predecessor, George Bush has maintained a low profile. But President Reagan has followed the precedent set by Carter by giving his vice-president significant duties and influence, especially in foreign-policy crises where Reagan himself has had little experience.
For example, as chairman the administration's crisis management body, Vice-President Bush did more than guide the discussions at the time of the Lebanese crisis. He actually advocated withdrawing the US Marines from Lebanon. He also opposed having the President attend the funeral of Soviet leader Yuri Andropov. Bush went instead, and was treated by the Soviets as the President's emissary.
Today the vice-presidency is a good jumping-off place for politicians with presidential ambitions, Light says. A vice-president has contact with state and local officials who could become his allies. He gets good on-the-job training, improving his political skills. It gives him opportunities to demonstrate his loyalty to the president's wing of the party. And it assures him of extensive media coverage.
Light points to the importance of choosing a vice-presidential nominee wisely , cautioning, ''the qualities that make for an appealing running mate may not make for a smooth working relationship in office.'' The general pattern, he says , is to seek ''balance'' in a ticket on the basis of geography, ideology, or, as it is now being suggested, gender.
But the most important balance for a strong vice-presidency, writes the scholar, is ''the one between Washington insiders and outsiders.'' Thus, the most recent ''outsider presidents'' - Eisenhower, Carter, and Reagan - selected ''insiders'' as their vice-presidents, all of whom extended their role and power in office.The opposite combination - insider presidents with outsider vice-presidents (as in the case of Nixon-Agnew) ''is the least likely to succeed.''
Historically, the balance with the most uncertain outcome has been an insider teamed with an insider, Light says. That pattern has occurred the most frequently in the past four decades. In some cases (Roosevelt-Wallace), the vice-president has played a signficant policy role. In others (Kennedy-Johnson), he has not.
Political factors are bound to weigh heavily in vice-presidential selections. But, argues Light, presidential nominees should supplement political considerations with a second set of criteria: ''compatibility, leadership qualities, experience, intellect, and savvy.''
The pressure by women's groups to fight for a woman nominee on the convention floor has potential pitfalls, according to Light. ''If the Democratic convention nominated someone for vice-presidentwithout the presidential nominee's involvement, that would be a blow to that office,'' he said in a telephone interview. ''As much as one sympathizes with the desire to nominate a woman, it would be damaging to the women's movement and to the vice-presidency to come to the floor without Mondale's approval.''