With the return of Sen. Howard H. Baker Jr. (R-Tenn.), there are now a dozen of them -- a club within a club that spans more than three decades of squelched presidential ambitions.

They are the senators who reached for the brass ring and missed, the ones who continue to ride the congressional carousel even after losing the big prize, knowing it will probably never be theirs.

Every four years their ranks grow, even though history indicates the odds are against an incumbent senator winning the presidency, or even his party's nomination.

They run even though the odds keep widening as presidential campaigning stretches into a full-time job spanning three or four years, making it increasingly difficult for a senator to run for president while tending, even negligently, to his legislative charges.

And they run even though the qualities that make many of them effective senators -- workhorse as opposed to showhorse skills -- tend to bomb on the presidential campaign trail.

When they return, they liken the experience to a trip that was exhilarating right up to the crash-landing. "There's no question that it's a let-down," said Sen. George McGovern (D-S.D.), who came back to the Senate after winning the Democratic presidential nomination in 1972 and then losing to then-President Nixon.

"You're out of the limelight, you're out of the main arena. It's difficult for anyone to watch yourself night after night on network television, to see yourself on the front page of metropolitan dailies, and then, all of sudden, silence. You are back in the ranks, one of 100 senators. But I can truthfully say I don't have any regrets -- except that I lost."

Since Franklin D. Roosevelt, most presidents have served at one time or another as senators, encouraging the Senate's reputation as a presidential pre-school. But most of them entered the White House through the back door of the vice presidency. The only senator since Warren Harding in the 1920s to move directly to the presidency was John F. Kennedy in 1960.

Of the former presidential candidates now in the senate, only two, Barry Goldwater (R-Ariz.) and McGovern, won their party's nominations, and both were buried in their general election campaigns.

Yet they keep running, as many as half a dozen at a time, each hoping to be the exception.Every four years, the notion of the Senate as presidential springboard gets reinforced by the fact that so many of the candidates are senators. Actually, it is less of a springboard than a revolving door, moving them through what may be a valuable, broadening and humbling experience but dumping them out where they started in terms of personal ambition.

At one point or another, there were five senatorial entrants in the 1980 presidential race. Now there is effectively just one. Sens. Lowell Weicker (R-Conn.) and Larry Pressler (R-S.D.) bowed in and out before the race really got started. Sen. Bob Dole (R-Kan.) hardly got going before washing out (though he has yet to issue a formal statement of withdrawal).

Baker concluded that his campaign was headed nowhere, and ended it after a demoralizing string of third- and fourth-place finished in the first few primaries, straw polls and caucuses.

This leaves Sen. Edward M. Kennedy (D-Mass.), whose identification is more with a family tradition than with the institution of the Senate. He could be the exception that proves the rule, but his colleagues are keeping a chair warm for him, too, just in case.

The Class of '76 is a large one also: Henry M. Jackson (D-Wash.), Frank Church (D-Idaho), Birch Bayh (D-Ind.), and Lloyd Bentsen (D-Tex.), who, together with former senator Fred Harris (D-Okla.) and Rep. Morris K. Udall (D-Ariz.), fell victim to Jimmy Carter, who never served a day in Congress.

Earlier classes include Goldwater, McGovern and Edmund Muskie (D-Maine), who was a candidate for president in 1972 as well as the Democratic nominee for vice president in 1968.

But they are all late-bloomers in comparison to the unofficial dean of the group, Sen. Strom Thurmond (R-S.C.), whose Dixiecrat crusade of 1948 is almost ancient history.

As a whole, these presidential alsorans have reconciled themselves to the nation's rejection of their highest ambitions and gone about their business, although many concede it was painful -- for some deeply so -- to lose.

"We're all very ambitious people, all of us with egos, or we wouldn't be here," said one who was reluctant, like many of them, to discuss his or his colleagues' wounds on the record.

"You want to accomplish the most you can, you want to leave some tracks . . . and the office you can do the most is in the presidency. You look around [at others who are running] and wonder what makes them any better qualified then you are . . . it's a tough experience. We're all achievers and we don't like to lose."

Like most others, McGovern spoke of new insights and broadened understanding of national problems, a gain that many old compensated for the losses.

There is also comfort in numbers back home in the Senate, a kind of collegial reassurance that there is no disgrace in running and losing, even losing badly. If there were, then why would the honor roll of losers be embellished with names like Hubert Humphrey and Robert Taft or be lengthened every four years with a Muskie, a Jackson or a Baker?

"After all," noted Jackson in a bittersweet observation about the fizzled campaigns of Senate luminaries like himself, "we haven't gone yet to a merit system for the selection of presidents."

Moreover, the return of a presidential campaign dropout becomes a ritual, a drawing together of the family at a time of one member's grief.

On his first day back, Dole said three or four members of earlier classes went out of their way to welcome him back to the fold, most of them, incidentally, Democrats. As Baker noted last week, after returning to his old job as Senate minority leader and receiving a courtly welcome from Majority Leader Robert C. Byrd (D-W.Va.), the warmth and camaraderie" of his colleagues was balm for the bruises.

The Senate itself -- its power as well as its pleasures -- keeps many from drifting off, despite the disappointment of unfulfilled ambitions. Of the two Minnesota Democrats who figured so prominently in presidential politics a decade ago, former Senator Eugene McCarthy chose not to return, but Humphrey came back after an absence of six years.

"Many who have paid the price for running -- and it is a high price -- are often also the ones who will by nature seek out something else to accomplish," and find it can be done best in the Senate, suggested Bentsen.

Muskie, who was probably stung as much as any senator by defeat, went on to become the principal budget man in the Senate, if not Congress. Jackson figures he is more active than before, and Church has stayed on to become chairman of the Senate Foreign Relations Committee.

Bentsen figures the day is over when a member of Congress can run with any reasonable hope of success without giving up his House or Senate seat. Citing the examples of Carter in 1976 and George Bush in 1980, he said, "There's a lot to be said for the notion that a person has to be out of work to be elected president." If he had to do it again, Bentsen said, he would have joined the ranks of the jobless before running.

Church points to the proliferation of state presidential primaries since John Kennedy ran in 1960, and says it puts a premium on freedom to campaign fulltime. Others noted that Kennedy was secure enough in his Senate seat virtually to abandon it for the campaign -- a luxury that few can afford today. v

Not only does this make it hard for a senator to run without quitting, but it will increasingly keep good people from trying, according to Sen. Adlai E. Stevenson (D-Ill.), who flirted briefly with the idea of running in 1980. "My father [the Democratic presidential nominee in 1952 and 1956] couldn't stand three primaries, let alone 37 of them . . . I don't think he would have even gone into that kind of situation."

Not all of the also-rans agree that a senator would have to quit to win. At one with a vantage point of having won his party's nomination, McGovern believes issues and organizational efforts, coupled with judicious balancing of time spent in the Senate and on the campaign trail, are the governing forces. Even some of the unemployed contenders are having problems, he noted.

Dole is perhaps an extreme example of what happens to a "weekend campaigner," as he called himself. But he also sees other problems for a senator who reaches for the presidency.

At one point during his nearly fulltime involvement in the crude oil tax debate late last year, he flew to Iowa and back one night for what turned out to be a one-minute introduction at a Farm Bureau candidate's meeting. Although he had been involved that day in pushing for a gasohol tax credit, presumably a matter of interest to Iowa's farmers, they refused to let him speak because he had missed his alloted time in the afternoon. "It's crazy, just crazy," he said.

But senators also often find that the skills they so deeply value can simply bore voters, Dole said. "You're so into issues that you sound like you're running for reelection to the Senate, not the presidency," he said.

"When people ask you what time it is, you tell them how to make the watch when all they want to know is the time. People want to deal in concepts, not specifics. They're happy to know that you know so much, but they really don't want to hear all the details."