The hand shakes, the jaw drops, the mind boggles at the thought of Smithsonian Secretary Robert Mc. Adams -- not known as a glad-hander -- having to stand in a receiving line for 19 days to greet the estimated 44,000 guests invited to 21 symposiums, dinners, luncheons and receptions celebrating the new Quadrangle.

The Smithsonian Institution answered that problem by leaving the receiver off the hook: it quietly cut receiving lines from the festivities.

But for the grace of Adams, almost a thousand people a night would have cursed the rain as they waited in line in the Enid A. Haupt garden last week at the openings of the Sackler and African museums and the S. Dillon Ripley Center. Instead, guests came in at their own pace, after celebratory drinks and crepes in the Arts and Industries Building, and then went down into the mysterious and marvelous underground museum complex. You might have found Jill Sackler (donor with her late husband Arthur Sackler of $4 million and priceless art objects), Warren Robbins (founder of the African museum), Adams and Ruth Adams (director of the MacArthur Foundation's peace project), Tom Lawton and Sylvia Williams (directors respectively of the museums) in deep discussion with some great art expert who wanted to say more than "how d'ye do," behind a Chinese bronze vessel, beside a case of silver ornaments, around the corner from a stone stele or by a tall textile.

"A receiving line only serves to hold up movement at an exhibition," says Joe Coudon, Adams' assistant.

"The secretary preserves ritual only when it has an important function that can't be handled any other way," explains Ralph Rinzler, assistant secretary for public affairs. "A formal receiving line makes a substantive exchange impossible."

"The Smithsonian has never been much for lines," says Barbara H. Spraggins, its head of special events. "We don't have formal receiving lines for big parties. They're bottlenecks." She pointed out that at the more intimate dinner of the Sackler Gallery in the Quadrangle (280 people), Adams and Jill Sackler stayed close to the door during cocktails. "They greeted people, but not formally."

However, Washington's custodians of customs stand fast to the belief that it's more blessed to receive than to give up on greetings.

"I am astounded!" Clement Conger exclaims at the thought of an end to the line. Conger is chairman of the State Department's Diplomatic Reception Rooms Fine Arts Committee, Blair House curator, former White House curator and a former deputy protocol chief -- dean of the profession of shaking money loose by shaking hands.

"Too bad, not to have a line when you have such an attractive person. Mrs. Sackler is so young and beautiful everybody wanted to be sure to meet her," Conger says. "I realize that with a thousand people, the line gets so long, you're stuck and can't circulate. At our biggest party of the year, we have a few more than 550. Even so, we receive for an hour and a quarter.

"We open the door to the Jefferson Room so those who don't want to go through the line can go on in and have a drink. Often they watch the line and double back when it isn't so long. You have to tell the architects all of this when a building is planned -- or spend a great deal of money straightening it out, as we have."

White House social secretary Linda Faulkner, a guest at some of the Quadrangle events, says: "Things at the White House are different -- we're stuck with tradition, a certain degree of protocol. But even here, sometimes, especially at a South Lawn party, the numbers are beyond what Mrs. Reagan can stand for. When there's a big party and the president speaks, it does happen that he comes in after the crowd assembles. Everyone has the opportunity to see him on the platform. Then he greets people afterward."

Selwa Roosevelt, U.S. chief of protocol, defends the line: "It's the only chance people have to meet the hosts. It may be different for shows and exhibitions, but at a formal dinner or reception, a receiving line is important -- though a formal line isn't necessary if there are less than 40 guests."

And Helen (Mrs. Gladstone) Williams, who for 24 years has held the Executive School of Protocol in her magnificent R Street house, says: "It's awkward to be a stranger and not be greeted by anyone. The only way to do it is have teams of officials taking turn receiving guests. And I can see, with so many floors, you'd have to have auxiliary greeters."

Miss Manners herself, syndicated columnist and novelist Judith Martin, has the last word: "You shouldn't invite more people than you can say hello to. The point of a receiving line is to facilitate saying 'how do you do' and 'thank you, I had a good time.' Anyone with manners is obligated to search for the host and guest of honor. The absence of a receiving line encourages the current belief that parties just happen and therefore guests are under no obligation to anyone."

And of the Quadrangle affair? "Apparently, this is just a public event," Miss Manners says. "I hope at least the guard says a warm word to guests."

Standing up for receiving lines, sitting down at cocktail parties -- is this the end of the whirl as we now know it? Who will hold the line