The Smithsonian Institution's newest building on the Mall -- it's been growing in a hole at 10th Street and Independence Avenue SW since 1983 -- is just about completed now. But still one can't help wondering: What is it they have built?

Its scale is deceptive, its architectural allusions intriguing but misleading. No wonder the new Quadrangle -- it will open to the public on Sept. 28 -- baffles passers-by. Its design is strangely mute. It doesn't tell you what it is.

You see: a trim Victorian garden with stately gates and gravel walks, clipped trees and parterres. That elegant, four-acre park -- it looks just about as old as the turreted and touching Smithsonian Castle to its north -- calls to mind a day of parasols, straw boaters and croquet. But it's actually brand-new. It cost $3 million. The Enid A. Haupt Garden (she gave the Smithsonian the money) feels comfortably earth solid when you step upon its lawns. But there is hollowness beneath you. It's been grown upon a roof.

You see: a pair of granite-faced pavilions. Both send out mixed messages, some new and some antique. One is roofed with pyramids that hint at ancient Egypt, though the new museum underneath it, the Arthur M. Sackler Gallery, holds no Egyptian art. The other is roofed with domes like those of the tiled mosques of Persia. It leads to the National Museum of African Art, a museum that, of course, contains no Persian art.

You see: a third building called the Kiosk. It is domed, round, almost cute. Built between the Castle and the Freer Gallery of Art, it has the friendly, slightly silly look of a folly in a park. The Kiosk is the entrance to the third part of the complex, the part least well understood.

What you can't see is enormous. What appears to be a trio of unprepossessing buildings is actually one vast one, a structure of 360,000 square feet -- 96 percent of which has been constructed below grade. The work of Jean-Paul Carlhian, a fanciful designer, it cost $73.2 million. In some ways it resembles a huge, flat-bottomed boat, double hulled and waterproofed and shoved beneath the ground.

Its first two decks are occupied by the new museums. The third (whose floor is more than 50 feet below the level of the street) includes an 8,000-square-foot concourse, a sort of indoor avenue 28 feet wide and nearly football-field long. The offices, mostly sunless, that flank that buried street will house the Smithsonian Institution's Traveling Exhibition Service (SITES), the National Associate Program, the Resident Associate Program and much else besides. There's a new Education Center (whose classrooms have been paid for by the Pew Memorial Trust) and a new International Center with a still-vague program and a gallery as well.

That third level will be named for S. Dillon Ripley, the former Smithsonian secretary who dreamed it into being. It is in part an exhibition space, in part an office building and in part something else.

Ripley says it "grew like Topsy." It doesn't have one founder, but more than half a dozen. Generosities and hauteurs, triumphs and defeats, real estate accidents and political affections called it into being.

Its seed was planted -- inadvertently -- by Charles Lang Freer (1856-1919), a businessman-industrialist-collector from Detroit. Had Freer been less particular, the new Smithsonian complex might not be there at all.

We think of lords of industry as rough-and-tumble guys. But Freer -- who made his fortune by merging 13 railroad supply companies -- found roughness appalling. Freer was a disciple of James McNeill Whistler, the art-for-art's-sake painter, and once he made his fortune, he gave himself wholeheartedly to the subtle contemplation of the high esthetic life.

The home gallery he built himself was sky lit, serene, bare. No cases held his holdings of Japanese and Chinese and Middle Eastern art. Instead, at his summons, his former coachman Stephen would bring out Freer's art treasures one object at a time. The master, while admiring them, would sip tea of his own blending, or perhaps fine old champagne. His decorous meditations would cease at fall of evening. The collector was convinced the beauties of his objects were diminished by the crassness of artificial light.

More than half a century ago, when Freer agreed to build a new museum for the nation, a reporter sought an interview explaining that he wished to write a popular sort of article so that common folk could understand the new Freer Gallery of Art, which opened to the public here in 1923. Freer refused the interview. He thought dealing with the public entirely inappropriate. No touch of commonness must blight his new museum on the Mall.

Had Freer been more tolerant, the next-door Sackler Gallery might never have been built. The Smithsonian does not really need two separate museums of oriental art, or wouldn't if the Freer worked like other institutions. It doesn't. At the insistence of its founder, who shuddered at the thought of taste less exquisite than his own, the Freer remains apart from the wide museum world. It neither lends nor borrows art.

In his day, art museums stressed their own collections. But that's no longer true. Borrowed exhibitions are now central to their mission. But not at the Freer. If a collector as distinguished as, say, the emperor of Japan wants to let this city see his rarest, finest treasures, he will have to find a venue outside the Freer.

The Sackler fits that bill.

It, too, will be a gallery of oriental art, but unlike its older neighbor, it will not strive to seem unchanging. Its 18,000 square feet of exhibition space will welcome borrowed shows. It will lend from its collections. Though scholar Milo Beach, 47, who has come to Washington to run it, does not use the word, the Sackler he envisions will be less "elitist" than the Freer.

Stands will be constructed in front of many Sackler cases so that children can peer in. One inaugural exhibit, "Monsters, Myths and Minerals" will include an explanation of the Chinese zodiac. There will be photos on the wall, and folk art on exhibit. Beach would be delighted if carpenters and craftsmen came to learn a thing or two from the Chinese furniture.

Beach says, "I see the Freer as a sort of Courtauld, an institute of advanced study, an extraordinary graduate school for specialists and scholars already committed to their subject. The Sackler comes in as a kind of undergraduate college, a place where students can be introduced to oriental art."

Freer valued high refinement and absolute decorum. Sackler, who was Brooklyn-born, was an earthier and friendlier and more ebullient man. "Even in his seventies, he was happy to climb ladders, in the coldest days of winter, in the Quadrangle's construction pit," Milo Beach remembers. "He had always been interested in the roots of human genius. That's one reason why he loved the oldest Chinese art."

The Sackler, as it opens, owns perhaps a thousand pieces of fine Japanese and Chinese and near eastern art. Though all of them are gifts from the late Arthur M. Sackler (1913-1987), it was not he who chose them for the new museum. They were picked from Sackler's holdings by scholar Thomas Lawton, the director of the Freer. Sackler, a New York medical researcher and publisher (who made much money from Valium), was also a collector of far-ranging taste.

He might have built a very different sort of institution; he happily collected pre-Columbian figurines, 19th-century French paintings, Piranesi prints and Renaissance terra cottas in addition to the oriental works (worth considerably more than $50 million) that he gave the nation.

Although they share a staff, a library for research and a conservation laboratory, the two oriental galleries, the Sackler and the Freer, will never merge. But they'll eventually be linked. Construction will begin in about a year on a suite of four connected galleries that will tie the two museums together underground. Selected objects from their holdings, as well as works from elsewhere, will then be shown, as Lawton puts it, "if not together, cheek by jowl."

The Sackler has three fathers -- Sackler, the acquirer and donor, Lawton, who selected the things in Sackler's gift, and Beach, who's most responsible for how they'll be displayed. The National Museum of African Art might be said to have a parentage of a different sort.

The museum has a father, its founder, Warren Robbins. It also has a mother, or at least a stepmother. She is Sylvia H. Williams, who was appointed its director in 1983. Sometimes striving toward a common goal -- and sometimes working at cross-purposes -- they together are responsible for the partly old, but mostly new, museum on the Mall.

Most museum founders, the Mellons and the Hirshhorns, the Sacklers and the Freers, were men of mighty wealth. Robbins never has been rich. He'd always earned his living -- as a school teacher in New Hampshire, as a cultural attache' in Germany and Austria -- and yet he somehow managed to create his own museum of art.

It opened to the public in the 300 block of A Street NE, a few blocks from the Capitol, in 1964.

The museum was, at least at first, a '60s institution. Crosscul -- tural communication and interracial understanding and similar boundary-breaching linkages were crucial to its theme.

Robbins, who will be 64 on Friday, quit the diplomatic corps in 1962 with his heart set on a grand but not very precise dream. The first thing that he did was found something called the "Center for Cross-Cultural Communication." It had a grand "board of consultants" -- among them Margaret Mead, Buckminster Fuller, S.I. Hayakawa, Mike Wallace, mythologist Joseph Campbell, novelists Saul Bellow and Ralph Ellison and painters Jacob Lawrence and Ben Shahn. Then armed with all those weighty names, he set out to raise some cash.

He says, "One of the 22 projects I submitted to the Ford Foundation was one for a museum. It took five years, but then, in 1967, they finally came through with a $250,000 grant. We also got the first grant -- for $20,000 -- handed out by the National Endowment for the Humanities. We were the nation's first African museum. We tried to make it work."

Actually it was more than a museum of African art. At first its programs sprawled. It opened on Capitol Hill because Robbins had acquired there the modest little row house that once had been the home of abolitionist Frederick Douglass. (His museum grew and grew. It eventually sprawled through nine houses, 18 garages and two carriage houses between 316 and 332 A St. NE.)

It collected many sorts of art. For instance, Robbins much admired the paintings of Philadelphia's Henry O. Tanner, then but little known. Tanner had had very little to do with Africa -- he'd been raised in Philadelphia and trained by Thomas Eakins -- but he was American and black and highly skilled as well. So Robbins snapped up Tanners. His Afro-American collection eventually included 60 pictures by that painter, as well as about 200 other works by 19th-century black American painters.

School children came in bus loads. They were told about Frederick Douglass. They explored the "Afro-American Panorama" with its various portraits of 50 key black figures. African musicians, and story tellers, too, were on hand to give performances. Robbins' beloved "comparison gallery" stressed the debts he felt were owed by Paul Klee and Picasso and other Europeans to African tribal art. The shop was inexpensive. The place was often jammed.

The Museum of African Art also was collecting African material, most of it donated. But much of it, feels Williams, was of second or third rank.

Robbins, unsurprisingly, eventually got tired. He says, "I was running out of money. I was running myself ragged." So he conceived another plan. He spoke to Dillon Ripley ("I told him, 'Now you've got the Hirshhorn, how would you like the Museum of African Art?' ") He contacted the Humphreys, Hubert and his sister Frances, both longtime supporters. He lobbied on the Hill. The appropriate legislation passed in 1978. On Aug. 13, 1979, the Museum of African Art became the newest branch of the Smithsonian Institution.

Don't expect to find that Capitol Hill museum re-created on the Mall. It might not be too much to say that it's gone out of existence. Its Afro-American paintings have been distributed to other Smithsonian Institutions. And though Robbins lectures still on "Picasso's World and the African Connection," his theories aren't reflected in the new gallery's displays. One of the museum's inaugural exhibits is called "The Permanent Collection of the National Museum of African Art." I have only had a glimpse, but it seems a stunning show. It is not a Robbins exhibition. He gave up the directorship in 1982. Of its 140 objects, only 26, mostly tiny pieces, were owned by the museum before 1983.

It is abundantly apparent that Sylvia Williams, who came to Washington from the Brooklyn Museum's department of African, Oceanic and New World Cultures, has set her sights on building a thoroughly professional -- and exquisite -- art museum. She says, "It was clear the collection needed to be strengthened. So I went out after gifts." (Williams has also spent about $2 million on choice new acquisitions.)

She says, "In any art field, quality counts. The auction record for a piece of African art is now close to $800,000. It's too late for an art museum to think it is going to be comprehensive. So what do you do? It seemed the right way to move was to move selectively ... Warren is extraordinary. There are very few human beings with his tenacity and stamina. He started this place from scratch. But he had a broad agenda. The word 'museum' was not as restrictive to him as it is to me."

The Quadrangle's two museums seem to have evolved in completely different fashions. The new Sackler sees its mission as less restricted than the Freer's. The African Museum, at least considering its past, has moved the other way.

There would not be a Sackler Gallery had it not been for Charles Lang Freer. There would not be a National Museum of African Art had it not been for Warren Robbins. Without Dillon Ripley, both those new museums, and many more in Washington, might not now exist.

Ripley, who retired in 1984 after 20 years as secretary of the Smithsonian, is a scientist, a dreamer and a builder with few peers. He played the government like a harp. The Smithsonian, while he ran it, opened the Hirshhorn, the Air and Space Museum, the Anacostia Museum, the National Portrait Gallery and the new version of the National Collection of Fine Arts, now the National Museum of American Art. It acquired the African Museum and the Cooper Hewitt in Manhattan and Arthur Sackler's gift. It refurbished the Renwick Gallery, the Arts and Industry Building and the Castle, too. But as if that was not enough, Ripley, in his final years in office, had something else in mind.

When he looked out at the Mall, he sensed a sort of western bias. "Our entire awareness of others," he wrote in 1982, "has been concentrated until recently on the so-called Western world: Europe -- extending East to Russia, south to the Mediterranean -- and parts of Latin America, our traditional neighbors." But what about those parts of Asia south of China and Japan? What about Oceania? What about Africa? "How do you convince Americans," he asks, "that the people who live there -- they are, after all, two-thirds of the human population -- are not all dirty and poor and alien?"

He began to draft a plan.

He was busy at the time solving other problems. There was first of all a need for a new African museum. ("When the legislation passed," says Warren Robbins, "Sen. {Claiborne} Pell told Ripley, 'come back in two years and tell us what you've done to find a more appropriate place for that museum.' Then Pell turned to me. He said, 'Pardon the pun, but what you've got is a rabbit warren. The place needs another home.' ")

Ripley was also struggling with what he calls "the golden wall" wrapped about the Freer. How could it be punctured? "At first we thought of an extension," says Ripley. "Way back, when we were building the Hirshhorn, I asked {architect} Gordon Bunshaft to design one for the west side of the Freer." But Congress showed no interest in putting up the money. Ripley's plans were stymied. But only for a time.

When Ripley first met Sackler, he began seeing a solution. Ripley had something to offer. "Sackler was looking for something -- posterity," says Ripley. Sackler had something to offer, too -- a remarkable collection, and with it a new way of breaking through that "wall" around the Freer.

Sackler, who had suddenly pulled his oriental art out of the Metropolitan Museum, was thought by some museum folk a touchy man to deal with. But when Ripley went to see him, they formed a friendship from the start.

"I was lucky," says Ripley. "As I walked through his apartment, I saw a piece, an antique Chinese bed, Ming Dynasty as I recall, that I thought I recognized. Its design was rather simple. It was made of extinct Chinese holly. I said, 'Didn't that bed once belong to Bill Drummond?' "

Indeed, it turned out that it had. Sackler was delighted. And, it seems, amazed. ("Drummond," explains Ripley, had grown up in China. I'd known him for years. We'd been in the OSS together during World War II. I recognized the bed.")

Congress, Ripley knew, was not yearning to deed to the Smithsonian still more space on the Mall. But there was one plot, only one, there that he did not have to ask for. The Smithsonian Institution already owned the Quadrangle outright.

"We needed space for Sackler's gift, and for the African museum," says Ripley. Both collections dealt with faraway places, with Asia, the Near East, Africa. We were at the core of a problem demanding a solution."

The Quadrangle solved these problems. It also opened up a chink through which Ripley glimpsed a new International Center, that new Smithsonian window on the nonwestern world of which he had long dreamed.

He did his best to raise money. He talked to John Rockefeller. He talked to J. Paul Getty. He got some backing from the Saudis (but the arrangement raised some hackles). All in all his fund raising met with small success.

But the center was built anyway. It is there on the Concourse level. Its International Center Gallery, built 50 feet below the ground, may be difficult to find, but at least it's there. Two shows have been commissioned. "Generations," the first one, which opens with the building, will deal with the way birth is regarded and celebrated in a variety of cultures. The second, which is scheduled to open in May 1988, will focus on tropical rain forests.

The future of the center, at least after that, is anybody's guess. "At least we provided a setting. I only hope to God they develop the program," Dillon Ripley says.