WHAT WE SEE in the museums of the Smithsonian Institution is just the tip of the iceberg.

It's been said that, at any one moment, the Smithsonian can only exhibit between one and three percent of its holdings -- which number well over a hundred million items, including the research collections.

It grew by simple addition.

First, fortunately for us, James Smithson's nephew died without issue, and Smithson's estate fell to this country, as he stipulated in his will: "to found at Washington, under the name of the Smithsonian institution, an establishment for the increase & diffusion of Knowledge among men."

Smithson being a British citizen, the money came from England: $515,169 in gold sovereigns. That was in 1838, nine years after he died.

There were other resources for the Smithsonian. Early Secretaries of the Smithsonian were scientists with collections of specimens to contribute. Government expeditions went West and came back to fill storage rooms. From the 1876 Centennial Exposition, trainloads of things chugged from Philadelphia to Washington. The Patent Office contributed shelves full.

Then there was Harry Winston, who gave us the Hope Diamond, and unsung little old ladies who passed on curios.

Last year, the Smithsonian was given the space shuttle Enterprise (now at Dulles Airport); a John Wilkes Booth wanted poster (he was only at large for about a week); a 10.2 carat hot pink sapphire; a Harlem Globetrotters uniform; a 1935 Girl Scout uniform; and two uninhabited Pacific Islands.

Ten miles from Panama, the islands were donated by a woman in memory of her husband, for the study of birds and vegetation. That brings us to Smithsonian research -- an iceberg in itself. The facilities range from the Environmental Research Center in Annapolis to a tropical research center in Panama to a telescope in Arizona. Not to mention the research done in the museums themselves.

The Smithsonian Institution is best known for its museums -- where 24 million visits were counted last year. Where, unless the labels tell you otherwise, you're looking at the real thing -- not a re-creation of the Wright Flyer, but the one the Wright Brothers really flew.

One of a kind.

Just like the Smithsonian.

Herewith, we attempt to list, where possible, the must-sees of the permanent collections. Unless otherwise noted, the Smithsonian Museums are open daily 10 to 5:30. Because of federal budget cutbacks, there will be no extended summer hours this year. ANACOSTIA NEIGHBORHOOD MUSEUM -- Produces temporary exhibitions on the history and art of Afro-Americans, and on Anacostia. "The Renaissance: Black Arts of the Twenties" will remain there through 1986. Plans are to move the Museum to nearby Fort Stanton Park in early 1987. Weekdays 10-6; Saturday and Sunday 1-6. Free. 2405 Martin Luther King Jr. Ave. SE. 287-3369. ARTS & INDUSTRIES BUILDING -- A time-tunnel experience, transporting visitors to Philadelphia's Centennial Exposition of 1876. A plethora of Victoriana, the show reopened for the Bicentennial and has been there ever since with its steam engines, French lace, totem poles and hundred-year-old whimsy. Free. 900 Jefferson Dr. SW. 357-2700. BARNEY STUDIO HOUSE -- In the mornings, Washington artist Alice Pike Barney painted under the skylight here in her Sheridan Circle home. In the evenings, she held a salon for friends and artists. She was a millionaire with a bent for stirring things up -- placing a nude statue on her lawn, marrying a man 28 years her junior and the like.

Decorated in a "baronial revival" style, with her paintings prominently displayed, the 1903 house is open for guided tours by appointment only, Wednesdays and Thursdays at 11 and 1, and the second and fourth Sundays of the month at 1. Closed August and September. Free. 2306 Massachusetts Ave. NW. Call 357-3111. FREER -- A collection of Oriental and American art given to the Smithsonian by Charles Lang Freer. Don't miss "The Peacock Room," created by Freer's friend, James McNeill Whistler, using oil paints and gold on leather, wood and canvas. The Japanese folding screens gallery is another inviting environment.

See also: the Chinese bronzes (such as an ancient "chimera" and a ceremonial vessel called a "kwei"), the Japanese wooden "Bodhisatva Miroku," the Indian bronze "Parvati," the Syrian brass canteen with silver inlay, and the Korean Celadon-ware sprinkler. Under the terms of Freer's will, objects from the collection may not leave the Freer, nor may objects from other collections be displayed there. But when the new Sackler Gallery opens at the Quadrangle site on the Mall in about June 1987, it will provide space for traveling exhibitions of Oriental art. Free. Jefferson Drive at 12th Street SW. 357-2700. PAUL E. GARBER FACILITY -- Attic and restoration center for the Air and Space Museum, this is one for airplane buffs. Tours of the five warehouses take three hours -- two buildings of finished planes, two buildings of planes in pieces and stacked waiting their turn, and Building 10, the workshop. None of the warehouses are heated or air-conditioned, so be forewarned.

On weekdays and at the annual open house (usually the last weekend in April), visitors see craftsmen at work, sometimes refabricating missing pieces or hand-sanding a plane layer by layer, looking for markings and colorings that tell the plane's history.

World War II aircraft, such as the Enola Gay, are the big draw. Even without wings it's too huge to accommodate anywhere else, so they're working on it very slowly. Other biggies are a Corsair, a P-38, a MiG-15 and an RAF Hurricane; if these ring a bell, the Garber facility is the place for you. On Old Silver Hill Road in Suitland, Maryland, tours of the facility are given by reservation only, weekdays at 10 and weekends at 10 and 1. Free. Call 357-1400. HIRSHHORN MUSEUM & SCULPTURE GARDEN -- One of the world's great collections of modern sculpture -- with a large number of 20th-century American paintings to set it off. The nucleus of the collection came from the late Joseph H. Hirshhorn. You must pose for pictures with these, in the Sculpture Garden: "Burghers of Calais," and other Rodins. David Smith abstractions, "Cubi" and "Voltris," in the cul de sac. Matisse's "Backs." Henry Moore's "Draped Reclining Figure" and "Seated Woman." In the Plaza: Oldenburg's "Geometric Mouse," and Snelson's 60-foot-tall "Needle Tower."

And look for these inside the Museum: Frank Stella's 1985 "Quaqua Attaccati La!" relief, Brancusi's "Sleeping Muse," Robert Arneson's "Elvis," and the Abram Lerner room with Miro and Masson paintings and Calder mobiles. Also small Degas sculptures and Matisse's "Heads of Jeanette." Free. Independence Avenue and Eighth Street SW. 357-2700. NATIONAL AIR & SPACE MUSEUM -- The most popular of all the Smithsonian museums, it attracts 1 1/2 million visitors per month in the summer. The high flyers there: The 1903 Wright Flyer. Lindbergh's Spirit of St. Louis. John Glenn's Friendship 7. Skylab Orbital Workshop (a walk-through). Chuck Yeager's Bell X-1 Glamorous Glennis. The Apollo 11 spacecraft. The Lunar Module. Rowland Emett's S.S. Pussiewillow II (so what if it's a fantasy flyer? It's a spacecraft to the artist). And don't miss the movie, "The Dream Is Alive." Free. Sixth Street and Independence Avenue SW. 357-2700. NATIONAL MUSEUM OF AFRICAN ART -- After a visiting exhibit of Bamana figurative sculpture closes on June 15, the museum itself will be closed for a year -- to reopen at the Mall's Quadrangle site (behind the Smithsonian's administration building, the "Castle"). There it will finally have a permanent exhibit area for its rich collection of traditional African sculpture, masks, headdresses, textiles and musical instruments.

Temporarily at 318 A St. NE. Monday-Friday, 10-5; weekends, 12-5. Free. 287-3490. NATIONAL MUSEUM OF AMERICAN ART -- The Old Patent Office Building provides a Greek Revival architectural setting for this must-see sampling of American artists: Thomas Eakins, "William Rush's Model." Thomas Moran, "The Grand Canyon of the Yellowstone." Thomas Hart Benton, "Achelous & Hercules." John Singleton Copley, "Mrs. Humphrey Devereux." Frederic Edwin Church, "Cotopaxi." Gene Davis, "Raspberry Icycle." George Catlin, "Old Bear, a medicine man."

The gallery owns 500 Catlin works and hangs a mere 15 of them. It also boasts the world's largest collection of works by Albert Pinkham Ryder ("Jonah") -- as well as, in the lobby, the aluminum foil "masterpiece," James Hampton's "The Throne of the Third Heaven of the Nations' Millennium General Assembly." Free. Eighth and G streets NW. 357-2700. NATIONAL MUSEUM OF AMERICAN HISTORY -- The way we've been and continue to be -- national cultural landmarks. Here are the sorts of things you'd expect to stumble over in "the Nation's Attic" (another name for the Smithsonian). You can't miss: the Star-Spangled Banner, the Foucault Pendulum, the First Ladies' Gowns and old No. 1401, a steam locomotive of the Southern Railway, with sound effects.

Don't miss: Dorothy's ruby slippers; General Sheridan's stuffed horse, Winchester; the interior of JFK's campaign plane, the Caroline; the Palm Court (old-fashioned ice cream parlor) and Howdy Doody. Newest permanent installation: "After the Revolution: Everyday Life in America, 1780-1800." Free. 14th Street and Constitution Avenue NW. 357-2700. NATIONAL MUSEUM OF NATURAL HISTORY -- From anthropology to geology to zoology, the museum chronicles humans and their natural habitat. Behind the scenes, the encyclopedic research collection encompasses more than 80 million specimens, ranging from slides of one-celled organisms to whale skulls. Here are some must-sees on exhibit: the mummies -- Peruvian, Egyptian, Aleutian and Philadelphian; this last being one Wilhelm von Ellenbogen by name, who died of yellow fever in 1792 and whose body turned to soap. These can be found near the ghastly exhibit of skulls that demonstrates the rate of population increase. See also the Egyptian painted and hieroglyphed mummy cases -- rare finds hereabouts.

The old standards: the living Coral Reef, the Easter Islands giant stone head, the elephant in the rotunda. And Fossil Hall's dinosaurs, of course; among them look for a fish within a fish, fossilized lunch. And the Hope Diamond, and the California gold nuggets collection.

For hands-on, The Naturalist Center, with its drawersfull of minerals and arrowheads, and microscopes set up. For hands off, the live Insect Zoo. Free. 10th Street and Constitution Avenue NW. 357-2700. NATIONAL PORTRAIT GALLERY -- Housed in half of the Old Patent Office Building, highlights are the Hall of the Presidents (with Peter Hurd's "LBJ," the one the subject hated); "Mary Cassatt" by Degas; George and Martha Washington as painted by Gilbert Stuart; John Singleton Copley as painted by himself.

Plus: the Time magazine cover collection of original artwork, Jo Davidson sculpture and the Meserve Collection, a monumental Mathew Brady photo collection. Free. Eighth and F streets NW. 357-2700. RENWICK GALLERY -- showcases American design, crafts and decorative arts. In the sumptuous Grand Salon hang paintings primarily from the Victorian era, and cushiony sofas encourage a leisurely pace.

But despite the Second Empire facade that recalls an elegant past, this is a lively gallery for visiting contemporary shows of very American furnishings and crafts, from Frank Lloyd Wright's chairs to Wendell Castle's clocks. Free. Pennsylvania Avenue at 17th Street NW. 357-2700.