It began with a bequest from James Smithson, an Englishman, who sent half a million dollars in gold sovereigns to bestow an institution in his memory.
The heart of the Smithsonian is the Castle, a slightly ludicrous stronghold that dispenses information on the gems scattered around. It also holds Smithson's remains, after the city of Genoa - where they previously rested - dug up the cemetery. Nine wonderful museums line the Mall, not a shopping complex, but a verdant avenue. To avoid drowning in an ocean of swirling cultures, you have to pick and choose.
The star-spangled banner that inspired the national anthem cannot be seen by the dawn's early light, but is on show at half past the hour from 10.30am to 4.30pm at the Museum of American History. The flag, torn but not destroyed, by the British attack of 1814 inspired Francis Scott Key to write the poem that later became the anthem. No other museum gets so close to the heart of Americana. Jewels of history include Judy Garland's ruby slippers from The Wizard of Oz and George Washington's false teeth. The costumes of the first ladies are featured in a chamber devoted to all the presidents' wives, with a strange fascination for JFK's widow.
High-definition television is demonstrated, as is computer-aided management - hands-on control of your own bicycle factory. In among early steam engines and corn mills, it is possible to trace a direct technological lineage from Samuel Morse's signalling equipment to modern digital processing.
Other museums in the Smithsonian Mall have equals elsewhere in the world, but the Air and Space Museum is in a class of its own. It has the greatest hits of flight from the Wright brothers' Kitty Hawk to the command module for Apollo XI.
The great attraction now is the Star Trek exhibition - the series has endured longer than the moon landing. Mr Spock's ears, Captain Kirk's chair and Scotty's Transporter are on display, together with models used for the Enterprise and Klingon spaceships. Scotty would have been appalled by the astronauts' ice-cream on sale in the gift shop: 'Ye cannae change the laws of physics, Captain'. Freeze-dried space-shuttle ice-cream - just add water - is as disgusting as it is fascinating. It probably has as much taste as the dilithium crystals that power the starship.
And you haven't even started on the National Gallery of Art yet. Restrict your visit to the 20th-century work in the newer East building, whose foyer is terrorised by a huge Alexander Calder mobile resembling a whale skeleton. The present exhibition of Indian Frontier Art displays everything from kickapoo moccasins to ornate headbands. It traces the displacement of Native Americans as Europeans pushed further into their territory, and how Indian fashions were influenced by contact with the newcomers, with beads and ribbons traded for furs. It is something of a jolt to move swiftly on to work by Roy Lichtenstein, Mark Rothko and Andy Warhol, including the 32 soup cans and the green Marilyn (Monroe).
John F Kennedy and his brother Robert lie at Arlington Cemetery. The rolling green hills nudge up against the Pentagon, the five-sided megalith housing the Defense Department. Something of America's skewed view of the world can be discerned from the huge headstone of a US ambassador to a Central American country, misspelt as 'Guatamala'. The cemetery is a big attraction, with Tourmobile trolleys rumbling through all day. Arlington is best visited in late afternoon, when the crowds have thinned out and the calm matches the serenity of the surroundings. Across the Potomac the light gently subsides over the city. The summit is Arlington House, former home of Robert E Lee, who led the Confederate South to defeat against Abraham Lincoln's Union.
The grave of Pierre L'Enfant marks the best point for surveying the city planner's elegant creation. The centrepiece of this beautiful park, steeped in tragedy, is the flame burning above the remains of President Kennedy. In stark contrast, the grave of his brother Robert is a plain white cross in a nearby corner of the field. The meadow is splashed with thousands of crosses for the dead of numerous wars, and the tomb of the unknown soldier symbolises all who have died defending American interests.
The cemetery even has its own underground station, but the best way to leave it is to cross the Arlington Memorial Bridge. This leads to the Lincoln Memorial, erected in tribute to the winner of the Civil War. The monument is modelled on the Parthenon in Athens and contains a huge, gaunt, moody statue of Abraham Lincoln. The figure looks down the length of the ceremonial city, mirrored in the steely pool are the Washington Monument and beyond it the Capitol building.
Almost 60,000 names are inscribed in black granite 'in the order they were taken from us' from 1959 to 1975. This tragic arc of stone is the Vietnam Veterans Memorial, a chronological list of those who died - and the 1,300 still listed as missing - in the war in Indochina. The first to die was John H Anderson Jnr, the last Jessie Calba. Relatives can locate the position of their loved one's name by computer, and make pencil rubbings of the names.
You would not visit Washington to shop but - this being America - there is plenty to buy besides imitation parchment copies of the Constitution. Many of the shopping opportunities have moved out to malls on the Beltway, Washington's smaller but equally congested version of the M25. The areas to look in are around the Metro Center, in particular two department stores: Woodward & Lothrop (known as 'Woodie's') and Hecht's.
The Kennedy Center is a massive monolith containing five auditoriums - the foyer alone is longer than the Washington Memorial is high, and is one of the largest rooms in the world. The view from the roof terrace at sunset is awesome: the Washington Monument winks at passing aircraft, Lincoln's Memorial is stoical and the dome of the Capitol glistens as the rich and powerful prepare to be entertained.
The awkwardly curved concrete lump next door is the Watergate Center, an apartment and office block with an ordinary branch of Safeway's, a hotel and a history, where Nixon's CREEP (Campaign for RE-Election of the President) carried out its dirty work.
Close by is Georgetown, an old tobacco port that predated Washington but has long been engulfed by the capital. It has charm and history, as well as fearsome crowds at weekends. Some of Washington's best-value restaurants are here, notably at the junction of Wisconsin Avenue and M Streets. This crossroads is the oldest in the city; it was from here that Pierre L'Enfant set out in 1791 to survey the site of the nation's capital - accompanied by George Washington.
Getting there: Via Boston on Northwest Airlines, pounds 226, including tax, from Bon Voyage (0703 330332). The lowest fare on a non- stop United flight through the same agent is pounds 232.
Dulles, the main international airport, is 20 miles west of the city centre. The Washington Flyer bus operates every hour and takes 45 minutes to the city centre. Connecting flights such as Northwest's arrive at National Airport, only 15 minutes and a dollar on the Metro from the city centre.
Getting around: The Metro is the best way to travel. Begun 20 years ago, it is a system of heroic proportions. Lines are colour-coded, known as Blue, Red, Yellow, Green and Orange. Tickets are sold from automatic machines; watch how the locals do it. A dollars 5 ticket gives unlimited travel all day from 9.30am.
Taxis abound. Instead of meters, fares are calculated by the driver according to the distance travelled as interpreted by a formula baffling to the newcomer. Scope for cheating customers is therefore wide, but most drivers are honest. Tip 15 per cent.
Accommodation: Autumn is an excellent time to visit. I stayed at the Howard Johnson Lodge (2601 Virginia Avenue, 965 2700; dollars 82 single/dollars 90 double per night), and at the tattier University Inn (2134 G Street, 342 8020) for dollars 57, including breakfast. Cheaper still is the Youth Hostel (1009 11th Street, 737 2333), dollars 15 for Hostelling International members.
Washington has numerous bed and breakfast agencies; try Sweet Dreams & Toast (363 7767). Double room rates range from dollars 45-dollars 130; book several weeks in advance.
Attractions (admission is free for all those listed):
FBI headquarters, J Edgar Hoover Building, E Street between 9th and 10th Streets
Ford's Theatre, 511 10th Street
Library of Congress, corner of 1st Street and Independence Avenue
National Air & Space Museum, 6th Street and Jefferson Drive
National Gallery of Art (East Building), Pennsylvania Avenue between 3rd and 4th Streets
National Archives, Constitution Avenue between 7th and 9th Streets
White House, 1600 Pennsylvania Avenue
Further information: The US tourist office does not accept personal callers. You must write to PO Box 1EN, London W1A 1EN or telephone 071-495 4466.
Visitor information in Washington is available from 1455 Pennsylvania Avenue, next to the Willard Hotel; telephone 789 7038.
The code from the UK for the US is 0101. The area code is 202.
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