The National Air and Space Museum is the most popular tourist attraction in Washington, and the most visited museum in the world. On an average day, 27,000 people (almost all of them from out of town) will pass through its doors - more than visit the White House, the United States Capitol, the Lincoln Memorial, and the Washington Monument, combined.

''Some days,'' sighs an Air and Space guard, ''it gets so crowded in here you have to walk sideways.''

First authorized by Congress in 1958, the museum wasn't dedicated until the bicentennial year of 1976. It is not so much a building as a luxurious hangar, as long as three city blocks, set down on the south side of the Mall. Its exhibits cover everything from ballooning to ballistic missiles; from its ceiling hang such artifacts of American flight as the Wright Brothers Flyer, the Spirit of St. Louis, the X-15, and a mint-condition DC-3.

Just inside the front doors, two Project Mercury capsules stand like sentries , flanking a sliver of moon rock that the public can touch. In the World War II galleries, nostalgic veterans show their wives the planes they flew. Children swarm around the spacecraft, climbing on railings, peering in portholes, invariably asking ''What is this thing, what is this?''

The effect of the museum is to impress a visitor with the difficulty of breaking gravity's bond, and to emphasize the bravery of those who have done it: the Wrights, Lindberg, Earhart, Glenn, Armstrong.

One man, camera dangling from his shoulder, stares a long time at a backup Skylab. It is the largest thing in the museum, a thick two-story cylinder of polished metal. ''Wow,'' he says, apparently awestruck. ''Now I know why the space program is so expensive.''

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