THE most ambitious TV series ever produced in Washington is off and running, five years after WETA and the Smithsonian Institution hatched the idea.

"Smithsonian World" will be a "TV magazine" focusing on Smithsonian research, expertise and artifacts. But with a first-year budget of $4 million, it will wander far from the museums on the Mall. Executive producer Martin Carr, a network veteran whose credits include the CBS special "Hunger in America," plans to film stories in Egypt, Pakistan, Australia and Hawaii, among other sites, on subjects ranging from skyscrapers to art conservation to the language of squid.

"It's the first time on television that art and science will be combined in the same program," says historian David McCullough, who will host the show and who dismisses all efforts to classify people according to artistic or scientific bent as "abundant nonsense."

McCullough, the prize-winning author of "The Path Between the Seas" and "Mornings on Horseback," was chosen for his host's duties, say the producers, after a methodical search for "a combination of Alistair Cooke and Jacob Bronowski."

McCullough says he is "thrilled" with the assignment, although, as a humanist, he ought to have misgivings about the TV medium. He compares his reaction to Teddy Roosevelt's upon learning that, because William McKinley had been assassinated, he was now president. Roosevelt knew he was supposed to act grief-stricken, says McCullough, "but it wasn't in him."

The powers at WETA, Washington's 21-year-old public TV station, sound equally fired up about "Smithsonian World." It will be "by far the largest of any television production in Washington--by a commercial or a public television station," says WETA President Ward B. Chamberlin Jr.

More than 20 corporations and foundations were approached about funding the show, Chamberlin says, but the cost proved forbidding until the McDonnell Foundation--established by James S. McDonnell, the founder of the McDonnell Douglas Corp.--came through with $500,000 in seed money followed by $3 million for production.

The Smithsonian itself sees the series as an "experimental and pioneering" venture that will result in "greater and wider distribution" of its knowledge and materials, according to the institution's under secretary, Phillip S. Hughes.

The series will focus on the people who work at the Smithsonian, as well as the work they do. "The greatest treasures in this institution are the treasures between the ears and in back of the eyes" of its staff, McCullough says.

One major segment, to be filmed in Panama over the next few weeks, will involve the Smithsonian Tropical Research Institute on Barro Colorado, an island created by the flooding of the Panama Canal 75 years ago, where scientists are studying such matters as howler monkeys, brown pelicans and the overall problem of maintaining tropical forests. While in Panama, "Smithsonian World" also will look at the engineering feat of the canal, a story told by McCullough in "The Path Between the Seas."

Another segment will deal with Douglas Ubelaker, the National Museum of Natural History's "bone detective," who serves as consulting forensic anthropologist to the FBI and recently established the identity of a murdered prostitute by matching a skull fragment with an X-ray taken when she was suffering from sinus headaches. Still another segment, shot last month in Puerto Rico, involves Tom Soderstrom, the Smithsonian's expert on grasses and bamboo, and his efforts to learn why one species of bamboo (phyllostaches bambusoides) flowers and dies at 120-year intervals all over the world.

"He's really devoted his life to bamboo," says Carr.

"We're going to take those people," says McCullough, "who have devoted their lives to what seems to be obscure or meaningless fields, and show how wonderful they are."