Andrew W. Mellon (1855-1937), the financier who founded the National Gallery of Art, was not overly endowed with what the politicians like to call charisma. His speech was nigh inaudible, his manner was laconic, his taste was slightly prudish. He looked, said one observer, like "a double-entry bookkeeper afraid of losing his job--worn, and tired, tired, tired."

It is difficult to think of a less dramatic character on which to base a movie, but they have made one anyway. "Legacy: Andrew Mellon Remembered," a respectful portrait of that blandest of the billionaires, was premiered last night in the East Building. A thriller it is not.

Of the appreciative guests at last night's world premiere, only two or three had ever gazed on Andrew Mellon. One of them, Mrs. George A. Garrett, recalled meeting Mr. Mellon in Pittsburgh in 1918. "I walked into the parlor--in those days we had parlors--and there he was," she said. "He was not at all impressive. He wasn't very tall. He had the most wonderful piercing blue eyes, and he was extremely charming. I knew his daughter, Ailsa. I used to serve as a chaperone at the Mellon's Sunday dinners. In those days we had chaperones," she said.

Paul Mellon, the chairman of the gallery, and Andrew Mellon's son, told one of the guests that although robust Remak Ramsay (who plays the frail financier) often whispers in the movie, Father spoke so quietly that Ramsay seems to boom.

With its masterworks and presidents and million-dollar deals, its flamboyant English lord, cash-hungry Russian commissars, and its accurate account of a vindictive prosecution, the film is not exactly dull. But it sure is deferential. "Legacy" recalls a formal painted portrait of the sort that institutions hang in the Founder's Room.

Conoco Inc., as a public service, spent more than $1 million on the 58-minute movie which will be shown to gallery visitors. It was written and directed by DeWitt Sage Jr., who describes his hero as "a quintessentially undramatic character--a man who considered smiling eccentric behavior."

Andrew Mellon made his fortune founding Gulf, Alcoa and half a dozen other money-spinning firms. By the time the movie opens, he is already rich. He appears in a cloud of steam, stepping from a train, an austere, lonely figure rather unconvincingly lugging his own suitcase. He is on his way to meet president-elect Warren Gamaliel Harding, who is about to name him secretary of the treasury. A reporter rushes to the phone to described the appointee: "He's got a big white mustache, a little black hat, and they say he's worth about a billion dollars."

Pretty soon, in Washington, we find him in his office, bargaining, by telephone, for a Goya portrait that he has never seen. The seller wants a hefty $225,000, but Mellon will not bend. He eventually gets the painting for $190,000.

Why, the viewer wonders, is that far-from-ostentatious man haggling for pictures? Is it merely greed? Nope, he will in time give them all away. Could it be he's overcome by an esthete's lust for lovely works of art? Mellon, in this film, seems devoid of passion. The movie does, however, offer a slim motive for his buying art. The poor fellow is lonely. Or so he tells his former wife, Nora McMullen Lee (played by Maria Tucci). "Since our divorce," he says, nodding with affection at his Rembrandts and Vermeers, "these are my real companions, the ones I confide in." "They took my place," she says.

Joe Duveen, later Lord Duveen of Millbank, that most extravagant of art dealers, played, if slightly broadly, by actor Joseph Maher, does provide the movie with a modicum of humor. Duveen, who loved to stalk the buyers he called "squillionaires," contrives to corner Mellon in a London hotel's lift. Soon they're doing business. After learning that his quarry has taken an apartment here at 1785 Massachusetts Ave. NW, Duveen cunningly arranges to take the flat below, fills its walls with masterworks, most of them Italian, and then permits his neighbor to come in an browse. Mellon appears pleased with the 42 pictures that he sees there. Eventually he buys them all--for $21 million.

That was not Mellon's greatest coup. During the Depression, at a time when Josef Stalin was in need of cash, Mellon managed to acquire 21 pictures from the Hermitage--among them Raphael's "Alba Madonna," Botticelli's "Adoration of the Magi," and Titian's "Venus With a Mirror"--for $7 million.

The Roosevelt Administration, which was far from fond of extremely rich Republicans, accused Andrew Mellon, whose annual income taxes had averaged in excess of $1 million, of purposeful tax evasion. Mellon's plans to build his gallery came out at the trial, which dragged on for years. Though Mellon was eventually vindicated, the lengthy legal battle clearly caused him pain. He died in 1937, four years before his remarkable museum opened to the public.

The movie, most of which was filmed on location here, may give a slightly false impression of the size of the collection that Mellon gave the nation. The West Building contains 5 1/2 acres of exhibition space. There were only 132 works in Mellon's original collection. "It goes without saying," John Walker, the gallery's director emeritus, has written, "that he hoped for a greater density than 24 to the acre." Thanks largely to his children, and to hundreds of other collectors who have followed Mellon's lead, his hopes have been fulfilled.

"Legacy: Andrew Mellon Remembered" will be shown in the gallery's auditorium, free of charge, today and Thursday at 12:30 p.m., and regularly thereafter.