WHAT IS, in effect, a vast new museum of American art opened to the publc Wednesday in Manhattan.

It has four times the exhibition space of the Museum of Modern Art. It is larger and more gracious than the nearby Whitney Museum of American Art. Made of glass and limestone, and filled with filtered sunlight, it stands in Central Park at the northwest corner of the Metropolitan Museum of Art. The Met's new American wing is at once enormous and enormously imposing -- and yet it represents a somewhat hollow triumph.

Its collections are far-ranging. Its architecture works. Its garden court is elegant. Its park views are delightful. Its exhibition galleries are nicely unpretentious. And nowhere in New York are there period rooms as fine. Yet those who believe firmly that the best old U.S. pictures can withstand the competition of those of other nations will leave these halls displeased.

Displayed on the walls are pictures we grew up with: Leutze's "George Washington Crossing the Delaware," known to every schoolboy; Sargent's "Madame X," which scandalized the French; "Fur Traders Descending the Missouri" by George Caleb Bingham; Winslow Homer's "Gulf Stream"; and "The Heart of the Andes" by Frederic Edwin Church. Why is it, one wonders, that these familiar friends, newly seen in sunlight here, tend to leave the viewer feeling slightly sad?

One factor may well be the installation. The canvases on view have been boringly lined up, in rough chronological order, one after another. But that minor defect is bound to be corrected once the Met's designers grow used to those new spaces and fine-tune their displays. (The Hirshorn, for example, which opened with a survey comparibly tedious, looks vastly better now than it did when it was new.)

But there is another problem with the paintings on display that will not soon be solved: their context. The painful question here is whether any sweeping survey of older American painting and sculpture can truly bear comparison with comparable surveys of the best of other lands. Nowhere in America is that question posed as sharply as it is today at that vast, overwhelming instituition, the Metropolitan Museum of Art.

Not so very long ago, most 19th-century American painting and sculpture was dismissed by connoisseurs, both here and abroad, as essentially provincial There was, we have since learned, much ignorance and prejudice -- and not a little spite -- in that widespread condescension. Since World War yiyi, however, those eager younger scholars known as the Americanists have mounted many shows and written many books intended to revise the patronizing view. The iluminist exhibit, which closes today at the National Gallery of Art, is but one of their efforts. Many fans of our old art have, of late, decided that or 19th-century painting and sculpture is just as good, by God, as any made in Europe. Isn't Remington first-rate? they ask. Isn't Frederic Church, whose pictures now cost millions, an acknowledged master?

Despite its many graces, despite its splendid objects, the new American wing -- just because it's at the Met -- focuses what may well be embarrassing attention on the American-first chauvinism that supports that point of view.

Consider, for example, the many marble statues installed in the bright sunlight of the 70-foot-high Engelhard garden court that is the most successful feature of the Metropolitan's new wing.

As those who must place art in the National Gallery's East Building will eventually discover, larger-than-life statues look particularly splendid in such airy, glass-roofed spaces. (The operative word is "statue," here; mere sculpture, for example, abstract works of Cor-Ten steel, simply will not do.) Yet still one tends to pity Palmer, Rimmer, Story and many of the other 19th-century carvers on view. For they were minor talents. Most of them enjoyed carving marble heroines who bare their marble breasts. And none of them can stand the searing competition from Rodin, for example, or from the life-size Chinese terracotta soldiers, or from the lifelike horses -- from Greece, from Rome and from the Basilica di San Marco, Venice -- currently on view elsewhere at the Met.

Similar competition frequently humiliates the weaker 19th-century portraits and genre scenes and landscapes on display inside the new wing. In the new Andre Meyer galleries of 19th-century European art, which opened just last March at the other side of that huge museum, are whole walls of Cezannes, of Courbets and Corots, of Manets, Monets, van Goghs, Turners and polished academic paintings. One entire room is filled with Rodin's bronzes; another is devoted to the pictures and the sculptures of the great Degas. Most 19th-century American art pales in comparison.

The visitor who, as I did, sees these treasures first, or who goes to see "The Horses of San Marco," or "The Great Bronze Age of China," will discover that, by doing so, he has used up the awe he otherwise might feel in the Met's new wing.

"That is a problem, I admit," said Philippe de Montebello, the Metropolitan's director. "This museum must educate the public in the optimum way of visiting museums. One no longer can simply come to town to visit the Metropolitan Museum of Art. It is now far too big. You must think of it, instead, as a large conglomerate of separate museums. There simply is no way that the visitor can survey a full 5,000 years of the history of art in a single day."

Those who last explored the Met, say, half a dozen years ago would hardly recognize the place today. Bit by bit, with little fanfare, the museum and its architects, Kevin Roche/John Dinkeloo Associates, have doubled the exhibition space in the past six years.

Its new 25,000-square-foot Lehman wing opened to the public in May 1975. ("The Horses of San Marco" are currently on view there.) The new 18,080-square-foot Islamic galleries were opened in October of that year. In October 1976, the first phase of the reinstallation of the Egyptian galleries was completed; the second phase was finished in November 1978. When phase three is completed, the museum will have a new 44,000-square-foot space for Egyptian art. Another gallery, whose 5,000 square feet of space was filled with new French period rooms, opened in May 1977. In September 1978, the Metropolitan inaugurated its new 24,000-square-foot Sackler Wing, some of which encloses the Egyptian Temple of Dendur, some of which is used for such special exhibitions as the Chinese bronze show presently on view.

In November 1979, a new 12,500-square-foot store for selling books and reproductions opened by the central stair. The 24,000-square-foot Andre Meyer wing opened last March. The 150,000-square-foot American wing opened Wednesday. This fall, a refurbished gallery of 7,500 square feet will open with a new display of the museum's prints and drawings. And a new 44,900-square-foot space, this one set aside for the Rockefeller collection of "primitive art," is scheduled to open in the fall of 1981.

"When we complete the southwest wing, the one for 20th-century art and the decorative arts, we'll be through," says De Montebello. "The Landmarks Commission of the City of New York has set our limits -- up, down and laterally. Once we've filled the profile, that's it. We cannot grow."

In any other setting, in any other city, the new wing would be viewed as among the very grandest of American museums. If it does greatly change the way that we regard our cultural accomplishments, it is probably because, it is just another volume of that vast encyclpedia, the Metropolitan Museum of Art.