As the summer haze thickens over the Potomac, the greatest painter of Mississippi and Missouri river haze -- George Caleb Bingham (1811-1879) -- has turned up in two Washington exhibitions.

The two shows, one of paintings at the National Gallery of Art, the other of preparatory drawings at the National Museum of American Art, should have been together. Until May, in fact, they were together, in a major retrospective organized by the St. Louis Art Museum in Bingham's proud home state of Missouri.

It is the St. Louis show that the National Gallery has here dismantled, to the public's great loss. The curators decided they wanted to show only the best Binghams, those mist-shrouded genre scenes of boatmen and trappers floating on silent, silvery shallows, transporting furs, lumber or supplies from the Northwest to St. Louis or New Orleans and back again. They are, without doubt, Bingham's masterpieces, and it was a perfectly good idea -- but they failed to carry it out.

If this show proves anything, it's that Bingham made some great paintings, but he was not a great painter. The third of the three rooms of his works here is filled with some of the worst English- and German-derived landscape paintings ever to be shown at the National Gallery. The artist has been done a great disservice -- just the opposite of what St. Louis intended.

Yet, for what the gallery called "space" and "quality" reasons, this wrong-headed show eliminates all the portraits (though Bingham was the best-known portraitist in the thriving port of St. Louis) and all the figure drawings of the various frontier types who people Bingham's works: the fat politicians and straw-hatted kids, the stump speakers and toothless boozers, the farmers and boatmen who talk and drink, smoke and think, passing the time of day at election rallies or on flatboats that float dreamily through his pictures.

Fortunately, we do get to see these characters, thanks to the National Museum of American Art, which organized the drawings into a separate and fascinating show on view in its main-floor graphics gallery. The only problem here is that the these captivating drawings make you yearn to have the paintings at hand to make comparisons.

For instance: The first drawing in the NMAA show is that of the trapper in Bingham's 1845 masterpiece "Fur Traders Descending the Missouri" -- a single figure, vividly observed and superbly rendered in graphite with ink wash, as he paddles his dugout canoe. He stares out at us from the drawing, as he does from the painting, as if he were holding still to be photographed, his pipe clenched in his teeth. In the painting -- and you can see this from a photograph of it thoughtfully hung nearby -- he glides by, accompanied by a young boy and an adorable black bear cub.

What we can't see, however -- the photographs are too small -- is that in the painting, the trapper has been transformed into an old man with a scraggly beard, and his pipe has been lighted, its little puffs of smoke providing the only temporal touch in what is an otherwise timeless, nostalgia-laden icon.

Even by the mid-19th century, this was an image of river life that was disappearing, quite literally, in the wake of the steamboats and encroaching urbanization. It was this essence of America unspoilt, of happy days before the Civil War, that brought Bingham back to popularity in the dark Depression days of the '30s, when the Metropolitan Museum bought this painting.

Each of the 50 drawings at NMAA is an individual figure, set and centered against a white ground, and nearly all are related to known paintings. Some -- like that of the trapper -- are highly individualistic, others archetypes appropriately titled -- "Family Man" or "Jolly Old Landlord" or "Village Character."

The last figure, like many others, appears in several different paintings, usually as a member of a large crowd listening to a political spiel, such as "The County Election" or "The Stump Orator." Politics as well as painting was key in Bingham's life, and he held several elective and appointed offices in Missouri. "The next frontier in Bingham studies," says Michael Shapiro, chief curator in St. Louis, "will be to more closely examine how the drawings were used."

The most extraordinary thing about this drawing, however, is that it has incised lines on the back, suggesting that, despite its finished look, it was probably drawn primarily to be transferred onto canvas. According to new scholarship, this was presumably done by placing the drawing against the gessoed canvas and, probably by using transfer paper, traced over, leaving lines that could then be painted in. The figures in all of these drawings are precisely the same size as the figures in the paintings, and that may well be why.

But this brings up an amazing conundrum: Bingham's Old Master-based compositions, starting with his election paintings and going on through his famous pyramidal "Jolly Flatboatmen," were of prime importance to him. Yet not a single extant compositional drawing has ever turned up.

Could it be that he actually made up his compositions as he went along? It is possible. Highly formulaic, some may have required nothing more than a triangle as a guideline. Some are even laughable in their references to the Old Master paintings he had seen in his travels to New York and Philadelphia, and later in Germany.

The painting titled "The Emigration of Daniel Boone," for example, showing him leading his family, his wife perched on a horse, looks more like a classical "Flight Into Egypt" than a narrative about a folk hero. Others, especially the early crowd scenes, are really less compositions than accumulations of figures that invite an anecdotal reading.

So far as Binghams are concerned, the most integrated, organic paintings are the simplest ones, especially when they are enveloped in his magical atmospherics. There may well have been compositional sketches that Bingham threw out, or that are still in a trunk somewhere. But their absence makes these drawings all the more precious. That there are 55 intact here at the NMAA is a tribute to their owners. Proudly labeled "Lent by the People of Missouri," the drawings were purchased with funds raised by public subscription in 1979, after the collection was threatened with dispersal. They are currently on long-term loan to museums in Kansas City and St. Louis.

Bingham was actually born in Virginia, in the Shenandoah Valley, but his family moved to Missouri when he was 8, two years before it became a state in 1821. Basically self-taught, he worked as an itinerant portrait painter before traveling east to have a look at what was going on. What he discovered was a love of Western genre scenes, which he swiftly began to provide.

He was immensely popular for the dozen years covered by the National Gallery show, from 1845 to 1857, and, at that time, a great favorite of the American Art Union, an extraordinary organization that bought paintings each year with dues paid by its 10,000 members and then distributed them by raffle. Members who didn't win a painting were given an engraving of a painting, which were published by the thousands. The union bought 19 Binghams during those years, and while one was at the engravers (which sometimes took two years), the artist often painted a second version, or a third.

The NMAA show ends with just such an example: three states of the engraving of "The County Election," two versions of which hang at the beginning of the National Gallery show. Engraved by John Sartain of Philadelphia, it is a tour de force.

It is interesting to note, by the way, that the NMAA -- then known as the National Collection of Fine Arts -- actually held a comprehensive retrospective of Bingham's work in 1967, when scholarship on him had just begun. Earlier, after the Museum of Modern Art show in 1934, he had been an inspiration to American regionalists such as Thomas Hart Benton.

The two Washington shows will overlap for five weeks, until the NMAA's closes Aug. 19. The paintings will continue to be shown at the National Gallery East Building through Sept. 30. The exhibition is sponsored in Washington by Hecht's and by Monsanto Co.