"How do you paint air?"

If a single thread connects the vast art collections of Swiss industrialist Hans-Heinrich Thyssen-Bornemisza -- his old masters, his 20th-century masters and now his "American Masters," starting a nationwide tour at the Baltimore Museum of Art -- it is the pursuit of an answer to that question.

"I was born at sea level in Holland, and lived there till I was 18 -- which may explain my love of landscapes," says Thyssen, 63, whose relatively new hoard of American paintings (113 are on view in Baltimore) includes atmospheric panoramas spanning two centuries, from Thomas Cole to Georgia O'Keeffe, and luminous evocations of sea air, from Fitz Hugh Lane to Edward Hopper.

"First I saw it only in the old masters," he says. "This new affection I have with American paintings comes from these beautiful landscapes -- the air, how they paint the air, how they paint the sunset. How do you paint air?"

Thyssen is best known for his peerless collection of old European masters, housed in a villa on Lake Lugano in Switzerland and shown in 1979 at the National Gallery. He has also been amassing -- and upgrading (most recently, with a $3.5 million Gauguin) -- a 20th-century collection, shown at the National in 1982 and due to open at the Royal Academy, London, this month.

Begun only seven years ago, Thyssen's American collection would probably not make him famous if he were not so already, given its vast inconsistencies. But it is remarkable in several respects, notably the fact that it is the only private collection in Europe that attempts to span the entire history of American art, from the colonial portraiture of John Singleton Copley to the photo-realism of Richard Estes. Most Europeans who collect American art think it all began with Jackson Pollock.

Thyssen has also acquired some first-rate paintings, including a wall of Winslow Homers that would make any museum proud. The glory of the collection is his grippingly dramatic "Signal of Distress," for which Thyssen paid $2 million, his most expensive American acquisition. A close second is Homer's splendid watercolor of a deer swimming a crystalline mountain lake.

There are other fine works, including the trompe l'oeil still life by William Harnett of an old pewter tankard and glowing pipe, and a Martin Johnson Heade "Orchid and Hummingbird." There are also some notable mediocrities, the inevitable result of reaching for historical comprehensiveness without equal dedication to quality.

Some of the most striking works are by lesser-knowns, such as James G. Clonney, whose 1847 "Fishing Party on Long Island Sound off New Rochelle" stands in for the George Caleb Bingham that Thyssen would like to own but doesn't. "My father did a similar thing," he says. "He also collected very good pictures from secondary artists. You can't find primary American pictures any more -- they're always a million dollars."

Thyssen has a sharp eye for the beginnings of abstraction, whether in the work of the Russian avant-garde or American immigrant Max Weber, represented here by "Grand Central Terminal," one of Thyssen's first American acquisitions. Stuart Davis' "Sweet Caporal," a wonderful 1922 takeoff on the early Cubist collage-makers, is one of the show's most memorable surprises.

But the modern section, on the whole, is extremely weak -- which Thyssen explains by saying that some of his best 20th-century American paintings have been commandeered for the touring "20th-Century Masters" show, his major concern at the moment. By the time the tour of that collection ends, he hopes to have built a Museum of Modern Art in Lugano to house it.

When that happens, his American collection will be permanently split, with the best of the 20th-century pictures going to the new museum. The rest -- the 18th- and 19th- century paintings -- will go to Daylesford, Thyssen's English country house, which he admits is no place for masterpieces. He recently shipped several paintings -- including his Caravaggio -- back to Lugano after a long stint in Daylesford because, as he put it, "they looked a bit silly in a country house."

Thyssen's more decorative 19th-century American acquisitions, notably John Singer Sargent's "Portrait of Millicent, Duchess of Sutherland" -- a study in pretentious grandeur if there ever was one -- should be right at home in Daylesford. As to the fate of his great 19th-century American pictures -- which are currently appreciating like mad -- one can only guess whether they will ultimately be sold to acquire major modern works for the new museum.

Thyssen's "American Masters," in the meantime, can be seen in Baltimore through Oct. 28, after which the International Exhibitions Foundation will tour them nationwide.