The Dahesh Museum of Art announced a few weeks ago that it won’t remain long in the space it has occupied since 2003, the former IBM Gallery of Science and Art at Madison Avenue and 56th Street. Though the museum holds a lease until 2013, the high costs of operating the three-story space — which includes a large shop and a fancy restaurant in addition to the galleries — has caused the Dahesh to seek to sublet the premises, and to look for a new home. At one time, the Dahesh pursued space in the former Gallery of Modern Art at 2 Columbus Circle, before the Museum of Arts & Design got hold of it. The Dahesh would have preserved Edward Durell Stone’s building, but perhaps the whole scenario was just too good to be true. Now, the Dahesh appears seriously to be considering a move out of New York City. For the Dahesh, but even more so for New Yorkers, that would be a disaster.

Years ago, the Dahesh seemed like a joke. A Manhattan museum showing 19th-century academic paintings? It seemed, indeed, to be the Gallery of Modern Art redivivus, only instead of Huntington Hartford the museum had the mysterious Salim Moussa Achi, aka Dr. Dahesh, aka “Beloved Guiding Prophet” (according to www.dahesh.org, which is not the museum’s site). (“Dahesh” is Arabic for “inspiring wonder.”) The Lebanese spiritual leader, who died in 1984, amassed an eye-popping collection of academic art — the stuff the impressionists and other modernists rebelled against from the middle of the 19th century on. The collection, or parts of it, went on display in 1995 on an upper floor of a building at Fifth Avenue and 48th Street. While special exhibitions took place in that 1,800-squarefoot space, nothing like the museum’s current “Napoleon on the Nile” could have been accommodated there.

That exhibition opened in June 2006, and is the third in a series of Dahesh shows that rank among the best in New York in the last three years. “The Legacy of Homer: Four Centuries of Art from the École Nationale Supérieure des Beaux-Arts, Paris,” which ran between October 2005 and January 2006, and “Stories to Tell: Masterworks from the Kelly Collection of American Illustration,” which ran between February and May 2006, round out the trio of brilliant exhibitions of the sort one returns to over and over, and which it’s hard to imagine taking place in any other New York venue.

In addition to the splendid “Napoleon on the Nile,” the Dahesh has on show its two most recent acquisitions: Jean-Léon Gérôme’s oil sketch of the actress Rachel, and Eugène Guillaume’s plaster sculpture of Theseus. No other New York institution would have acquired these, and we are much the richer to have them here.

Gérôme made his portrait of his friend, France’s most famous actress, Rachel Félix, known simply as Rachel, after her death. The work was a commission from Rachel’s sister, Sarah, and Gérôme relied on photographs and his own memory to portray Rachel as Melpomene, the muse of tragedy. The Dahesh has the first of four preparatory oil sketches that Gérôme made. It’s a full-length portrait, showing Rachel leaning back, somewhat languidly, on a pillar bearing the mask of tragedy. Behind her ranges a row of fluted columns, and the tilt of her body plays beautifully off the column’s taper. In the first sketch Gérôme wants to get the composition right, to position her body correctly in the frame, get the angles to work out, figure out what to do with her arms. What’s missing is facial detail. In the final painting, shown at the 1861 Salon then sold to the Comédie Française, where it remains, Rachel’s gaze is Melpomene personified, a gaze as great as any in 19th-century French painting — and we have no trouble believing that the painting inspired Henry James in his creation of Miriam Rooth in “The Tragic Muse.” Well, the Dahesh has that gaze in its collection, for the museum owns a photogravure of the finished painting. One wishes museum officials had displayed it alongside the oil sketch.

Gérôme’s name resonates with some museumgoers, if only because the artist pops up in history books as one of the more vociferous critics of the Impressionists. The sculptor Jean-Baptiste Claude Eugène Guillaume, on the other hand, shares the fate of Jules-Félix Coutan, the sculptor of “The Glory of Commerce” atop Grand Central Terminal: These teachers at the École des Beaux-Arts (as was Gérôme), these masters who garnered state commissions, once bestrode the Paris art world like colossi. But the historiography of modern art sent their names down the memory hole. Yet Guillaume for many years served as director of the École, helped to decorate the façade of the Opéra, and, in 1845 sent his career into orbit by winning the Prix de Rome competition at the École with a masterful sculpture of “Theseus Discovering His Father’s Sword beneath a Rock.” The artist made a plaster cast for himself, as the original belonged to the École. Student rioters destroyed the original in the spring of 1968 and, it turns out, the Dahesh’s cast appears to be the only intact version of the sculpture in existence. It’s a tour de force of contrapposto, as young Theseus holds aloft in his right hand his father’s sword, supporting his weight entirely with his left arm, the hand pressed down hard upon the rock. It’s well worth a view.

May the Dahesh never leave New York City.