It comes down, alas, to this.

What's left when the dance goes by: photographs, film clips (if you're lucky), notes, letters, costumes and the music, left hanging like a jilted date.

Yet while there's no going in back in time to relive past performances, the ephemera of dance can still bear compelling witness to former glories, as seen in the exhibit "Dance for a City: Fifty Years of the New York City Ballet," at the New-York Historical Society through Aug. 15.

The installation is the latest in a series of events that began last fall to honor the New York City Ballet's half-century mark (it was founded in 1948). It chronicles the company's development and emergence as a world-renowned artistic power, and the parallel growth in dance awareness and sophistication of New York City, as well as the country at large. The New York City Ballet became one of the cornerstones of the mammoth Lincoln Center for the Performing Arts, where it is still housed in the New York State Theater. Under George Balanchine's direction, the company contributed mightily to the artistic life of the city, nurturing generations of fans and drawing avid followers from across the dance world and other arts.

Balanchine, in fact, is largely responsible for the growth of ballet throughout the country; there was scant appreciation of the art form before the Soviet emigrant's arrival on these shores in 1933. His lavish production of "The Nutcracker" in 1954 whetted an appetite for the ballet that became a holiday fixture across the nation.

Thus one of the first items on display can make a ballet fanatic's hair stand on end. "This will be the most important letter I will ever write you, as you will see. My pen burns my hand as I write," begins the 16-page handwritten missive. It is from the wealthy arts patron Lincoln Kirstein to a friend, dated July 1933 and detailing Kirstein's impassioned first impressions of Balanchine, the choreographer with whom he would later found the New York City Ballet. These words, written on hotel stationery, were the first step in bringing the incomparable Balanchine to New York, where his fastidious standards--the result of a steeping in the great Russian classicism of the Maryinsky Theater--and exquisitely streamlined choreographic style were to alter the course of modern ballet throughout the world.

Then, as now, starting up a dance company was a risky venture. Kirstein and Balanchine organized and disbanded three troupes--the American Ballet, Ballet Caravan and Ballet Society--before successfully launching the New York City Ballet in 1948.

The exhibit rightfully adopts a high tone. There's music by Stravinsky--the composer most readily associated with Balanchine--wafting over the costumes by Karinska, the photos by Martha Swope and others, and the posters, souvenir program covers and serigraphs as speed-driven and stylized as Balanchine's ballets.

But what truly brings the past into focus are the videos. Two screens offer snippets of the dancing that raised the NYCB to international stature. There is a majestic view of Maria Tallchief in a 1951 "Firebird"--her signature role--dancing with Michael Maule. The legendary ballerina seems to be melting in her own flames.

The most poignant films are of young Tanaquil LeClerq, a dancer of incomparable airiness, clarity and delicate beauty who was stricken with polio at the age of 27. She is paired with the great Diana Adams in the leading roles in "Concerto Barocco," where LeClerq's endless line and throwaway ease are astonishing. Her impish wit enlivens a later film of "Western Symphony," with Jacques d'Amboise; this footage was shot shortly before the company's tour of Scandinavia, where LeClerq contracted the crippling disease that would end her career.

Nearby hangs Karinska's "Firebird" costume re-created for Gelsey Kirkland in 1970--it is a work of art in itself, a heart-shaped sculpture in satin and silk the colors of a Tuscan sunset, with a trailing tail. And tiny as a lampshade. Other costumes add jots of color to the otherwise decidedly black-and-white surroundings. You can't miss the Marzipan Shepherdess's charmingly whimsical tutu, one of several costumes on display from "The Nutcracker"; like a layer cake it is edged in bright icing with a parade of rosebuds around the hoop.

The best "Nutcracker" memento, however, is a shot of 4-year-old John F. Kennedy Jr. and cousin Anna Christina Radziwill gleefully pelting each other with fake snow backstage during an intermission of the ballet in 1964--the year the company moved into Lincoln Center.

To be sure, the rooms are plastered with hundreds of deeply moving photos--some haunting, some sly, as is the Vogue magazine shot of ballerina Suzanne Farrell dressed only in a man's blazer and heels, standing over Balanchine, who sits with his head bowed at her feet. A metaphoric image of the complicated relationship between the boss and his muse.

Nothing photographs as well as dancers, especially the extremely leggy, thin ones cultivated by Balanchine. You can see the root of them all in a picture of the ribbon-like Felia Doubrovska from 1927. She danced with Balanchine in Serge Diaghilev's Ballets Russes, and was the first Siren in his "Prodigal Son." In another photo, she is shown in a luxuriously deep lunge and back bend, demonstrating for a class at the School of American Ballet, the NYCB training program.

In addition to Balanchine and Kirstein, the exhibit recognizes two other forces in the company's development: Jerome Robbins and Peter Martins. There is a wall of documentation devoted to Robbins, the only other choreographer to contribute works regularly to the company's roster under Balanchine's administration. He joined the company just after its founding, and apart from a departure in the '60s, remained with it until his death last summer.

Martins, the company's director since Balanchine's death in 1983, gets his own room, brightly lit and adorned with his photo on the covers of Esquire and Newsweek, and more photographs. Martins hasn't had an easy time taking over from Balanchine; he has come under almost constant criticism, which has grown especially sharp lately. Some Balanchine devotees and critics say the dancers don't dance as well now as they did when Balanchine was alive, and that his ballets have been treated carelessly. Martins is a gifted choreographer, though he's no Balanchine (but then, who is?), and his works have received mixed reviews.

Yet what is clear in this exhibit is the difficulty of capturing dance--whether in a museum, or onstage. Longing for the past is futile. The heart of the company is not here, under glass or on film. It's across town at the New York State Theater and upstate in Saratoga Springs, the company's summer residence. One can wish for consistency, for quality, for adherence to the artistic principles that elevated the company. Such things are timeless. Moving bodies are not.

The New-York Historical Society, 2 W. 77th St. at Central Park West. 212-873-3400.

CAPTION: Leaps toward distinction: Included in the New-York Historical Society's exhibit on the New York City Ballet are photos of Francisco Moncion and Maria Tallchief, above, and Tanaquil LeClerq in 1953's "Metamorphosis," below; and a costume design for 1972's "Polchinelle."

CAPTION: George Balanchine in 1950. The NYCB co-founder led the troupe to greatness, but was moreover responsible for the growth of ballet throughout the United States.