One of the enduring mysteries of Long Island’s brief run as a capital of silent movie production is where exactly the 1921 blockbuster “The Sheik” was filmed. Was it, as local lore suggests, among the wind-swept Walking Dunes of Montauk, or along a five-mile stretch of beach near Amagansett, where a town historian, then 8, remembers playing with palm fronds left behind by the production company? Or, as some of you are already asking, do we really care? We do, if only because one of us spent a holiday weekend trying to find the answer. So head with me to Queens, where today’s Kaufman Astoria Studios serves film crews working on everything from “Sesame Street” to “Nurse Jackie.” Built in 1920, the building originally headquartered a conglomerate called Famous Players-Lasky, a merger of companies owned by film pioneers Adolph Zukor and Jesse Lasky and the flotsam of six other firms, including the George M. Cohan Film Corp. At the time, New York was still America’s film capital, having transformed Edison’s 1890s invention of the moving picture camera into the industry that today is known simply as “Hollywood.” But while studios in the boroughs and ’burbs were still cranking out hundreds of silent shorts, the shift was already on to Southern California, where filmmakers, Lasky among them, could count on 300 days of sunshine a year. Hollywood was also where a young Italian immigrant named Rodolfo Guglielmi had settled after middling success as a New York City taxi dancer and tango instructor. Rudolph Valentino, as he called himself, landed bit parts in several films, almost always as a swarthy gangster or other villain. His breakthrough role came in 1920, when Metro Pictures cast him as the lead in the epic war drama “The Four Horsemen of the Apocalypse.” The film became one of the first silents to gross seven figures – even topping Charlie Chaplin’s “The Kid” – and popularized both Valentino and the gaucho pants in which he appeared. A sudden star, Valentino demanded better pay and more control over the parts he played, but Metro refused the raise and cast him in a B-grade flick titled “Uncharted Seas,” then a pair of flops, “Camille” and “The Conquering Power.” In a fit of pique, Valentino quit Metro and signed on with Famous Players, lured by Lasky’s offer of a $50 raise and promises of bigger money to come. Valentino’s first film for the new studio was an adaptation of “The Sheik,” a popular bodice-ripper by British novelist Edith Maude Hull. Released in October 1921, “The Sheik” was panned by critics as pure camp – “Valentino depicts lust by widening his eyes and baring his teeth,” one said – but it was a runaway hit with American women fresh from the suffrage victory of the previous year. Film historians say it appealed perfectly “both to women’s fantasies of autonomy and their desire to be swept up in love’s protective embrace.” Largely avoided by male moviegoers, “The Sheik” still smashed attendance records at the Rivoli and Rialto chains in New York, drawing 125,000 in less than four weeks and quickly grossing more than $1 million. It also spawned a craze for all things Arab, including fashion, architecture and home décor. And at least one spoof, a Mack Sennett short called “The Shriek of Araby,” in which a cross-eyed Ben Turpin whisks away a baffled damsel on the back of a white dray horse. Valentino, of course, ended up as the James Dean of his time, dying of peritonitis in 1926 at the age of 31, after just four more films. Final words, to his brother: “I’m afraid we won’t go fishing together.” What, then, of the sands of eastern Long Island? Simple suburban legend, apparently.