Paris has its baguettes and Dublin its soda bread. San Francisco trades heavily in sourdough, while New Orleans greets each morning with beignets. It wouldn't be Philadelphia without soft pretzels and it couldn't be Bonn without pumpernickel. But no city, perhaps in the history of the world, is so closely identified with a breadstuff as New York is with the bagel.

  The bagel is to a Sunday in Manhattan as the mint julep is to Louisville, Ky., on the first Saturday in May — an indispensable accompaniment to ritual, whether that be a brunch on the Upper West Side or the Kentucky Derby itself. Whether eaten plain or with a "schmear" of cream cheese, with whitefish salad or a slice of Nova, with sesame seeds or salt, toasted or untoasted, by Jew, gentile, Muslim, Buddhist or agnostic, the bagel has, for more than a century, helped define breakfast in New York.

  But what is a bagel, really? What makes it more than simply, as an article in The New York Times declared in 1960, "an unsweetened doughnut with rigor mortis"? And, most important to anyone with even a passing interest in the subject, where can you find the best bagel in New York City?

  It was with these questions and more in mind that I set out, scarcely a month ago, to eat bagels in all five boroughs and to determine, to the best of my palate's ability, what makes a great and authentic New York bagel. I visited more than 50 establishments. I ate more than three times that number of bagels. In the process, I both horrified practitioners of the carbohydrate-phobic Atkins diet and discovered no less than half a dozen varieties of bagel so good they need no cheese, butter or smoked fish to accompany them.

  Absolute Bagels on the Upper West Side, I salute you! Terrace Bagels, in Windsor Terrace, Brooklyn, huzzah! Cheers to Bagel Oasis, in Fresh Meadows, Queens, and to Murray's Bagels in Chelsea. Hot Bialys in Jamaica, Queens? Bagelry in Murray Hill? They are all superb.

  But I also had bagels so despicably bad the people responsible for baking them should be incarcerated. New York may be the nation's bagel capital, but street vendors selling rubbery steamed bagels abound, not to mention local McDonald's franchises selling bagels topped with egg, cheese and bacon. Even such Midwestern depredations as blueberry bagels have gained a stronghold in certain precincts of New York City. The bagel as concept is ubiquitous in New York. But not all bagels are the same. Some are to be derided.

  A definition of terms, then. A bagel is a round bread made of simple, elegant ingredients: high-gluten flour, salt, water, yeast and malt. Its dough is boiled, then baked, and the result should be a rich caramel color; it should not be pale and blond. A bagel should weigh four ounces or less and should make a slight cracking sound when you bite into it instead of a whoosh. A bagel should be eaten warm and, ideally, should be no more than four or five hours old when consumed.

  All else is not a bagel.

  A few more stipulations. Bagels do not need six ounces of cream cheese on them. They only need a schmear. Cream cheese made without guar gum is optimal, but it is hard to find. (You can still find fine natural cream cheese at the Fairway markets and Russ & Daughters in New York, and Zingerman's in Ann Arbor, Mich., makes a great, larger curd cream cheese that is available by mail.) On the subject of salmon, it should be Nova, and it should be sliced to order. A good bagel with cream cheese and smoked salmon does not have to be toasted, as contrast with the fat and salt will be provided by the crunchy crust of a properly made bagel exterior.

  But a buttered bagel should almost always be toasted, so that you get that great, rich melted butter taste. Better yet, you can achieve the same effect if you buy your bagels fresh, still warm from the oven. No toasting needed!

  The derivation of the word bagel is unclear. Joan Nathan, the author of "Jewish Cooking in America" (Knopf, 1998), says it comes from the German verb "biegen," "to bend." The late Alan Davidson wrote in his "Oxford Companion to Food" that the word arose from the Yiddish "beygel," itself taken from the German "beugel," meaning ring or bracelet. One bit of bagel lore has it that the bagel was invented in 1683, when a Jewish baker in Vienna baked a hard roll in the shape of a stirrup — "bügel" in German — as a thank-you gesture to the cavalry-leading King John III Sobieski of Poland, who had saved the city from Turkish invaders.

  But no matter the etymology, it is indisputable that Eastern European immigrants arriving in the United States at the turn of the 20th century brought the bagel with them to the streets of the Lower East Side, where they were baked and sold on the street stacked on sticks.

  And it is likewise indisputable that in the manner of so many great American movements, the rise of the bagel is inextricably tied to that of a trade union, specifically Bagel Bakers Local 338, a federation of nearly 300 bagel craftsmen formed in Manhattan in the early 1900's.

  Local 338 was by all accounts a tough and unswerving union, set up according to strict rules that limited new membership to the sons of current members. By 1915 it controlled 36 bagel bakeries in New York and New Jersey. These produced the original New York bagels, the standard against which all others are still, in some manner, judged.

  What did they look like? At a mere three ounces, about half the size of the bagel you'll find at a corner coffee cart in Midtown Manhattan, union bagels were smaller and denser than their modern descendants, with a crustier crust and a chewier interior.

  They were made entirely by hand, of high-gluten flour, water, yeast, salt and malt syrup, mixed together in a hopper. Rollers would then take two-inch strips of dough and shape them. A designated bagel boiler would boil the bagels in an industrial kettle for less than a minute, which gave the bagel its tight skin and eventual shine. Finally, a third bagel man would put the bagels on thick redwood slats covered with burlap and place them in a brick or stone-lined oven.

  The finished bagels were put on strings five dozen at a time and left on the doorknobs of retail accounts.

  Local 338 held its ironclad grip on the bagel market for nearly half a century, until industrial bagel-making machines were introduced to the market in the early 1960's. According to Mike Edelstein, who is an owner of Bagel Oasis, and a bagel maker for more than 40 years, "A machine could roll 300 dozen bagels an hour with one man operating it, while two experienced hand rollers could only produce 125 dozen in the same amount of time."

  The introduction of industrial bagel machines meant any retailer or retail-bakery owner could make bagels with nonunion help. Local 338 was essentially broken. Only a few bagel bakers — the best bagel bakers, is how I think of them — would uphold its ideals.

  Sam Thongkrieng of Absolute Bagels on the Upper West Side is one of those bagel makers — a member of a large group of Thai bagel makers spread throughout New York's most prominent bagel shops. Mr. Thongkrieng came to New York in 1980 via Bangkok and college in London, and immediately, he said, started working in bagel shops. "The moment I ate a bagel," he remembered, "I said to myself `This is something different.' " After apprenticing at a chain bagel restaurant called Bagel Nosh, then at Zaro's and Ess-a-Bagel, he opened Absolute in 1990.

  If you ask for a dark, well-baked bagel there, you'll taste something near perfection: a bagel that is crunchy, not too dense or sweet, and just chewy enough. But still quite large. For a real retro taste, it is necessary to order Mr. Thongkrieng's minibagel — a perfect simulacrum of the 1950's New York bagel.

  Also in Manhattan, there is Murray's Bagels, Adam Pomerantz's minichain of excellent and beautifully appointed bagelries, named for his bagel-loving father. Mr. Pomerantz left a successful career on Wall Street to open Murray's, but he surely has his dad's soul. His hand-rolled bagels are crisp and chewy and dark, with a terrific shine. They would be even better, I think, if he used malt to sweeten them, not sugar.

  The Bagelry is the third of Manhattan's triumvirate of bagel gems, owned by Bobby Madorski, whose grandfather was also a bagel man, and who won the family's first bagel bakery in a poker game 60 years ago. The younger Mr. Madorski seems to be a bit of a gambler himself. He is the first serious bagel baker in New York to make his regular-size bagels exclusively by machine (he still hand rolls his minibagels, which must be special ordered). The gamble has paid off. Mr. Madorski's bagels are about the smallest regular-size bagels available in New York, and they are absolutely delicious; crusty, chewy and just salty enough. (Not to speak heresy, but his flat bagels, perfect for vertical toasting, are also fantastic, crunchy and just barely pliant.)

  Terrace Bagels, which sits regally near a corner of Prospect Park in Brooklyn, across from the storied Farrell's bar, is a wonderful example of New York food purveyors at their maddening best: it is lamb dressed as mutton. The bagel bins are small. There is no evidence anywhere that bagels have been boiled, much less baked. Most of the other food on display is Italian, rather than Jewish. But the bagels that miraculously materialize from Louis Thompson's hidden ovens are extremely flavorful; yeasty, with just a hint of sourness. Mr. Thompson's principal bagel roller is Vicharn Tangchitsumran (also known as Boone), who has been hand rolling bagels for more than 30 years. As the Michelin guides put it, he is worth a detour.

  As is a trip up to Fresh Meadows, Queens, where Mike Edelstein and Abe Moskowitz run the incomparable Bagel Oasis, overlooking the nearby Long Island Expressway (heading east, you take Exit 25). Mr. Edelstein and Mr. Moskowitz are former members of Local 338, and together they have more than 100 years of experience baking bagels. The result is a bagel that is fairly petite by today's standards, that has decent chew, excellent flavor, and manages to be dense without being leaden. Marvelous. They also make a fine bagel twist and a terrific pretzel made of bagel dough. If you like that sort of thing, that is.

  I don't much like the eponymous bialys at Hot Bialys, Kitti Phongtankuel's little shop on Queens Boulevard, a stone's throw from the Queens County Courthouse, but I sure do admire the bagels. Mr. Phongtankuel, another alumnus of Bagel Nosh, bought the place in 1983 from Nettie Berkowitz — and promptly set about making fabulous bagels, including a newfangled flat bagel he calls a Bagel Delite. Some malt in the recipe would improve things, but these are still terrific bagels, far superior to the large doughy orbs that many New Yorkers have come to think of, incorrectly, as "good bagels."

  How and why did bagels get so big? The bagel sold at the excellent Ess-a-Bagel on First Avenue is a whopping seven ounces now, or more than twice the size of the traditional union bagel of yore. (It's a pretty good bagel, truth to tell, though sweetened with honey.) The ones at H&H; Bagels on the Upper West Side (and at the unrelated H&H; Midtown East) aren't much smaller than that, and are baked with so much sugar that they almost qualify as a dessert.

  Barbara Kirshenblatt-Gimblett, a professor of performance studies at New York University who is working on a social history of the bagel, said, "The increase in size was an attempt to make a more competitive and more profitable product consistent with the supersized trend" of the 1980's. Bagel cafes, she explained, were a trendy, quick-service franchise concept that spread the gospel of fresh bagels across the country. The bagels served by chains like Bagel Nosh, Einstein Brothers and Bruegger's gradually became bigger and bigger as the notion of supersizing spread, and as the businesses morphed from breakfast and coffee operations into full-fledged sandwich-making restaurants. The bagels needed to be bigger to hold the fillings. New York's independent bagelries soon followed suit.

  Chain bagel shops also popularized the seemingly inexhaustible array of bagel flavors. Mr. Edelstein of Bagel Oasis said that when he began baking bagels, there were only plain, salt, poppy and sesame bagels, and that he made 10 plain bagels for every salted, poppy or sesame bagel. Now, there are bagels flavored with blueberry, cranberry-orange and pesto, even curry. I'm begrudgingly willing to let cinnamon-raisin into the bagel pantheon, and certainly pumpernickel, even "everything."

  But if God had wanted sun-dried tomatoes put into bagels, he would have put more bagel bakers in Italy.