A few days after the exhibition opened, two Dutch historians issued a press release claiming to have identified the dress’s owner. One of the scholars knew of a letter from 1642—written partly in a secret code, which she had cracked—describing the clothes belonging to the ladies-in-waiting of Henrietta Maria, the Queen Consort of Britain’s King Charles I, which had sunk in a shipwreck en route to Rotterdam. “The maides . . . haue lost all theire clothes there bagage ship sprong a leake and sank,” the king’s sister, Elizabeth, wrote. At the time, Henrietta Maria and her entourage had been on a secret mission to Holland to pawn the crown jewels of England to fund the English Civil War. The dress, rumored to be large, was thought to have belonged to one of the four women in the Queen Consort’s service, Jean Kerr, the Countess of Roxburghe, who, in 1642, was nearing the end of a long career as both royal governess and spy. The story that the dress belonged to a royal spy was picked up by the Guardian and Dutch News and went viral.

When I visited them last year, the divers explained that they had never been convinced by the scholars’ version of events. “It just doesn’t make sense,” van den Bor, who is blond and burly, told me politely. As he and Dijker explained, the shipwreck mentioned in the missive was a hundred and eighty kilometres away. The dress is also not especially large. Jacco Bakker, a forty-three-year-old Texel native and the club’s videographer, had his own theories about the dress’s owner. “I think the first crate were her favorites, with the dress and the pomander and the cape, and the other things were her second choice,” he said. The divers’ explorations had led them to suspect that the ship held a mixture of personal effects from an élite European or British woman and goods from the Ottoman Empire. (Historians recently arrived at the same conclusion independently.)

I was talking to the divers and Hordijk at a small café serving fish, next to the Kaap Skil, a building with an exterior made of wood reclaimed from the Noord-Hollands Canal. We had just visited one of the several “jutter” collections on the island—this one part of the Kaap Skil, and housed in a shack in the museum’s courtyard. “Jutter” means “wreckage” or “debris” in the West Frisian dialect, and includes what the divers call the “strange and funny stuff”—mammoth bones, a box marked “cocaine,” thousands of messages in bottles—that beachcombers come across.

As Gilles van Mil, the longtime steward of the Kaap Skil’s jutter museum and a local historian, told me, when he came to join the divers and Hordijk at the cafe, the tradition of “jutter” is related to an old Texel code, that what the sea gives, the finder keeps.

“Whenever you are cold in winter, you would go to the beach looking for wood for the stove,” van Mil said. He was dressed in a homespun tunic and a navy-blue sailor’s cap. “If you wanted to build yourself a ship, you’d go to the beach several times and carry everything you could in planks and boards and take it home. This whole shed”—he gestured in the direction of the shack next door—“are all masts of sailing ships, and the top are the beams.”

The rules for divers are stricter than for beachcombers. In 1992, the Netherlands signed the Malta Convention, which meant that archeological finds, including underwater ones, had to be preserved “in situ,” and excavated only by “qualified, specially authorized persons.” According to Dutch and E.U. law, when the divers salvaged the dress and ship’s treasures, they did so illegally, regardless of the fact that they donated their finds to the Kaap Skil. There are good reasons for the law. In archaeology, as one staff member at Huis van Hilde told me, “context is king.” The inexpert rending of objects from the place where they are found deprives archaeologists of critical tools to understand the objects’ history and significance. From a conservator’s perspective, the account of the divers stuffing a seventeenth-century dress into a bag, bringing it up to the surface, hosing it down, and then hanging it to dry is a horror story. (Sarah Scaturro, the lead conservator for the Costume Institute, at the Metropolitan Museum of Art, told me that “it is a miraculous find, but it is even more miraculous that it survived their improper handling.”) For some I spoke to, the divers seemed not much better than looters; little matter that, as the archeologist Michiel Bartels speculated, if they had not found the ship, its contents would likely have been washed away within weeks, if not days.

“That was already done and we didn’t want to throw it back,” Hordijk said, when I brought up the objections to the divers’ methods. A tall, frank woman, she has a warm rapport with the men. Since finding the dress, she has acted as a go-between for them and the government. In the fall of 2016, Bartels and Alec Ewing, a conservator, were hired to work with the divers to create an inventory of their finds and to draw up an archaeological map of the Wadden Sea. Bartels believes that the government is working toward finding a place for diving volunteers in underwater archeology. Still, when I met them, the divers reminisced about the time before the Malta Convention.

“It was very open,” Bakker said. “But now it’s sh-h-h”—he placed his finger to his lips—“or you go to jail.” At the same time, he acknowledged that there were few on the island who would report them for diving.

“We live in the same streets,” Dijker said.

“I get my pizzas from Hans,” Hordijk said, referring to Dijker’s business.

“It's a small community,” van den Bor said. Policy and supervision now come from the Province of North Holland, on the mainland. “It’s what we call ‘overkant’: ‘The Opposite Side of the Water.’ ”

“A different culture?” I ventured.

“No culture,” Dijker said.

Hordijk smiled. “There’s only one culture. That’s Texel,” she said.

On my last day on Texel, Dijker took me for a tour of the island in his pizza-delivery truck, pointing to the spot where they’d found the shipwreck, and pausing at a pair of wells where, in the seventeenth century, the island’s orphans had earned their keep by pumping water and selling it to sailors anchored on the Texel Roads. The tour ended at a corrugated-metal shack, the divers’ clubhouse. Inside, it was organized with an eye for beauty. There was a high shelf lined with austere clay pots: the sort of thing you commonly find on a seventeenth-century ship’s deck, Dijker explained, casually. I caught sight of a glimmering pile of seventeenth-century sewing pins and another of thimbles in a homemade display case.

The divers knew that their time with the wreck was almost up; soon, government divers would cast a massive net over the sunken ship, to protect it from erosion and infestation. (The ship was shrouded in August, 2016; the net has remained in place ever since.) The diving club had been learning more about the vessel, they told me: the location of the ship’s galley, which showed signs of a fire, and the quarters of the ship’s doctor. It struck me that their findings, if only they had been able to share them, would have been invaluable to the historians and archeologists who so disapproved of the divers’ methodology. Dijker pointed out a blue-and-white porcelain jar, which had been filled with some kind of medicine. He had washed it out because it smelled. “It was before we knew,” he said, sheepishly. The club was using it as a cutlery holder.

The divers invited me to sit at their wooden table and Bakker played me some of the films he has made of the club’s dives, which he sets to music. In one video, he follows a fish, to the soundtrack of the theme from “Mission: Impossible.” The men described diving as a “hobby,” but it seemed more like a calling. “We are the only diving club on the island,” Bakker said, explaining that, when people have a car accident and crash into the sea, the club’s members are not legally allowed to rescue them. “But, of course, we jump into the water anyway.”

Dijker’s cell phone rang; it was his wife reminding him that it was time to open the pizza shop. The men were planning to go diving together the following weekend. “The dress is gone from the museum, and it’s a little bit hurting for us,” Dijker said, going on to lament the net that would soon prevent them from exploring the ship. Bakker still dreamed of discovering the ship’s bell, which he suspected would be engraved with the vessel’s name and date. He was sure that it was still out there, waiting to be found.