The fisherman was diving near Whidbey Island gathering sea cucumbers when his air hose snagged on a massive object jutting from the muck at the bottom of Puget Sound.

Doug Monk followed his hose back until he reached a barnacle-encrusted hunk of metal as tall as him. It was the massive arm of an old ship’s anchor.

Since stumbling upon the 9-foot-long anchor in January 2008, Monk and a group of amateur sleuths have argued with historians, scoured books and explorers’ journals, unearthed centuries-old patents and British court documents and asked the U.S. government’s weather experts to recreate 18th-century currents....