It was the morning rush in New York Harbor on Thursday when the Eagle, a majestic, 295-foot, three-masted Coast Guard ship, set sail from beneath the Verrazano-Narrows Bridge. On the Eagle’s starboard side, a Staten Island Ferry chugged toward Lower Manhattan, while on its port side, a Fire Department fireboat shot plumes of water in front of the Statue of Liberty.

Standing on the deck among the ship’s crew and its guests were Sydney James Harcourt and Kamille Upshaw, two cast members from “Hamilton,” the popular Broadway musical about the nation’s first secretary of the Treasury and, not incidentally, the father of the United States Coast Guard. They were there to celebrate Coast Guard Day, observed every Aug. 4 to commemorate the founding of the maritime service branch.

“Heave,” called a group of senior cadets, or cadre, from the Coast Guard Academy, who were holding the ropes leading up to the towering masts. “Ho,” yelled some 30 first-year cadets, known as swabs, as they tugged in unison.