Officer O’Gorman, who is assigned to the Midtown North Precinct, stood in front of Junior’s, near Shubert Alley, where the smell of fruity martinis and the sound of forks and knives click-clacking on ceramic plates fill the air. In his Irish accent, Officer O’Gorman declared, “This is the Mason Dixie,” the invisible line on 45th Street that divides Midtown South and Midtown North.

Later, on a corner of Seventh Avenue and West 45th Street, a throng of impatient tourists hedged into the street, though they did not have the light. Officer Reyes spread out his arms, holding back the crowd as a taxi breezed through the intersection. A man dressed as Spider-Man had jumped in front of jaywalkers on the other side of 45th Street. He remained in character. “Get back; stand back,” Spider-Man said, playing the role of crossing guard as if life or death.

“Thank you, Spider-Man,” Officer Reyes said, eliciting laughs from those nearby.

Police officers are stars here. Every few feet, tourists stopped Officers Reyes and Hemme and asked them to pose for photographs. A woman pulled out an iPhone, its pink rubber case topped with rabbit ears, and snapped a photo.

At 11:39 p.m., officers Reyes and Hemme climbed back into the van. It was time for a much-needed caffeine run and they made a pit stop at the Dunkin’ Donuts on 34th Street, where they bought two 20-ounce bottles of Coke Zero. The respite was short. The radio was abuzz: “Disorderly. One Park Avenue.” “Disorderly, outside Duane Reade.” “Black BMW with trunk open.”

And then came, “Female being assaulted.” Officers Reyes and Hemme arrived at 34th and Broadway. Other officers were already there. A woman stood on the corner and explained that the man she was with had choked her before throwing her out of the car. She wore a gray sweatsuit, the pants streaked with dirt. Her long dark hair was tangled. Minutes later, at midnight, an ambulance pulled up.

“She didn’t break anything, so that’s good,” Officer Hemme said, as her partner steered the van back toward the precinct house, their 4 p.m.-to-midnight tour long done.