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Down the street, artist Arlene Rush said she didn’t require extra security in her third-floor studio, because it required several keys to access from the street.

“I don’t really need the cops,” added neighbor Guy Kloppenburg, a teacher. “We knock on each other’s door to make sure everyone is OK.”

Bloomberg promised “a very heavy police presence” in the darkened neighborhoods, which include much of Manhattan south of the Empire State Building, from the East River to the Hudson River. Even outside the blackout areas, police deployed vans and patrol cars with their roof lights on, along with officers on the streets in a robust show of force.

For the 8 million people who live here, the city was a different place one day after being battered by the megastorm — a combination of Hurricane Sandy, a wintry storm and a blast of arctic air.

Schools were shut for a second day and were closed Wednesday, too. The New York Stock Exchange was closed for a second day, the first time that has happened because of weather since the 19th century, but planned to reopen Wednesday, with Bloomberg ringing the opening bell.

Problems to high-voltage systems caused by the storm forced the utility to cut power Tuesday night to about 160,000 additional customers in Brooklyn and Staten Island.

Consolidated Edison, the power company, estimated it would be four days before the last of the 323,000 customers in Manhattan and Brooklyn who lost power have electricity again. For the Bronx, Queens, Staten Island and Westchester County, with more than 450,000 outages, it could take a week.

The city modified its taxi rules and encouraged drivers to pick up more than one passenger at a time, putting New Yorkers in the otherwise unthinkable position of having to share a ride with a stranger.

At a small market called Hudson Gourmet, in Manhattan’s Greenwich Village, cashiers made change by candlelight and shoppers used flashlights to scour the shelves.

Lee Leshen used the light from his phone to make his selections — three boxes of linguine and a can of tomatoes. His power was out, but the gas in his stove worked, so he could cook.

He said he almost never cooks but is learning.

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Associated Press writers Meghan Barr, Verena Dobnik, Frank Eltman, Tom Hays, Larry Neumeister, Karen Matthews, Alexandra Olson, Jennifer Peltz, and Hal Ritter contributed to this report.