The institute, where famed physicist Albert Einstein once was a faculty member, plans to build 15 housing units, screened by trees, on seven acres. It will permanently preserve the remaining 14 acres.
Thursday's planning board decision is "a win-win for the institute and the battlefield," said institute spokeswoman Christine Ferrara.
Opponents, though, say they will appeal the decision within 45 days of the planning board's final written approval.
"This is not the end," said Jerry Hurwitz, president of the Princeton Battlefield Society, a nonprofit that has opposed the housing proposal since it first came before the planning board in 2003. The board's "decision was a mistake and its reasoning highly flawed," he said.
"It came down to the institute being famous all over the world," he said. "They're nice guys and should be able to do whatever they want on their land."
Any effort to stop the housing development was viewed by the board as taking its land, Hurwitz said. The board voted unanimously in favor of the project in its fourth and final meeting on the issue.
"One of the board members said, 'You're taking [land] but not offering any money for it,' " Hurwitz said. "We would be able to get the money for it, but they're not selling it."
Two Pulitzer Prize-winning historians, James McPherson and David Hackett Fischer, proposed the compromise that the board later accepted.
In additional to preserving some land and building the new housing, the compromise also called for archaeological work to recover artifacts, a 200-foot buffer zone next to the park, interpretive markers to help visitors understand the battle, and removal of trees and brush not present in 1777.
"We have focused on the positive impact of creating more open space and access, and boosting the interpretive level of information on the battlefield," Ferrara said. "We'd be more than a willing partner with the battlefield society or another entity to make that happen."
The American victory at Princeton on Jan. 3, 1777, followed a success over Hessian mercenaries at Trenton on Dec. 26, 1776.
Washington's army was brushed aside by Redcoats at the Second Battle of Trenton on Jan. 2, 1777. That night, he marched around the British army's left flank to attack its rear at Princeton.
At one point during the fight, Washington urged his soldiers on. "They faced about, and the arms were leveled at both sides - Washington between them - even as though he had been placed between them as a target for both," wrote an American colonel who was there.
"Instantly there was a roar of musketry followed by a shout," the officer wrote. "It was the shout of victory. On raising our eyes, I discovered the enemy broken and flying, while dimly, amid glimpses of the smoke, was seen Washington alive and unharmed, waving his hat and cheering his comrades in pursuit."
Institute officials said they valued that history and believed the McPherson-Fischer plan addressed the needs of both sides.
They say the Princeton Battlefield State Park would not exist if not for the institute, which provided 60 percent of the land to the state in 1973.
The sale of those 32 acres was made based on a commitment that the institute's land east of the battlefield state park's boundary could be used as a future site of housing, officials said.
The additional housing would allow faculty members more time on campus and encourage collaboration between them and visiting scholars.
Einstein was a faculty member from 1933 to his death in 1955, and sometimes walked to the campus from his home less than a mile away.
Plans call for the construction of eight townhouses and seven single-family houses.
The project's opponents say the housing would undermine the historic integrity of the battlefield, where numerous artifacts - musket balls and cannon grapeshot - have been discovered.
"We knew that [winning] was a long shot with the planning board," Hurwitz said. "But we still hope to win the Battle of Princeton."
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