It was then that they began to rely on advice from Tunisia, Serbia and the Academy of Change, which had sent staff members to Cairo a week before to train the protest organizers. After the police used tear gas to break up the protest that Tuesday, the organizers came back better prepared for their next march on Friday, the 28th, the “Day of Rage.”

This time, they brought lemons, onions and vinegar to sniff for relief from the tear gas, and soda or milk to pour into their eyes. Some had fashioned cardboard or plastic bottles into makeshift armor worn under their clothes to protect against riot police bullets. They brought spray paint to cover the windshields of police cars, and they were ready to stuff the exhaust pipes and jam the wheels to render them useless. By the early afternoon, a few thousand protesters faced off against well over a thousand heavily armed riot police officers on the four-lane Kasr al-Nile Bridge in perhaps the most pivotal battle of the revolution.

“We pulled out all the tricks of the game — the Pepsi, the onion, the vinegar,” said Mr. Maher, who wore cardboard and plastic bottles under his sweater, a bike helmet on his head and a barrel-top shield on his arm. “The strategy was the people who were injured would go to the back and other people would replace them,” he said. “We just kept rotating.” After more than five hours of battle, they had finally won — and burned down the empty headquarters of the ruling party on their way to occupy Tahrir Square.

Pressuring Mubarak

In Washington that day, President Obama turned up, unexpectedly, at a 3:30 p.m. Situation Room meeting of his “principals,” the key members of the national security team, where he displaced Thomas E. Donilon, the national security adviser, from his seat at the head of the table.

The White House had been debating the likelihood of a domino effect since youth-driven revolts had toppled President Zine el-Abidine Ben Ali in Tunisia, even though the American intelligence community and Israel’s intelligence services had estimated that the risk to President Mubarak was low — less than 20 percent, some officials said.

According to senior officials who participated in Mr. Obama’s policy debates, the president took a different view. He made the point early on, a senior official said, that “this was a trend” that could spread to other authoritarian governments in the region, including in Iran. By the end of the 18-day uprising, by a White House count, there were 38 meetings with the president about Egypt. Mr. Obama said that this was a chance to create an alternative to “the Al Qaeda narrative” of Western interference.

American officials had seen no evidence of overtly anti-American or anti-Western sentiment. “When we saw people bringing their children to Tahrir Square, wanting to see history being made, we knew this was something different,” one official said.