THE PRESENCE of British Prime Minister Tony Blair made clear that President Bush addressed not only Congress and the American people last night, but the world.

The leadership he put on display was measured, not impetuous. Because Mr. Bush rose to the responsibility imposed on him, the American people have a clearer idea of what happened last week and what it is they need to do.

Mr. Bush himself appeared to have heeded what Federal Reserve Board Chairman Alan Greenspan earlier told the Senate Banking Committee about economic measures: "It's far more important to be right than quick."

The president was asking the American people to be "calm and resolute," not mindlessly revengeful. Even as U.S. forces converge on the Middle East and Central Asia, he was not promising their immediate use, but sketching systematic measures intended to eradicate the scourge of terrorism.

One of these, indeed, was the ultimatum to the Taliban leadership of Afghanistan to surrender Osama bin Laden and his network. That was the toughest part of the speech, and, chillingly, brought the most enthusiastic applause.

But his main promise was more sophisticated: using "every means of diplomacy, every tool of intelligence, every instrument of law enforcement, every financial influence and every necessary weapon of war, to the disruption and defeat of the global terror network."

Mr. Bush called on foreign nations to choose sides, but asked for the help of their "police forces, intelligence services and banking systems," not their bombers.

To security experts who had warned that the mission to quell terrorism is fragmented in Washington, he proposed a new office of homeland security. Gov. Tom Ridge of Pennsylvania will coordinate the many agencies involved.

The American people are remarkably unified at this moment, as was shown by the visit of clergymen of all major faiths to the White House before the speech. Mr. Bush made clear that the struggle is not against the great religion of Islam practiced by many Americans, but against terrorists who abuse it.

The people will rally behind the presidential call to purpose, patience, resolution and, if need be, sacrifice. Moving as his performance was, it was not Mr. Bush who unified them, but the suicide terrorists last week.

Most of the nations of the world are also rallying round. The attack on the World Trade Center, given its international work force, was an assault on some 80 nations and peoples, not just this one.

The war against terrorism must aim to extinguish the cells and networks, as the president emphasized, not just get one leader. It must break up the financial lifelines. Above all, it must cut down, not promote, recruitment.

Mr. Bush exceeded the promise of his previous performances last night. The nation is stronger for it.