American presidents often find their true voice in a crisis. In 1861, on the eve of the civil war, Abraham Lincoln put the case for the acceptance of majority rule in a democracy. In 1933, Franklin D. Roosevelt instilled confidence in a Depression-wracked nation with the words: "The only thing we have to fear is fear itself."

George W. Bush's address to a joint session of Congress on Thursday evening must rank among the most eloquent of presidential speeches. It was also one of the most important. In concise terms, Mr Bush explained to the American public and the world how his administration intends to wage a new war on terrorism.

The president spoke with authority. He moved his audience, Democrats and Republicans alike. He stressed the virtues of patience and working with allies. He made clear there could be no quick and easy response to the terrorist attacks on New York and Washington. He stressed, wisely, that his new war was not a campaign against the Islamic world.

In the initial phase of the crisis, the impression gained ground that the president was out of his depth. His advisers, notably vice-president Dick Cheney and Colin Powell, secretary of state, came across as more polished, more self-assured.

Mr Bush's language has not always struck the right chord. His pledge to capture Osama bin Laden, the fugitive Saudi terrorist, "dead or alive" came straight from the presidential gut; but it belonged more to the saloon bars of the wild west.

Some will ask whether Mr Bush can make the transition from sheriff to statesman. On the evidence of the first 10 days of the crisis, especially after his well crafted speech, there is some room for optimism.

Mr Bush has resisted the temptation to retaliate massively against ill-defined targets. Bill Clinton, his predecessor in the White House, lobbed missiles in the direction of Afghanistan and Sudan to no obvious benefit. The administration now seems to be preparing for commando raids against Mr bin Laden's networks in northern Afghanistan and the Taliban regime which harbours them.

A long struggle

The consequences of a strike against the Taliban are unpredictable. A wave of refugees could destabilise neighbouring Iran or Pakistan. There could be further terrorist attacks against the west. None of these risks is negligible; but the important message in the president's speech is that he is digging in for a longer struggle.

To this end, Mr Bush has listened to allies such as Britain and France urging the US to avoid actions that could provoke a backlash in the Middle East. He has also taken counsel - so far - from those pressing for the widest possible international coalition to pursue the narrow aim of punishing the perpetrators of the terrorist outrages and their sponsors.

Worldwide sympathy

There is a view that a broad coalition is an invitation to paralysis. But this is a crisis in which the US has attracted worldwide sympathy, from erstwhile enemies such as Cuba and Iran to long-time rivals such as China and Russia. As Gen Powell has recognised, there are diplomatic opportunities as well as risks in maintaining the coalition.

The crisis is also forcing the administration to review its own foreign policy prejudices. Mr Bush's circle has dropped the occasionally harsh unilateralist rhetoric that characterised his first few months in office. Multilateralism is no longer a dirty word.

The administration is now prepared to look at international co-operation against money-laundering and a crackdown on tax-haven secrecy. The goal of disrupting the terrorists' financial networks has superseded reservations about any measures that could weaken tax competition.

Elsewhere, the US is ready to ease sanctions against Pakistan, which were imposed after the regime carried out nuclear tests in 1998. The policy reversal - which would also apply to India - marks another step towards realpolitik as Pakistan is a key potential ally in any strike against terror networks in neighbouring Afghanistan.

In the coming weeks and months, the international coalition will come under strain. Military strikes will add to the stresses. But as long as the US remains realistic about its objectives, there is no reason why the coalition cannot hold.

Mr Bush has had a good week. He no longer comes across outside the US as a trigger-happy Texan. He has challenged another national stereotype: that Americans neither have the attention span nor the stomach for a protracted struggle that is likely to involve US casualties.

This crisis therefore marks the education of a modern American president. But we do not yet know whether it will end in the making of a president.