The United States is now that weary Titan. In the British case, the angst was a result of the unexpectedly protracted, bloody and costly Boer war, in which a small group of foreign insurgents defied the mightiest military the world had seen; concern about the rising economic power of Germany and the United States; and a combination of imperial overstretch with socio-economic problems at home. In the American case, it's a result of the unexpectedly protracted, bloody and costly Iraq war, in which a small group of foreign insurgents defies the mightiest military the world has seen; concern about the rising economic power of China and India; and a combination of imperial overstretch with socio-economic problems at home.

Iraq is America's Boer war. Remember that after the British had declared the end of major combat operations in the summer of 1900, the Boers launched a campaign of guerrilla warfare that kept British troops on the run for another two years. The British won only by a ruthlessness of which, I'm glad to say, the democratic, squeamish and still basically anti-colonialist United States appears incapable. In the end, the British had 450,000 British and colonial troops there (compared with some 150,000 US troops in Iraq), and herded roughly a quarter of the Boer population into concentration camps, where many died.

In a recent CNN/Gallup poll, 54% of those asked said it was a mistake to send American troops into Iraq, and 57% said the Iraq war has made the US less safe from terrorism. The protest camp outside President Bush's ranch in Crawford, which grew around the mother of a soldier who died in Iraq, exemplifies the pain. CNN last Sunday aired a documentary with top-level sources explaining in detail how the intelligence on Saddam's weapons of mass destruction was distorted, abused, sexed up and, as the programme was entitled, Dead Wrong. This will hardly be news for British or European readers, but the facts have not been so widely aired in the US. In another poll, the number of those who rated the president as "honest" fell below 50% for the first time. This week, he has again attempted to bolster support for his administration and his war. It doesn't seem to be working.

A recent article in the New York Times plausibly estimated the prospective long-term cost of the Iraq War at more than $1 trillion. If Iraqi politicians do finally agree a draft constitution for their country today, only the world's greatest optimist can believe that it will turn Iraq into a peaceful, stable, democratic federal republic. Increasingly, the Islamic Republic of Iran quietly calls the shots in the Shia south of Iraq. As the Washington joke goes: the war is over, and the Iranians won.

Meanwhile, oil prices of more than $60 a barrel put the price of petrol at American pumps up to nearly $3 a gallon for basic unleaded fuel. For someone from Europe this is still unbelievably cheap, but you should hear the shrieks of agony here. "Gas prices have changed my life," moaned a distressed Californian commuter. If higher energy prices persist, they threaten not just a still vibrant economy but a whole way of life, symbolised by the Hummer (in both its civilian and military versions). Besides instability in the Middle East, the main force pushing up oil prices is the relentless growth of demand for energy from the emerging economic giants of Asia. The Chinese go around the world quietly signing big oil supply deals with any oil-producing country they can find, however nasty its politics, including Sudan and Iran. When a Chinese concern tried to buy a big California energy company, that was too much - American politicians screamed and effectively blocked the deal.

China and India are to the United States today what Germany and America were to Britain a hundred years ago. China is now the world's second largest energy consumer, after the United States. It also has the world's second largest foreign currency reserves, after Japan and followed by Taiwan, South Korea and India. In the foreign reserve stakes, the US comes only ninth, after Singapore and just before Malaysia. According to some economists, the US has an effective net savings rate - taking account of all public spending and debt - of zero. Nil. Zilch. This country does not save; it spends. The television channels are still full of a maddening barrage of endless commercials, enticing you to spend, spend, spend - and then to "consolidate" your accumulated debt in one easy package.

None of this is to suggest that the United States will decline and fall tomorrow. Far from it. After all, the British empire lasted for another 40 years after 1905. In fact, it grew to its largest extent after 1918, before it signed its own death warrant by expending its blood and treasure to defeat Adolf Hitler (not the worst way to go). Similarly, one may anticipate that America's informal empire - its network of military bases and semi-protectorates - will continue to grow. The United States, like Edwardian Britain, still has formidable resources of economic, technological and military power, cultural attractiveness and, not least, the will to stay on top. As one British music hall ditty at that time proclaimed:

And we mean to be top dog still. Bow-wow.

Yes, we mean to be top dog still.

You don't have to go very far to hear that refrain in Washington today. The Bush administration's national security strategy makes no bones about the goal of maintaining military supremacy. But whether the "American century" that began in 1945 will last until 2045, 2035 or only 2025, its end can already be glimpsed on the horizon.

If you are, by any chance, of that persuasion that would instinctively find this a cause for rejoicing, pause for a moment to consider two things: first, that major shifts of power between rising and falling great powers have usually been accompanied by major wars; and second, that the next top dog could be a lot worse.

So this is no time for schadenfreude. It's a time for critical solidarity. A few far-sighted people in Washington are beginning to formulate a long-term American strategy of trying to create an international order that would protect the interests of liberal democracies even when American hyperpower has faded; and to encourage rising powers such as India and China to sign up to such an order. That is exactly what today's weary Titan should be doing, and we should help him do it.

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