LONDON — On the day that the president of America flew in to Slovenia to begin his last European tour, the BBC was much more interested in the visit of Donald Trump to Scotland, where the tycoon faces opposition to his plan for a golf resort on an unspoilt stretch of the North Sea coastline. Americans and Europeans may be impatient for a new, younger president who is more to their taste, but Mr. Trump is hardly a spring chicken himself. The fact that the leader of the free world receives so little attention here these days may, however, say more about Europe’s warped sense of priorities than it does about President Bush.

It goes without saying that Mr. Bush has not always handled relations with his allies in the most tactful way. He admits as much himself.

While crossing the Atlantic in Air Force One, he told the London Times that he regretted having sounded on occasion like “a guy really anxious for war.” He added ruefully: “I think that in retrospect I could have used a different tone, a different rhetoric.”

Well, maybe. It is easy to pick out a couple of presidential phrases from the years immediately after September 11, 2001, that gave ammunition to those Europeans who believe in the bellicose caricature of the Bush presidency: “bring them on” and “dead or alive” are examples. Yet compared to the rhetoric employed by such war leaders as Washington (“conquer or die”), Lincoln (“every drop of blood”), Roosevelt (“a date that will live in infamy”) or Churchill (“we shall never surrender”), the martial words of Mr. Bush are mild indeed.

If anything, Mr. Bush received much more obloquy for his premature announcement that the war in Iraq was over. And his pronouncements about the possible use of force to stop Iran acquiring nuclear weapons have been so circumspect, so carefully coded, as to have erred on the side of caution.

At all events, the latest report from the International Atomic Energy Authority makes the conclusion inescapable that America and Europe have utterly failed to deter Tehran from pursuing its uranium enrichment and the rest of its nuclear program.

Would that Mr. Bush had been a little more bellicose over the past eight years! Only this week, the Iranian president, Mahmoud Ahmadinejad, made a televised broadcast to his nation, declaring: “With God’s help today [the Iranian nation] has gained a great victory and [our] enemies cannot do a damned thing.” Now that’s what I call warmongering.

But what does the West do in response? The emissary of the European Union, Javier Solana, flies to Tehran with another package of incentives. Everybody knows that Iran will continue to ignore either carrots or sticks.

Yesterday President Bush stood side by side with Chancellor Merkel of Germany, the two leaders united in the resolve to do — what, exactly? The president’s talk of “tough multilateralism” turns out to mean doing what Europe wants — that is, not much. He isn’t helped by Senator Obama’s offer to talk to Mr. Ahmadinejad without preconditions, which undermines his own diplomatic aim of isolating Iran.

This week’s European visit by Mr. Bush, which culminates in Sunday’s symbolic farewell to Queen Elizabeth II at Windsor Castle, actually demonstrates that the transatlantic divisions over Iraq have largely been healed. Both Ms. Merkel and President Sarkozy of France are far more sympathetic allies than their predecessors, while Italy recently re-elected Silvio Berlusconi, another pro-American.

In eastern Europe fear of resurgent Russian nationalism has reminded even those who opposed the war of which friends they can rely on — and countries heavily dependent on Russian oil and gas, such as Germany, are not among them.

As for the perennial transatlantic bones of contention — climate change, human rights, military spending, the Middle East — they are, for the moment at least, much less prominent in Europe than, say, a year ago. The French have even mooted the idea of fully rejoining North Atlantic Treaty Organization, while both Al Qaeda and the Taliban have been losing ground. In the war on terror, as in everything else, nothing succeeds like success.

Paradoxically, therefore, Mr. Bush will bequeath the next president a legacy, not of transatlantic tension, but of comparative harmony. What is likely to vitiate the alliance for years to come is not the freedom or democracy agendas that we associate with the Bush administration, but their virtual abandonment. Cutting loose countries on the bloody crossroads between liberty and tyranny is a certain way to plunge the West into conflict, both internal and external.

For example, Lebanon — one of the great successes of the post-September 11 era — is already slipping back under the domination of Hezbollah and its sponsors, Iran and Syria. Another war between Israel and Hezbollah will inevitably pit the next American administration against Europe, whoever is president by then.

Indeed, a President Obama might feel even more obliged than a President McCain to demonstrate his support for Israel: “We should never seek to dictate what is best for the Israelis and their security interests,” he says. Europeans who expect that Mr. Obama would do just that are likely to be bitterly disappointed.

It was, after all, Mr. Bush who first committed America to a two-state solution, and no future president will retreat from that. But the growing lobby in Europe that wants to abolish Israel as a Jewish homeland in order to appease Arab or Muslim demands now prefers to speak of a “one-state solution.” There is plenty of room for future strife here. One day, Europeans may look back on Mr. Bush with nostalgia.

Mr. Johnson is the editor of Standpoint.