The president reinforced the impression that he was unenthusiastic about the target of “50 by 2050” by not using the phrase in his final press conference.

But Mr Bush had some success in shifting the terms of the climate change debate. The G8 did not set a target for the G8 – it commited to advocate a global target to which the big emerging economies would also have to commit.

This protects the US position that it makes no sense to define climate change objectives unless they are shared by China, India and other fast-rising nations.

Mr Bush also won increased emphasis on financing the development and diffusion of new technology, in keeping with his preference for a technology-driven rather than target-driven approach to addressing global warming. There was backing for nuclear power too.

On the world economy, the US president kept the focus on fundamental supply and demand forces driving high oil prices – and away from the view that speculators are to blame.

The G8 also issued a strong statement of support for Doha round trade talks, something Mr Bush would dearly like to see completed during his presidency.

Mr Bush was also able to point to “progress on alleviating sickness in Africa” along with new steps to increase accountability for G8 aid promises – a longstanding US complaint.

Many outside the US refuse to consider Mr Bush a champion of development or Africa, pointing to the still very low level of US foreign aid relative to the size of its economy.

But Mr Bush has increased US aid to Africa and for fighting tropical disease significantly since coming to office, something he regards as an important part of his legacy.

It remains true that no big breakthroughs were achieved at the summit – and that many at the G8 believe the progress on climate change was achieved in spite of rather than as a result of Mr Bush’s leadership.

Yet the president will be pleased with the general tone the meeting set. Five years on from the Iraq war, with Tony Blair, Jacques Chirac and Gerhard Schroder long gone from the G8 stage, much of the poison has gone out of transatlantic divisions, even though many in Europe still look forward to Mr Bush’s departure.

Mr Bush can also plausibly argue that relations with the rising powers of Asia are in better shape than they were when he took office. Following his bilateral meeting with Mr Bush, Manmohan Singh, the prime minister of India, said “our relationship with the US has never been in such good shape as it is today.”

Hu Jintao, the president of China, who also met Mr Bush on Wednesday, said “new progress has been made in China-US relations in recent years” adding that bilateral ties were on a “sound and steady course”.