The last time a Sinn Fein leader met a British prime minister was in 1921. That was the encounter between Lloyd George and Michael Collins. "I hope we make a better job of it than we did the last time," Sinn Fein's modern icon, Mr Gerry Adams, told the New Labour leader and Prime Minister, Mr Tony Blair, at Stormont yesterday afternoon.
Mr Blair by implication fully assented. "If we don't seize this opportunity now, we may not see it again in our lifetime," he said.
The meeting lasted between 15 minutes and half an hour. More than 15 minutes, according to a British government source. Almost 30 minutes, said Sinn Fein.
Whichever, of the 11 delegations Mr Blair met at Stormont yesterday, the longest encounter and, dare one use the word again, the most historic, was the Blair-Sinn Fein engagement.
There was consensus between the two camps that it was a "very positive, constructive, and friendly" meeting. The Sinn Fein president accepted that Mr Blair fully embraced the peace process, and could yet be the British Prime Minister to forge a viable settlement.
Mr Blair was accompanied by the Northern Secretary, Dr Mo Mowlam, and the North's Political Development Minister, Mr Paul Murphy. With Mr Adams were the party's chief negotiator, Mr Martin McGuinness, the Sinn Fein vice-president, Mr Pat Doherty, and its administrative head, Ms Siobhan O'Hanlon.
When the groups met in one of the offices of Castle Buildings, handshakes were exchanged away from the cameras. There was a big media brouhaha about the handclasping but Mr Blair made little of its obvious symbolism. "I treated Gerry Adams and the members of Sinn Fein the same way as I would treat any human being."
There was quite an interchange between the two sides, without either the British or the republicans so far compromising on fundamental principles. Mr Blair told Mr Adams that he (the Prime Minister) was a politician "who talked straight with people".
"If we don't seize this opportunity now we may not see it again in our lifetime," he said. "It is very rare for humanity to make sense of history, but this is what we have to do. We either end up as victims of history, or we make sense of it."
Mr Blair told the Sinn Fein team that before becoming Prime Minister he was warned that the Northern Ireland problem was insoluble, and if he had any sense he would steer away from the issue. "But I never accepted that, and that is not just a triumph of hope over adversity," he said.
"There are moments of history when things can be moved forward. I feel a deep sense of responsibility here - it is pointless to go back to the old ways."
Mr Blair, according to reliable sources, came away from his meeting with Sinn Fein, and all the other parties to the talks, convinced that "there was a real will from all sides to move things on".
Mr Adams, in his opening remarks to Mr Blair, "as an Irishman extended a cead mile failte to our country". While this was the first time since 1921 for a Sinn Fein leader to meet a British Prime Minister, he nonetheless hoped that he would be the last British Prime Minister with jurisdiction over Northern Ireland.
Mr Blair allowed this comment float in the air. He made no specific response. Mr Adams told Mr Blair, as British prime ministers have been told before, that he could yet go down in history as the Prime Minister who settled the Northern Ireland problem.
There was discussion on consent and on the absolute need for Sinn Fein to remain committed to the principles of non-violence and democracy.
At one stage Mr Adams suggested that if Mr Blair had been raised in an area like nationalist west Belfast he, too, might have joined the IRA. "If you lived where I lived, who knows where you would have ended up in all of this," he said.
While the encounter and the private handshake infuriated the DUP leader, the Rev Ian Paisley, who is boycotting the talks, the talks participants, even the unionist politicians, were fairly sanguine about the whole business.
The Ulster Unionist Party leader, Mr David Trimble, said he felt sorry for Mr Blair that he felt it necessary to shake hands with Mr Adams. He believed Mr Blair saw it as something "he had to go through".
Mr David Ervine, chief spokesman for the Progressive Unionist Party, said the handshake and the meeting were something that had to be done. "Now it's done, and one would hope it is a three-day wonder, and we can get on with the job in hand."
As far as the talks were concerned, it was a case of "so far so good". He was impressed that the talks were proceeding calmly. "There are plenty of histrionics outside Stormont, but not too many inside," he said.
The SDLP leader, Mr John Hume, said the visit of Mr Blair to Stormont demonstrated very clearly how high he has placed Northern Ireland on his political agenda.
The Minister of State for Foreign Affairs, Ms Liz O'Donnell, said the talks had now gone well beyond the politics of a handshake. "Sinn Fein are part of the process, and we are into substance. That is what is important, rather than the symbolism of handshakes."
Mr Seamus Close, deputy leader of the Alliance Party, said he was very impressed with Mr Blair's determination to make the negotiations succeed. "Tony Blair by coming here has set his imprimatur on the talks."