Such images demonstrate that the gulf between the two sides is narrowing. Yet Wednesday's fracas in Londonderry - and John Major's subsequent threat to cancel next week's first meeting between the republicans and Michael Ancram, the Northern Ireland minister of state - is a reminder of how long and tortuous is the road that lies ahead.
It is tempting, but inaccurate, to see both the Prime Minister's angry reaction to the violence in Londonderry and, indeed, the Speaker's decision this week to ban Adams's book launch party in the Commons as of a piece; illustrations of how difficult it is for the British establishment to accept the gradual transformation of a former terrorist enemy into a conventional political force. Betty Boothroyd's decision probably had more to do with the widely shared irritation among MPs at the years that Mr Adams spent as MP for West Belfast without ever taking up his seat.
Equally it is easy to depict Mr Major's response to Wednesday's demonstration as an impetuous mistake; to wait for an apology from Sinn Fein before agreeing to reinstate the meeting - as the Prime Minister hinted he might do - might well have meant an indefinite wait, followed by a messy "working assumption'' that Sinn Fein had repented and a possibly permanent blow to the Government's credibility. But if it was a mistake, he extricated himself from it with swiftness and even some elegance in the Commons by making it clear that he expected the talks would go ahead. And secondly, British officials argue strongly that it was anything but impetuous. He discussed his public reaction with Sir Patrick Mayhew at length; he wanted to reflect overnight on what had happened; and he had an important point to make.
That point was that if Sinn Fein wants to be treated as a conventional political party then it has to behave like one. Indeed some officials see Wednesday's events as precisely vindicating the need for the "decontamination" period offered by the exploratory dialogue - with arms decommissioning at the top of the Government agenda - which will now surely open at ministerial level on Wednesday. The Londonderry demonstration did not come as a complete surprise. There have been fairly frequent street demonstrations since the ceasefire began; the RUC reported to Mr Major on Wednesday on the obstacles they face in installing conventional civil policing.
One highly pessimistic interpretation of Mr Major's response is that he is under growing pressure from the more Unionist members of his own Cabinet to harden the Government line, and that Mr Adams is under pressure from those within his own ranks who want to abort the peace process.
That, for two reasons, would be to misunderstand the realities. First, the Government, while never losing sight of the possibility that the peace process could unravel, believes that the pressures - even on doubters within the republican ranks - are going towards peace.
Foremost is the continuing addiction to peace among ordinary people. But also cited are the strong words used about the need for arms decommissioning by both John Bruton and, after Mr Major's successful trip to Washington last month, President Clinton.
The Government also has faith in what it believes is the clear-sighted view of the Roman Catholic Church and in mainstream Irish opinion as illustrated by an Irish Times editorial yesterday which said: "It is vital to establish there is no twin track option of physical pressure and negotiation open to Sinn Fein. This applies as much to staged confrontations in the streets as it does to the decommissioning of arms." The final factor is the progress that Mr Ancram is said to be making in talks with the loyalist paramiliary representatives towards decommissioning.
Nobody, least of all in the British government, thinks it is going to be easy. It is perfectly possible that the talks are now set for a long and what one official yesterday called a "staccato" process which could take manymonths. It is significant that in what had been planned as a carefully balanced visit, Mr Major in his speech before the riot in Londonderry spoke in the strongest terms yet about the iniquity of punishment beatings by the paramiliataries.
But it is no less significant that he spoke with almost equal eloquence of his desire to see Sinn Fein eventually playing its full part as a peaceful democratic political party. Mr Major still knows where he wants to go.