There was little joy around the cavernous headquarters of the European Council in Brussels on Sunday as the treaty governing the UK's departure from the European Union was formally accepted by the 27 EU heads of government and the prime minister of the departing country.
Both Donald Tusk, who chairs the council of EU leaders and Jean Claude Juncker, head of the European Commission, the body of officials and offices which makes the Union's great machine work, expressed sadness that the UK's departure has passed a decisive - if not yet perhaps irrevocable - step. The summit venue was subdued, and not just because it is a Sunday.
Taoiseach Leo Varadkar echoed their laments, but stressed that Ireland and the EU respect the decision of the British people and the efforts of the British Government to carry them out.
Nonetheless there is general recognition in Brussels and among the member states that Ireland has done as well as it could have expected - and much better, perhaps - out of a bad situation.
The decision of Enda Kenny and his senior officials, carried through with some determination by Leo Varadkar and Simon Coveney was to cleave to the EU side, trusting that the Commission negotiating team, backed by EU leaders, would protect Ireland's interests as defined by the Irish Government.
This found concrete expression in the backstop in last December’s political declaration which has now been included in the formal withdrawal treaty.
But the exact form of that backstop - applying to the UK as a whole, rather than just Northern Ireland - now presents perhaps the biggest obstacle to Theresa May's efforts to secure the backing of the British Parliament.
And just as EU leaders were united in sadness at the British departure, so most people in Brussels this weekend share the awareness that Mrs May is unlikely to win enough support in Parliament - at least the first time round - to secure ratification.
Mr Varadkar told his press conference on Sunday that what to do in that event was not discussed by the leaders, and declined to speculate about what the next steps would be in that eventuality. Instead he and the other leaders were intent on sending the message that this was the only deal on the table. But you can be sure than conversations among officials have taken place. It would be remiss of them not to.
If and when the deal is rejected by the Commons, there will be a period of what some people in Brussels and Dublin are calling “uncertainty” but people in London are more likely to describe as “chaos”.
The Irish Government’s hope is that this period will be followed by a realisation in London that Mrs May’s deal is the best they are going to get. But the nature of chaos is that it is unpredictable. Several other less benign outcomes are possible too.
One of them is that the British seek changes on the backstop - specifically on the exit mechanism - in order to make the treaty more palatable to the Commons. That would put the Irish Government on the spot, exposing what has always been the contradiction at the centre of its negotiating strategy - that in insisting on the backstop, it could precipitate a crash-out Brexit and thus the danger of a hard border, the very thing that the backstop is designed to protect.
There is a nervous satisfaction in Irish Government circles about what has been achieved so far. For the foreseeable future, it is the nervousness, rather than the satisfaction, which is likely to be most prominent.
