In headline terms it might have looked like a split decision. In the latest instalment of the long-running Democratic primary election saga on Tuesday, Barack Obama won North Carolina and Hillary Clinton won Indiana. These results went roughly as expected – one for each camp.

So at least in terms of the state-wide winners it was a tie, and the race looks set to go on through the final few primaries in the next month.

But beneath the headlines, this was clearly a triumphant night – and perhaps even a decisive one — for Mr Obama.

First, the margins of victory in the two states were crucial. Mr Obama strolled home by 14 percentage points in North Carolina, while Mrs Clinton squeaked by in Indiana by just a couple of points.

That means Mr Obama will almost certainly emerge from the night with a net gain in delegates to the party’s presidential nominating convention. His lead among elected delegates — who are awarded in rough proportion to votes cast — now stands at well over 150, out of more than 3,000 in all, and it seems now completely inconceivable that he could lose in the delegate count with just a handful of states now left to vote.

The night’s results also gave Mr Obama a secure lead in the popular vote. This is, in strict procedural terms, irrelevant. The total vote cast across the country for each candidate is not what counts. It is delegates that matter in the race for the party’s nomination.

But in political terms the vote totals matter enormously. One of Mrs Clinton’s remaining slender hopes of persuading the party that she should be the nominee lay in finishing the primary contests ahead in the popular vote. This — unless she can convince the party that the disqualified primaries in Michigan and Florida should count — is now all but impossible.

The second reason it was a bad night for Mrs Clinton was that she needed a much clearer victory and didn’t get one. Even a straight split in the outcome in the two states would not have been enough to keep her in the race with a serious chance. She needed to win, not just claim a dead heat.

The arithmetic is now so firmly against Mrs Clinton that it would take a miracle for her to win the nomination. Mr Obama is close enough to a Democratic victory to taste it. His lead in delegates elected in state primaries and caucuses is, as we have seen, almost insurmountable. He now trails in so-called super-delegates, the 800 or so senior party officials who hold the contest in their hands, by merely a handful. All that means he now needs to win only about 37 per cent of delegates in the remaining primaries, and the super-delegates who have not yet declared their support.

A third reason for Mr Obama to celebrate Tuesday night was that the political momentum has clearly shifted back to the Illinois senator. He has had a terrible last two months. He lost three straight primaries — in Texas, Ohio and Pennsylvania. He appeared to be sinking in a mire of ranting reverends and condescending comments about the white working-class. Most worryingly, Mrs Clinton seemed to be having some success in convincing people that the liberal, slightly aloof Mr Obama might not be able to win a general election contest.

But his victory in North Carolina and the impossibly close outcome in Indiana have righted the boat.

A few more primaries remain — beginning next week in West Virginia. But the real struggle now moves to the minds of the super-delegates. These party grandees have been steadily moving into Mr Obama's camp in the last month even as his campaign has begun to stall.

After his very strong showing in Tuesday’s primaries, that movement is likely to become a stampede. An end to this apparently interminable contest is in sight at last.

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