PURRING. Readers will recall it was what David Cameron claimed the Queen did after he telephoned to say he had not stuffed up and lost Scotland. History does not relate her reaction on hearing he was not quite so lucky with Britain’s EU membership.

The same sound of purring could likely be heard over the roar of traffic in the Washington beltway yesterday morning as America digested the televised debate of the night before. It was Clinton versus Trump, round one, the DC champ, Clinton, versus the New York chump.

While The Donald did not swear, throw the furniture around or otherwise mess the stage, one would have to be a close family member to say that he distinguished himself with his performance. He claimed later that the questions by the moderator Lester Holt (a registered Republican) were biased, and that his microphone had been tampered with. What, no dog eating your homework, Donald?

Prior to the debate, the talking heads had been falling over each other to declare that his fortunes depended on “which Donald” showed up, as if this was a man known for swinging easily between Tarzan and Cary Grant in manner. Would it be the loud, obnoxious, thin-skinned Trump who entered the hall at Hofstra University in Hempstead, NY, or would it be the other one his supporters say exists, the humble, affable, Trump, the one who has put in fewer appearances than Big Foot? Surprise, surprise, it was the former. If Mr Trump had been prepping like crazy for the debate, he was astonishingly successful at hiding it.

Hillary Clinton, for her part, had a simple brief to keep. With decades of debating experience behind her, she can do the facts and argument stuff standing on her head. Here, her job was to appear warm and presidential, not to roll her eyes in exasperation (she’s quite the eye roller is Hill, as you might be, married to Bill), and generally to play the role of the twinkly-eyed grandma who could, if required, multi-task between changing a nappy and giving a 2am shoot-to-kill order against a terrorist.

In large part she succeeded. She did particularly well in not flying for Mr Trump on any one of the umpteen times he interrupted her. Twitter was happy, too. As the writer Laura Hudson put it: “I can’t believe I’m watching a presidential debate between a Secretary of State and an internet commenter.”

So the DC beltway should have been purring with satisfaction, right? But what about that other America, the rust belt? What of all those states in the middle of the country and towards the east that have seen jobs disappear to other parts faster than you can say, “How much did you earn for those Wall Street speeches, Hillary?” Mr Trump took some heavy blows, certainly, but he is far from out for the count.

Think how many times the pundits have been wrong about him to date. It was predicted he would be out in the early stages of the race. The Republican hierarchy would never let him proceed; he didn’t have enough money to keep going; no-one could survive the press he was receiving … on and on the assumptions came. Every one of them was overturned. There is a new biography of Mr Trump which is well worth reading by anyone quick to dismiss him as some dumb old rock on Mrs Clinton’s petal-strewn path to the White House. Trump Revealed: An American Journey of Ambition, Ego, Money and Power (Simon and Schuster) is by Michael Kranish and Marc Fisher.

Mr Kranish and Mr Fisher led a 24-plus team of Washington Post reporters who looked into Trump’s life, from soup to nuts, from his mother’s leaving of Scotland to his run for the presidency. It is the kind of painstakingly researched political biography American journalists do so well. British journalists tend to go, more entertainingly, for the jugulars of their subjects.

Americans prefer to let the facts, ma’am, do the talking. Done badly, the approach can be as dull as watching the paint dry on a picket fence; not so here. How could it be otherwise, given Mr Trump’s endlessly fascinating, Rosebud-tinged, life? The one thing that stands out above all about Mr Trump in the book is just how long he has wanted this run at the White House. If Mrs Clinton has been around forever, so has Mr Trump. The two have haunted the same circles for so long their lives have at times become intertwined. He used to contribute to her Senate campaigns. The Clintons were guests at his third wedding. He once called Bill “a terrific guy”. While he might sound like an amateur just off the bus, he is not.

Next, it has to be remembered how insignificant, in the grand scheme of things that is a presidential run, initial success in televised debates can be. The impact of a five o’clock shadow and a sweaty lip on Richard Nixon’s chances against John F Kennedy has been wildly exaggerated. Jimmy Carter and Walter Mondale were better briefed than Ronald Reagan, but Mr Reagan had the charm. Al Gore took George W Bush back to school, but who did the voters much prefer to have a beer with ( hanging chads notwithstanding)? Mrs Clinton did well on Monday night, but for those who cannot stand the Democrat candidate, and plenty cannot, that will not have mattered one iota. In any contest between two such polarising figures as Mr Trump and Mrs Clinton, a single debate will not shift opinions much among the decideds. What matters, what always matters, is the undecideds. While they might be warming to Mrs Clinton as more presidential and better briefed, there are still two more debates to go, on October 9 and 19.

For those who care to look again at this week’s debate, Mr Trump has strengths that can be built upon. His message in the first 15 minutes was directed straight to blue-collar America, and it was dazzlingly successful. These phoneys, these Washington politicians, he was saying, they have done nothing for you. Put another one in and they will stiff you all over again. Critics might call this dog-whistle politics, but that does not mean the underlying message should be ignored. From Idaho to Inverness via Berlin and Paris, “they”, the political class, still do not get that many voters are sick and tired of a status quo that they believe is doing little to nothing for them.

Mrs Clinton will never have her husband’s ability to connect easily with voters and it is often painful to watch her try to do the folksy stuff. But it was notable that it was Mrs Clinton, accompanied by Bill and the rest of the family, who went into the audience to shake hands with its members, while the Trumps stayed on stage before walking off en masse.

Two sets of elites in action, but one managing to look a little more appealing. Mrs Clinton has to remember touches like that, while not forgetting, along with many others, that Mr Trump is a man who should never be underestimated.