This scene gives you none of that.
Ron was back in McGonagall's office, shaking his head. "It's like there was a purge, Professor," he was telling her. "I mean, I'm sure the ministry must have something, somewhere, but Scrimgeour thinks I'm talking out my--"
McGonagall raised one eyebrow.
"--er, my hat, talking through my hat!" Ron blurted, then continued on quickly. "So he's not going to waste valuable elf-hours digging through old records. Outside of the ministry, it's all like the registrar's office. The records are just gone. Not just the Continuing Education thing, but everything that happened here during Prince-Hedges' time as headmaster. I've spoken to many wizards the right age to have attended then, but every one of them claims they just missed his term. Flourish and Blott's won't even release a list of textbooks Hogwarts ordered during that time!"
McGonagall tutted. "It was a dark time for Hogwarts, Ronald. I was working for Madame Maxine at Beaubaton's, and, of course, Albus was still on sabbatical after the Grindlewald affair." She smiled for a moment. "Poor Albus. They wanted him to take a post at the ministry, for goodness sake! Deputy Minister for Magical Defense! He had to go all the way to Nepal to get away from them. You'll see, when you and Mr. Potter and Miss Granger finally defeat You-Know-Who."
Ron scoffed, and she looked seriously at him. "Yes, Mr. Weasley, I said 'when.' There isn't a doubt in my mind that that will happen. You'll bring them back to us, Mr. Weasley, and the three of you will bring him down. I have faith in you, Mr. Weasley. I have all the faith in the world, and so did Albus. Not just faith in Harry. Faith in the three of you. He believed in each of you, and he believed in the three of you together."
This time Ron did scoff. "He also believed in Snape."
McGonagall's eyes darkened, and she looked down at her desk. "Yes, well..."
"Indeed, I did, Minerva," chuckled a voice from behind her. Ron started, and looked up at the portrait of Dumbledore, which gazed down fondly at them. "I did and I still do."
"Yes, well, Albus, there's a reason you're a portrait," said McGonagall tartly.
"Indeed there is, Minerva," agreed the painting, not at all put out by the criticism in McGonagall's words. "But I'm glad I can, er, hang about, as it were, to offer my help."
The portrait looked inordinately pleased with its atrocious pun, and Ron chuckled. Then, in an instant, the smile fell from his face, and he snapped his fingers.
"Yes!" Ron was on his feet, past McGonagall, looking at the identifying tags on portrait frames, while various past headmasters glowered down at his impertinence.
McGonagall watched him with growing approval, and suddenly touched Ron's shoulder. He paused and looked up at her. "I just wanted to point out to you, Mr. Weasley, that it was you who thought of this. Not Mr. Potter. Not Miss Granger. You're nobody's sidekick, Ronald Weasley."
Dumbledore's portrait gazed proudly down at him. "My very thoughts, Ronald. My very words."
Ron smiled for a moment at them, started to turn back to the wall, then stopped, and smiled brightly, and called out, "Professor Prince-Hedges?"
"Over here, lad," said a small voice. "Just below the portrait of my good friend, Armando Dippet."
Ron smiled and stepped over to Dippet's portrait, and noticed, for the first time, that, beneath it, Sell-O-Taped to the wall, was what looked like a small panel torn from comic-book. It was a simplistic line drawing, reminding Ron a lot of the illustrations in some of the old issues from the 1950s that his father had collected of The Adventures of Martin Miggs, the Mad Muggle. It showed a handsome, bland-looking man with a neat, short hair-cut, holding a smoking pipe.
Ron sat on the floor, putting himself at eye-level to the little drawing. "How do you do, Professor," he said. "I'm Ron Weasley."
"Arthur's boy, I imagine? Yes,yes, you would be. He was a good student, your father. Well, Ron, it's a pleasure to meet you. How can I be of help?"
"Well, sir, my friends have sort of, er, gone missing--"
"Oh, I know that, I've heard about it from the other portraits, my lad. Touched some object and went who-knows-where, yes?"
Ron nodded. "That's exactly it, sir. I think the object they touched was created by a student of yours, from your, er, 'Continuing Education' experiment."
"Experiment! Is that what they're calling it these days? Of course they are.It's only a breath away from 'Failure,' after all." He smiled cynically at Ron. "Don't think I don't know why I'm where I am on this wall, and why my good friend Armando's retirement and return are now called a 'Sabbatical.'"
Ron chuckled. "Well, you know more than me, then, sir."
"As is frequently the case between headmasters and students, young Ron. But you're not here to listen to a bitter old man witter on about politics. Your quest has nothing to do with why I left Hogwarts. What would you like to know?"
"Well, sir, as I said, the sign -- that's the artifact that seems to have transported my friends, sir -- I think it was created by one of your 'Continuing Education' students, and I was hoping you could give me some insight into what sorts of magic she was studying."
"Of course, my boy, of course! Who was the student?"
Ron smiled. "Her name was Cassiopeia Black."
Prince-Hedges' face fell. "Oh, dear," he said, bitterly. "She was why I left Hogwarts."
Ron's mouth dropped open as he heard McGonagall gasp behind him.
"A student, Morrison?" Her tone was reproachfull.
"Oh, do me a favour, Minerva," said Prince-Hedges' portrait, testily. "She was four years my senior at the time."
"Still, Morrison, what were you thinking?"
"Not an awful lot, I fear, dear lady." The portrait sighed. "In any case, it was a trap on her part, wasn't it? Prove how bad it was to have a half-blood headmaster and all that. And as unpopular as I was at the time, well, it's hardly surprising, is it, that... er... spending time with an older woman who was here to take adult-level dimensional transcendence charms was enough to see me out?"
Ron's eyes widened. "Dimen-what?"
"Dimensional Transcendence," replied Prince-Hedges' portrait and McGonagall in unison.
McGonagall regarded Ron's baffled expression for a moment. "Dimensional Transcendence is the Magical principle that things' dimensions do not, in fact, have to relate to one another. It's the basis for things like magical tents. They're bigger on the inside because they are dimensionally transcendent."
Ron grinned. "Brilliant! So there could be a whole health club, right inside that sign!"
McGonagall shook her head. "In theory, perhaps, but in practice, there are very real limits to the extent to which an object's internal and external dimensions can be mismatched."
"Well, now, Min," said Prince-Hedges' portrait,and McGonagall's eyebrow lifted, "that's an interesting point, because that was what Miss Black seemed most interested in.I had done some work on increasing that ratio while I was working for the Ministry, don't you know, co-authored a paper that suggested that there really was no limit, and she asked me about it frequently. When she found out that all the real innovations from that project came from my overseas partner, she turned me straight in to the Board of Governors for our, er... involvement, and hopped a floo to Burgas to attach herself to Fyodor!"
Ron was starting to get a sinking feeling. "Where the hell is Burgas?" he asked, eyes closing against the answer he somehow knew was going to come. "And who's this Fyodor bloke?"
"Bulgaria," said McGonagall,while Prince-Hedges' portrait told him, "Why, my overseas partner, young man. Fyodor Krum!"
Ron sat on the floor in front of the small portrait of Prince-Hedges, and nodded sagely for a long, long moment, before shifting sidewise, slightly -- it was only polite, really -- and banging his forehead repeatedly against the wall.