"Right, so," said Professor Leek.

The class watched him. He didn't say anything else for a while; he simply stared at the class and cleared his throat multiple times.

"Right, so," he said again. "Right. So. Er. I'm your new Arithmancy teacher—Professor Leek. That's L-E-E-K, for those who care about spelling. Erm… yeah. Like the vegetable."

"You look a little like the vegetable," said James loudly.

The class laughed, and Leek joined in awkwardly. "Yeah. Erm. So I have been told. Er. Yeah. Right, so I'm Professor Leek, and this is the intro-level Arithmancy class, right? If my notes are correct."

No one responded for a while, and Remus felt bad. "Yes," he said.

Professor Leek gave him a relieved, grateful look. "Thanks, Remus," he said. "Now… could somebody tell me what you've been working on?"

No one responded, so Remus sighed and took it upon himself to answer once again. "We're learning about how the velocity of a cast spell affects the outcome," he said.

"Ah! Parke's Theory of Spell Velocity. Yes, I know all about that."

"We'd sort of expect you to, seeing as you're the professor," said James, and Remus nudged him.

"Don't be rude," he whispered.

Professor Leek granted Remus another grateful look and then walked up to the board. "All spells travel at a constant speed," he said. "If I were to roll a ball, it would lose velocity as it rolled, right? Anyone know why that is?"

Long silence. Remus didn't want to answer another question—drawing attention to himself was always dangerous—but he felt so bad for the perpetually awkward Professor Leek. "Friction," he said.

"Right!" said Professor Leek. "Good! And what force typically slows down an object moving through air?"

No answer. "Air resistance," said Remus.

"Very good! Is magic bothered by air resistance or friction? Does anyone know?"

Long silence.

"No, it isn't," said Remus, hating himself more by the second. He probably looked like such a teacher's pet, and Remus didn't typically like looking like a pet of any kind. It hit far too close to home.

"Good, good," said Leek. "That means that the velocity of the spell—all the way through its path, from the initial cast to the final hit—or when it fizzles out, of course—is directly proportional to the velocity at which one's wand is moving when the spell is cast. Now, knowing all that, how will the effect of a slowly-moving spell differ from the effect of a quickly-moving spell? Any ideas? Raise your hands."

Long, long silence.

Remus raised his hand.

"Remus," said Professor Leek, clearly relieved that someone had bothered to respond. "Go ahead."

"I don't know," said Remus.

More awkward silence.

Leek furrowed his eyebrows. "All right… so, why did you raise your hand, may I ask?"

"I was trying to break the tension. Maybe someone else will raise their hand now that I've already gotten the question wrong. They can't possibly look stupider than me at this point."

The class laughed, and Remus wasn't exactly sure how to feel. He didn't like standing out like that, but they did seem to think that he was funny. That was good, because Remus was actually pretty disappointed in himself that he didn't know the answer (he'd read this far in his textbook, he knew, but he'd probably been too distracted to pay proper attention). Everyone would know who Remus was now. He stood out right now for sure... but Professor Leek was grinning, and he looked inordinately thankful, so Remus figured he'd done the right thing.

Now Evans raised her hand. "If the spell had a greater starting speed, and it ends with a greater final speed, then… the final impact will be greater, won't it?"

Professor Leek got so excited that he accidentally flung his chalk across the room. James caught it with one hand, waving it around like he'd just caught the Snitch, and everyone cheered (except for Snape, Evans, and some of the Slytherins). Even Professor Leek joined in after a while.

"All right, settle down," said Leek, but it was a full three minutes before the class finally settled down. "That's precisely right… er, was it Lily?"

"Yes, sir."

"Good. That's precisely right. Er… James. Let me ask you a question."

"Sure," said James.

"Good. Erm. So, James, let's say a Quidditch player on a broomstick flies directly into you. Would it hurt more if the Quidditch player was flying quickly or flying slowly?"

"Neither," said James, "because I wouldn't be hit either way. I'm a Beater on the Gryffindor Quidditch team, which is the best team. There's no way anyone could hit me. My reflexes are amazing."

Leek blinked. "Well, erm… let's just say they did."

"Then it would depend on the mass of the Quidditch player, wouldn't it? Because getting hit by someone like Remus would hardly hurt at all. That boy weighs about as much as Nearly Headless Nick."

Remus hit James' upper arm in protest, but James merely laughed. "Yeah, see?" he said. "That felt like getting swatted by a sheet of parchment!"

"Yes, well." Leek was thoroughly flustered now. "If they were the same mass, then which would hurt more?"

James grinned. "Oh, when you put it like that. The faster one, of course."

"Yes, precisely. Now, if this Quidditch player were to knock you over, would you move a greater distance if the Quidditch player were moving faster?"

"Yeah, duh."

"Right, so a spell with greater velocity is like a quickly-moving Quidditch player. The object it acts upon will have a greater effect at a quicker rate. And that is why you're told not to brandish your wands too much." Leek laughed a bit. "That could be quite dangerous!"

Remus had a question, but he considered not asking it, just because he didn't want to stand out… and also because it was about duelling. Professor Craff hadn't been very kind last time he'd asked a question about duelling in the middle of Arithmancy class. But he'd stood out enough already this class, so could one more question really hurt?

Remus raised his hand.

"Go ahead, Remus," said Leek, smiling.

"Well, I was just wondering… if more quickly-moving spells have more power, then why don't people brandish their wands in duels and things? The professional duellists I've seen—" Remus was thinking of Professor Questus, though he wouldn't say that out loud— "had very controlled, precise, small wand movements. Why is that? Couldn't brandishing help you win a duel?"

"Good question!" said Leek, and Remus nearly breathed a sigh of relief. No, this man wasn't like Professor Craff at all. "I'm rubbish at duelling, but I do know that it's all about aim. Smaller, tighter wand movements help with aim very much. But there is a certain flick of the wrist involved—the Plaudian Flick, it's called—that's designed to help the caster move his or her wand at a very quick velocity without brandishing."

Remus nodded. He recognized that from Questus' duelling notebook.

"Each spell, really, has a different technique involved for quicker casting. But you can ask Professor Flitwick about that. He has much more expertise in the area than I do."

"Thank you, sir," said Remus.

"You're very welcome. Now, I'd like to introduce what you'll be working on for the rest of the year. Checkpoints will be due, of course, but it's mainly independent. I heard that Professor Craff was having you do an individual project?"

Some people nodded, including Remus. At least they were participating more now.

"Right, so I'd like to start that up again—except with a slightly different structure. Some days will be devoted to the lesson, while other days will be devoted to the project. You won't be graded on whether you finish or not—rather, I'll give you a grade by the end of the year depending on how you did on the checkpoints and how hard you were working. We'll do a project like this every year, so you can even work on the same one every year you take Arithmancy. I'll be checking in with you individually every so often, too."

There were a few groans.

"Oh, don't be like that. It'll be fun!"

More groans.

"Hm," said Leek, flustered again. "Well. You can use the rest of the class to brainstorm, if you'd like."

There were even more groans, but the class did as he asked.

At the end of class, Professor Leek held Remus back—but first, he had to run out of the classroom to "get something". Remus waited for him to return, and James insisted on staying with him. "It's not anything bad," said Remus. "He just wants to talk about my project, I think. It'll be terribly boring. Do you really want to stay?"

"I do," said James with crossed arms. "It's a new teacher! I don't know how he's going to treat you, but I want to be here and make sure he's not a git."

"He's not a git. I've already met him, and I think he's fine."

"Yeah, well, I haven't met him, and I don't always trust your judgement, mate. No offense."

"What do you mean? I have great judgement!"

"Yeah, right. How many times have you said, 'It's all right! I'm fine!' and then it turned out that you weren't, in fact, fine?"

Remus frowned. "I am fine. I usually am. I've no clue why people don't always believe me."

"Because you say you're fine and then you faint or something, stupid."

"That was one time. My judgement is usually very good."

"Wanna bet? Just yesterday you assured me that the Astronomy quiz would be easy. Guess what? It wasn't!"

"Well, it would have been easy if you'd paid attention in class."

"Pah. Paying attention is for losers. My point is, Moony: your judgement is definitely questionable sometimes. You're simply too self-deprecating to see the truth."

"It's true. I'm pretty awful."

James rolled his eyes. "You idiot."

"I was joking."

"It was an awful joke."

"I know. It really was. My jokes are just terrible, aren't they?"

"I hate you."

"I hate myself, too."

"You self-deprecating twit."

"Guilty as charged."

After a few more moments of banter that devolved to a mild jousting fight with quills, Leek entered the classroom once again, carrying two mugs of tea. "Oh. What's this?" he asked. "James? Why are you here, too?"

"He already knows about me, sir," said Remus, "and he's also a paranoid git who's scared that you're secretly evil or something."

James crossed his arms. "I'm not."

"You are."

"I'm not!"

"Well," said Leek, "this is unfortunate, because I… er… only brought two cups of tea. James, do you mind…?"

"I don't need any tea," said James.

"All right. Good. I only have two. This is your last class of the day, yes?"

"Yes, sir," said Remus.

"Good. I really want to discuss your project for a bit. That's why I brought tea—I don't know how long it's going to take, and I know Arithmancy can be difficult and mentally taxing, and you've just had a long day, and I honestly felt bad about keeping you after without warning, so, er, I thought it might… you know. Help? I only thought—"

Remus interrupted his rambling. "Yes, sir, that sounds very nice. Thank you." Merlin's beard. Remus didn't think he'd ever meet somebody even more hopelessly awkward than Remus was at times, but Professor Leek was so awkward it was painful.

"Oh, good." Leek handed Remus the mug, obviously relieved. "So, tell me… what have you done with Professor Dumbledore so far?"

"Well, he told me that I needed a 'simulation' to do more trials in a short amount of time. And then he said that, in order to change the variables in the simulation, I needed a unique spell for each one. And then he helped me with the Tethering Charm—I managed to make a spell that moves a particular mug a couple of inches—and then I came up with lists of possible incantations for my variables."

"You've gotten quite a bit done!"

"Yeah. I've also been taking notes on… er, on full moons." Remus pulled his notebook out of his bag and showed it to Leek. "Taking stress levels. Madam Pomfrey and I rate the full moons afterwards, and then I take an average. I've been using a Pensieve to re-watch memories and get variable readings. Like the time, weather, et cetera."

"Yes, good. And…" Leek chewed his thumbnail, lost in thought. "May I ask what the end goal of your project is? I don't think Professor Dumbledore ever told me."

"Oh! I'm just trying to find out exactly what time I'll transform every month and how… well, how bad it'll be."

"And by 'bad' you mean…?"

"Violent. How violent I'll be." Remus could feel his cheeks growing red, and he rubbed at them as if to rub off the color entirely. "I'm always injured afterwards, and it'll be good to know exactly how bad it'll be before it happens. Sometimes I'm more violent than other times."

Leek nodded and said, "I see." Remus could not quite gauge Leek's emotions, so he settled for looking behind him instead of at him.

"If it works for other werewolves and not just me, it'll help loads of things. It'll help the Ministry know which full moons are the most dangerous, which would be really helpful—sometimes they don't have enough W.C.U. members on staff on dangerous full moon nights. It would help the werewolf hunters know exactly what time werewolves are expected to transform to and fro. It would help werewolves schedule things, if they knew exactly how long they were expected to take to heal… it would help St. Mungo's know which night were likely to receive the most werewolf patients… and it would just help with general anxiety, I expect."

Leek nodded again. "Yes, I can definitely see the benefits." He took a sip of his tea, and Remus mirrored him. "May I… I mean, I understand if you want to keep it, but I'd like to look at your notebook. If you'd like. If I may, I'd like to keep it for a while—run through what you have so far—come up with some ideas."

"Oh. Sure," said Remus. He began to hand his notebook to Leek… and then he stopped. "Wait, Professor. I should probably let you know that I… well, I had to measure my stress levels somehow, so I sort of rambled a little. Made lists of things I was stressed about. It's not really relevant, I was just… really, really bored in the Hospital Wing."

Leek laughed. "Oh, that's fine. The more information the better when it comes to things like this. Right, so if I could keep this for a few days…?"

"Yes, sir."

"Good. I'll look over what you have. Figure out how I want to proceed. I've done quite a bit of these, you know, and I know some tricks at this point."

"Really?"

"Of course. They're terrifically tedious, but there's some things you can do to speed up the process. Although I've never done a simulation with a werewolf before…." Leek trailed off, ruminating, and then he suddenly went quite red. "Wait! I didn't mean… I mean, it'll be the same as doing it with anyone else, of course—I didn't mean with a werewolf, I just meant with the conditions…"

Remus interrupted his rambling with a tight smile. "Yes, sir. I understand. It's a unique project."

"Yes, exactly! Yes. Exactly. I don't mean to offend."

"I think you'll find it's very difficult to offend me," said Remus politely.

James shook his head. Remus had almost forgotten he was there—but he was still sitting in the corner, crossing his arms, likely waiting for Leek to step out of line. "I disagree," James said. "He's very easy to offend, he just won't tell you that you've offended him. He'll keep it all pent-up, and turn into a little ball of rage from the inside-out…."

"James!" cried Remus, horrified. "I don't do that."

"Okay, fine. You don't. But you will act all hurt for a while. You don't outright tell us when you don't like something; you just make us feel bad about it for no good reason."

Remus sighed and finished off his tea. "It doesn't matter. Thank you so much for doing this, Professor."

"Oh, no problem at all! I'll give this back to you when I've finished, of course!"

"Thank you."

Remus felt a jolt: it was James, who was pulling Remus out of the classroom. As soon as they were clear down the corridor and out of earshot, James said, "I don't like him."

"What do you mean?"

"There's something fishy about him."

"There's nothing fishy about him."

"He secretly hates you or something."

"He doesn't. He seems very tolerant."

"You're wrong."

"I know these things, James. I can tell when someone's afraid of me. I've had plenty of experience."

"You can't tell. You thought I would hate you. You thought Peter would hate you. You thought Sirius would hate you. You're wrong all the time."

"I overestimate hatred, so if I'm not detecting any in Leek, then that just proves he's wonderful."

"It doesn't prove a thing."

Remus sighed. "Come off it, Prongs. He wasn't that bad. You shouldn't judge one Arithmancy teacher by the actions of another—that's basically what people do with werewolves, and it's very unpleasant. People tend to assume I'm secretly Fenrir Greyback in Gryffindor robes."

"Okay, fine," James conceded. "Leek wasn't that bad. You want to know the real reason I hate him?"

"Sure."

"I don't want to do this project! It's going to take forever! It's gonna be so much work, and I'm already working on a project with Sirius and Peter! Besides, there's Quidditch to focus on! I can't just up and take a new Arithmancy project!"

Remus patted James on the head sagely. "You're James Salazar Potter," he said. "You can do anything you set your mind to."

"That was never in question," James grumbled. "And my middle name is not Salazar."

"So," said Remus, accepting a cup of tea from Rowena and spreading his Mandrake notes on the table. "Say there was a container of sorts that could only be opened with a person's fingerprint. Hypothetically, how would I break in and steal its contents?"

"Fingerprint protection?" repeated Rowena incredulously.

"Yeah. That's how my friends plan to hide the Mandrake leaves next. The container can only be opened with James' fingerprint, and I need to break in."

"There's always Polyjuice Potion."

"I can't take Polyjuice Potion. It only works on humans, and I'm a werewolf."

"Ah. It was an unrealistically complicated solution, anyway. The best way to do it would be a duplication charm of sorts on a different object—some sort of putty would work best. There's a charm you can do to copy your friend's fingerprint and duplicate the pattern onto the putty."

"Where can I get the putty?"

"The best kind to use in this situation would be wolfsbane-based putty, but I'm assuming that's not an option. Flitterbloom-based will be just fine. I have the list of ingredients and spells here—you can start on it as soon as you'd like."

"Thank you, Rowena. This is so helpful."

Rowena smiled at him as she thrust the piece of paper into his hands. "I am always happy to help, Remus."

"AHHHHHH!" Remus heard James cry early one morning. "SIRIUS! PETER! REMUS! THE MANDRAKE LEAVES ARE GONE AGAIN!"

Remus smiled and hid his head under his pillows.

His friends would give up eventually. He just knew it.