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Hermione glanced at the time. Classes were almost finished for the day, only Arithmancy with the Slytherins and Divination with the Hufflepuffs left. She quickly walked to the Arithmancy classroom and settled into her seat in the front row next to Draco and Harry. She pulled out her book and glanced over at the two boys. Harry had his head on the desk and Draco was running his hand through his dark locks in a comforting manner, which made Hermione coo at them silently. Hermione looked askance at Draco, but the blonde wasn't even looking at her, just murmuring comforting words at Harry. Hermione hid a grin before sobering. There was clearly something wrong and she wanted to do what she could to help.

"What's wrong?" she asked quietly as more students filled in the seats around them.

Harry just mumbled something into the desk that Hermione didn't hear and shuffled a little closer to Draco. Hermione mentally cooed again. They were just too adorable. She didn't doubt that they would be together by the end of the year. She turned to Draco as he sighed.

"Sirius sent a letter. They had been planning to meet up in Hogsmeade so Sirius could show him around and tell him about all the pranks the Marauders got up to in their time, but with the dementors Sirius doesn't want to risk going into a panic attack or trance. He says it's more likely because of the amount of time spent around them in Azkaban, even while he was Padfoot, and with Harry also likely to pass out around them, Sirius figured it was not a good idea to have two people possibly pass out that we would need to help if the dementors come around. Harry agrees with him, but he doesn't like it. He had really been looking forward to this Hogsmeade visit."

Hermione sighed too, reaching over to pat Harry's hair before speaking. "How about we meet up to find a place to discuss our project? We can get Ron and Neville after supper and we can find a place and see about maybe finding some of our ingredients. We need to start that soon, it's almost Halloween, so we don't want to wait too long. Maybe it'll take your mind off the dementors for a bit."

Harry nodded into the desk, then Draco lightly tugged on the hair between his fingers as Professor Vector walked in and tapped the blackboard with her wand. Equations appeared on it and Hermione quickly started taking notes as Harry sat up and did the same.

"Today we will be learning the Arithmancy behind a simple Wingardium Leviosa." Professor Vector began. "I know we went over it a little bit just last week, but this is a review. Also, if I think you lot have got it by the end of class, we'll try a little exercise with this spell."

Hermione settled in to take notes. Arithmancy was one of her favorite classes. It reminded her a little bit of Muggle Chemistry, especially the part about balancing equations. If someone wanted to make a new spell or potion, they had to do a lot of Arithmancy for it. If the math wasn't just right, something could explode, and the equations they used to ensure something like that didn't happen were similar to the equations she remembered seeing in a chapter about balancing equations in her mother's old Chemistry book from university.

Nearly an hour later, Professor Vector was apparently pleased with how well the students had grasped the concept as she erased the board with nearly fifteen minutes until the end of class. She tapped her wand against the board again, and a blank equation went up.

"This is an exercise to see how well you lot have learned this. This is the base of the Wingardium Leviosa spell. As you can see here is the indication that it is a flight spell, this is the indication of how much power to use, and here is the indication that it affects something outside of yourself. Other more complicated spells will have more variables, like the Lumos spell and it's different counterparts to make it colored. Another way to make a spell more complicated is to have more complicated variables. A lighting spell that stays near the ceiling or a wall, or that stays a certain amount of distance away from you, that you will learn this year in charms if I remember correctly, is a more complicated spell than a simple Lumos charm, even when colored. The variable that dictates how far away from whatever you ground the light to is determined by intent, and the more precise the intent needed, the more complicated the variable." She looked at the board for a moment. "Now, what was I talking about?" she muttered under her breath. The class was silent for a moment while Professor Vector stared at the black board. Hermione hid a grin. This was one of the reasons she loved this class so much. Professor Vector was one of those teachers that loved her field so much that she often went on vaguely connected tangents when she was teaching and often had to take a moment to remember where she was going before she went into territory that went completely over the students' heads.

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