So Lockheart screwed up. He's human. Even wizards are still human. Even famous wizards were still human. Even those with dashing smiles that seemed spelled to charm girls already fascinated with the magical world she only fell into a year ago.
But he abandoned his classroom. That was absolutely unacceptable. And certainly must be against the rules. Hermione pouted.
The pixies were trashing the entire Defense Against the Dark Arts classroom. Two had even picked up Neville by his years. Wait a minute - tensile strength of human cartilage times the area of his ears at grip point compared to the boys approximate weight as well as friction force between the hand print of the pixies and his skin leave alone his skin's friction force against said cartilage...Hermione shook her head. No, that's muggle thinking. She had seen children take blows in quidditch matches that would hospitalize or kill grown adults. And it was not like the pixies were ever going to get airborne considering their wing size compared to their body weight at this atmospheric pressure no matter how fast they flapped those wings. Neville must be 'accidentally' casting to keep his self-conception intact - if only the boy had a compatible wand. Something more in a unicorn hair core?
The girl shook her head. The actual issue at hand, she chided herself.
Harry had taken to direct physical attacks. Sure, he had his 'seeker like reflexes' and could catch a single one in mid flight. But two just lifted a boy his size and set him upon a chandelier. So they must be impervious to destructive physical attacks that her and her friends might be able to generate. Considering their speed, Stupefy would only hit one out of the sheer number of targets in the air and automatically turn them into the pixies main target. Petrificus Totalis would be the same just slower. Incendio would be the same problem and if it did hit, even more destruction would befall the classroom.
Arresting their motion was the correct idea. It was the targeting component of the spells she had to eliminate. Was there anything she knew that did not have a targeting component? Reparo no, Alohamora no, no, no...Transfiguration spells? The ones she knew of those did the targeting by the wand motion and intent rather than part of a charm.
The girl knelt down and covered her ears.
Okay, focus on the Arithmancy. The postulation for Petrificus Totalus was...take out the targeting...that would auto back field into the focus and explode her wand, so replace it with the emitting of transfiguring...what was simple...matchsticks to sewing needles...the multiplier wasn't a multiplier but a disperser so that would do nicely to emit from her position near the front of the classroom. Okay freeform postulation, double check the Arithmancy, that could work.
Actual casting would require a pronunciation. The runes for the original spell...cross translate for intent, compensate for the targeting stand in...double check the Arithmancy on the runic...okay.
Any side effects. Arresting could implode but not explode, so no damage outside the classroom. Non-targets could get backdrafted into the spell but so would the atmosphere but with the amount in the room that would be an ear popping. Neville's in the blast zone but due to the ear lift his magic is already on a self integrity reinforcement and if he's immobilized then it would be easier to get him down.
Second year, muggleborn student, Hermione Jean Granger nodded to herself. After a few seconds of mental calculations she stood up she raised her wand from the shoulder and then straightened her elbow instead of bringing the wand down to complete the targeting. "Immobulus.", she tensed. Nearly instantly, at the speed of magic, all the pixies in her line of sight froze most of their body movement while conveniently only losing most of their momentum without any gravitational effect.
After the pixies had been collected (and Neville retrieved), Longbottom asked her. "When did we learn, what did you use - Im-o-bu-lus? I haven't missed a single class of Professor Flitwick's."
"Immobulus.", Hermione corrected. "It's not from any of his syllabae or curriculums that I've revised. But I'm sure he must have cast something similar to it when he was only the dueling circuits."
Harry appeared nearly as confused as Ron and Neville. "But then how did you know how to cast it?", he asked.
"Well, you've read Heny Malfoy's Arithmantic Divisors.", she started.
The boys shook their heads.
"Runmi Lestrange's Runes to Ruin Arithmancy?", Hermione hoped.
More shakes.
She took in a calming breath. "Fine. Give me four feet of parchment - continuous, a quill, and an ink well and I'll show you how this works."
"But it's nearly dinner.", Ron complained.
Longbottom got nervous again. "Is...is that the look you call 'the' look that she gives?"