The kid didn't have much of a poker face. That much was obvious to Richard. And something obviously bothered Arcturus about the idea of acknowledging distant kinship. Then it came to him. The Black family. That Blood Pride and the 28. Families so inbred that over time they descended into infertility, and even insanity. A family that actually blasted the names of members off the family tree if they married outside their approved limits. After 1600, the Summerbys could have bought any three of the 28 families out of lunch money, but we were 'in the trades', they were 'old money', and thought they were somehow better. Richard, you will just have to out-pureblood the pureblood.
"Well if that is how you feel your father would want you to behave, then that is how we will be guided. Still, if you find yourself with any wants or needs while you are in Preya, you can always come to me for assistance."
He accepted the papers with suitable gravity. Taking a 'muggle' felt tip pen out of an inner robe pocket, he began to quickly review the Arithmantic Equations.
"That's well done," he commented at one point and put a check mark next to an equation. A few minutes later, he ran his finger over a section and frowned. "I think this is a transcription error here; you flipped target connotations for part of the equation, but it doesn't carry through that way to the end." A bit later, "I had always wondered how far back that bit went in its current form. Sometime between your day and mine it evolved. I'll show you in a bit."
Finally, he came to the part where Arcturus had been more than a bit at sea. "I think what you were trying to do here..." and he began to write. His felt pen had a chisel tip, so his writing was calligraphic, and extremely precise, his font clean, modern, and since his felt pen flowed smoothly and didn't need to be refilled, very fast.
Richard passed the annotated papers back to Arcturus. "Not at all bad for someone who is still being subjected to sleep-inducing lectures rather than seeing how things apply in the real world. And step by step, which is why your enchantments interfered and had to be tuned. Let me show you."
He reached over to a nearby side table and picked up a bound journal of blank pages. H, he started writing at the first page, again with the speed and precision of someone used to turning out long legal contracts for certain customer where handwritten was the style. In very little time, he had turned out three pages of writing, one long equation, elements of the entire broom enchantment tied together, shared between different parts of the spell, and triggered by a single power word. With a slight smile, he passed the journal over to Arcturus. "When you play Quidditch, you have a broom failure, you get on your spare, go back into the game. Racing, you pull off the course with twigs on fire, broom shaft warped, and you have to finish the race on what you started with or you're disqualified. Take more than a minute to make repairs, you might as well be disqualified, because everybody will have left you far behind." Or the Snatchers are after your group, and anybody who can't fly, dies.