As Richard spoke of their familial connection, an anxious look crossed Arcturus' features, and he shifted uncomfortably in his chair. What he was suggesting went against all the etiquette he had learned at home. It was all very well for first cousins, but they were very far from being that, and Arcturus wasn't an infant. Why, then, was it being suggested? His father had warned him against listening to strangers who tried to make too much of very distant links of blood or marriage, and Richard Summerby was an adult and that just made it seem wrong and disrespectful for Arcturus to speak to him that way.
However, it also wouldn't be particularly polite to point this out directly, either. Once Richard had finished speaking, he dipped his head a little. 'I can't address you with such familiarity, sir,' he said quietly. 'My father wouldn't approve of it, not even if we are distant kin.' He had to believe that even in the distant future it was self-evident that obeying one's father was the right thing to do.
Barely pausing for breath, he steered the topic back to the matter of the broom, because his Arithmancy troubles seemed suddenly less of a difficult topic. 'The magical methods we choose depend on our levels of expertise,' he agreed. 'A small child would need the wand movements to lift that cup, and an incantation too, but for a grown wizard with full control over his magic it is far simpler and more natural.' He understood the rationale, at least, and handed over his collection of papers with only a small hesitation. They were very carefully and neatly written, by quill pen, and clearly laid out, and his intentions could easily be followed. The Arithmantic work itself, however, contained quite a few errors, some small, and others where he had known just what he wanted to express, but lacked the conceptual understanding to note it down correctly. Arcturus was limited to the spells that had been known in his own time, but with that considered, he had chosen them fairly well.
After a slight pause to allow Richard to briefly look over the material, he began to speak again. 'I know that it isn't quite right,' he admitted. My friend, Monty Carrow – do you know his family? Carrow always helped me with it at school.' That was one way to describe Arcturus' tendency to simply copy his friend's work. 'But I shall tell you how I did it. First of all I saw to the physical properties of the broom, trimming and polishing and the like, because it ought to be in the best condition before attempting any spellwork. Then I layered the enchantments from the base upwards, starting with the essential flying charm, then the directional awareness and responsiveness, then the braking charm, and finally the adjustments for cushioning and balance. Except-' here he frowned a little, 'when I tested it, the braking charm had upset the internal compass completely, and I had to recalibrate it, but it worked well afterwards. I could fly it without any trouble'