“By determining whether there was or was not some space in the castle unaccounted for.”
“I do not see.”
“Would you mind coming to my room? It will be a lesson for Davie too!”
She assented, and Donal gave them a lesson in cubic measure and content. He showed them how to reckon the space that must lie within given boundaries: if then within those boundaries they could not find so much, part of it must be hidden. If they measured the walls of the castle, allowing of course for their thickness and every irregularity, and from that, calculated the space they must hold; then measured all the rooms and open places within the walls, allowing for all partitions; and having again calculated, found the space fall short of what they had from the outside measurements to expect; they must conclude either that they had measured or calculated wrong, or that there was space in the castle to which they had no access.
“But,” continued Donal, when they had in a degree mastered the idea, “if the thing was, to discover the room itself, I should set about it in a different way; I should not care about the measuring. I would begin and go all over the castle, first getting the outside shape right in my head, and then fitting everything inside it into that shape of it in my brain. If I came to a part I could not so fit at once, I would examine that according to the rules I have given you, take exact measurements of the angles and sides of the different rooms and passages, and find whether these enclosed more space than I could at once discover inside them.—But I need not follow the process farther: pulling down might be the next thing, and we must not talk of that!”
“But the thing is worth doing, is it not, even if we do not go so far as to pull down?”
“I think so.”
“And I think my uncle will not object.—Say nothing about it though, Davie, till we give you leave.”
That we was pleasant in Donal’s ears.
Lady Arctura rose, and they all went down together. When they reached the hall, Davie ran to get his kite.