Very slowly he turned the dollar. "And there are three in a row," he said, indicating the scratches with his pencil, "and here are three more. You notice that the rows all radiate from the centre, like spokes in a wheel. I believe we are getting somewhere, boys."
"'Like spokes in a wheel,'" repeated Roy to himself. "Rows of letters like spokes in a wheel. Four scratches in one row or spoke—these must be the four T's. Three scratches in these other rows must be O's and A's and S's. I've got it! I've got it!" he suddenly shouted. "There must be as many spokes as there are letters in the alphabet."
"I believe you are right, Roy," said Captain Hardy, looking up with a gleam in his eyes. "That's exactly what I am beginning to think. We'll soon see if you are right. Make me another disc."
With a pocket rule he measured the diameter of the dollar. "Practically an inch and a half," he announced, putting down the figures 1.5 on paper. He multiplied those figures by 3.1416.
"That," said he, pointing to the resulting figures, 4.71+, "represents the circumference of a dollar. Now we'll divide the circumference by 26, the number of letters in the alphabet."
He performed the division. "Eighteen one-hundredths of an inch," he announced. "That's practically a scant fifth of an inch. We'll call it so, anyhow," he continued as he marked off the space on a sheet of paper with his rule. "Each sector," he said, "gets exactly that amount of space on the circumference."
He pulled open the drawer of the desk and began to rummage through a tray full of pens, pencils, and other drawing materials. "I wonder if there is such a thing as a pair of dividers here," he remarked. And a moment later he exclaimed "Good!" and drew forth the compasses he was looking for.
He set his dividers according to the space he had marked off with his rule, then proceeded to divide the circumference of the new paper disc. When he had gone completely round the disc, he seized pencil and ruler and began to draw lines from centre to circumference—the spokes of his wheel—each spoke running from the dot in the centre to one of the points indicated by the dividers. When he had finished, the disc was divided into twenty-six equal sectors, like tiny pieces of a pie.
"We shall soon know whether you are right or not in your guess, Roy," said Captain Hardy.
He laid the dollar beside the disc and began to copy on the disc the marks on the dollar. "We'll put four marks in this sector," he said, making four dots with his pencil. "They are like those four scratches here," and he pointed to the four marks in a row on the dollar. "They must be four T's. At any rate we'll call this the T sector. On the dollar you notice this row of three scratches—the next sector to the left of the T sector. You remember we had three O's, three A's, and three S's. These three scratches must, therefore, be O's, A's, or S's. Since they are next to the T's, they are doubtless S's. I'll mark the sector so anyway. That gives us the T sector and the S sector. If we are on the right track, then the sector to the left of the S space is the R sector, and so on. I'll mark the disc that way, anyhow."