He fastened the string down with a thumb tack, and then Bob took it and ran aft again to the cabin.
“Have you had anything about angles and circles at school, Gray?” asked the Chairman.
“Yes, sir, but I don’t remember much about ’em.”
“Well, I guess you’ll remember enough to understand what I am going to tell you.”
Then he pointed out the degree marks that ran along the curved edge of the half circular board.
“Now if you hold the board up with the straight edge on top and horizontal, you’ll notice that the plumb line falls at right angles to the horizontal line and, at the edge of the circumference, passes through a point marked zero—but you must have seen a thing like this before, haven’t you? It’s what they call a ‘protractor.’”
“I’ve seen something like it, I think, sir, but I never understood what it was for.”
“Well,” said the Chairman, “you’ll see now how easy it is to understand, when you put your mind to it! This point marked zero that the plumb line passes through when the straight edge is horizontal, is exactly in the middle of the curved edge of the semicircumference. Now, from zero along the curve to the end of the straight edge, on both sides of zero, are ninety little points marking ninety degrees, making two halves of a semicircle, or in other words, one-half of a whole circle of 360 degrees.
“If you hold the straight edge of the board up to your eye and move the further end upward from the horizon, while keeping the center steady, the plumb line moves away from zero toward your body, and at the same time along the face of the semicircle, and registers a certain number of degrees from zero. If you imagine yourself standing in the middle of a circle, you can also imagine a lighthouse or a church steeple at the circumference of the circle. This distance to the circumference will be the radius. Then imagine that radius held fast at your end, but swinging upward and pointing to the sky. It will measure ninety degrees when it is pointing straight up from where you are standing to a point in the heavens directly above your head, and forty-five degrees when pointing to a place in the sky half-way between the horizon and a point directly above, and less than forty-five degrees when pointing to a place in the sky nearer the horizon. The straight edge of this board represents the direction of the sight line, or radius; and, as you tip the end up above the horizon until it reaches the top of the tower or steeple you are measuring, the same number of degrees will be registered by the plumb line at the bottom of the board, counting from zero, as the line appears to move toward yourself. Now, if you are holding your board with your right hand, just put the finger of your left hand on the plumb line to keep it in place while you look to see what it registers,—this way,” and the Chairman went through the motion with his hands.
“Thank you, sir,” said Dick, “I understand that very well, but I don’t see how it gives the distance to the lighthouse.”