Chapter 11

BACKWOODS GEOMETRY.

The quarrel having ended in the way described in the last chapter, the boys were compelled to find something else to talk about, as they were under a pledge not to refer further to that matter. They were prepared, therefore, to take an interest in Sam's preparations for resuming the march without the assistance of a compass. Their curiosity was great to know how he meant to proceed, and it was made greater by what he did first.

The clouds were thick and heavy, as I have already said, so that there was no chance to look at the sun for guidance; but Sam Hardwicke was full of resources. He had a good habit of observing whatever he saw and remembering it, whether he saw any reason to suppose that it might be of use to him or not. Just now he remembered something which he had observed the evening before, and he proceeded at once to make use of it.

He cut a stick, sharpened it a little at one end, and drove it into the ground at a spot which he had selected for the purpose. Then he walked away twenty or thirty paces and drove another stake, sighting from one to the other, and taking pains to get them in line with a tree which stood at a little distance from the first stake.

"What are you doing, Captain Sam?" asked Bob Sharp, unable to restrain his curiosity.

"I am getting the points of the compass," replied Sam.

"Yes, but how are you a doin' it?" asked Sid Russell.

"Well," replied Sam, "I'll show you. Just before sunset yesterday I wanted to mark my map, and I sat down right here," pointing to a spot near the first stake, "because it was shady here. The trunk of that big tree threw its shadow here. Now the sun does not set exactly in the west in this latitude, but a little south of west at this time of year. The line of a tree's shadow, therefore, at sunset must be from the tree a trifle north of east. Now I have driven this stake" (pointing to the first one) "just a little to the right of the middle of the shadow, as I remember it, so that a line from the stake to the middle of the tree-trunk must be very nearly an east and west line. The other stake I drove merely to aid me in tracing this line. Now I will go on with my work, explaining as I go."

Taking his pocket-rule he measured off twenty feet east and west from his first stake, and drove a stake at each point.

"Now," he said, "I have an east and west line, forty feet long, with a stake at each end and a stake in the middle."

This is what he had:

"A north and south line will run straight across this, at right angles, and I can draw it pretty accurately with my eye, but to be exact I have measured this line as you see. Now I'll draw a line as nearly as I can straight across this one, and of precisely the same length."

He drew and staked the second line, and this is what he had:

"Now," he said, "if I have drawn my last line exactly at right angles with my first one, it runs north and south; and to find out whether or not I have drawn it exactly, I must measure. If it is just right it will be precisely the same distance from the south stake to the east stake as from the south stake to the west stake; and from the east stake to the south one will be southwest, while from the west to the south will be south-east."

With that Sam measured, and found that he was just a trifle out. Readjusting his north and south stakes, he soon had his lines right.

"Now," he resumed, "I know the points of the compass, and I'll explain how you can help me. Our course lies exactly in a line from me through that big gum tree over there to the dead sycamore beyond. If we go toward the gum, keeping it always in a line with the sycamore, we shall go perfectly straight, of course; and by choosing another tree away beyond the sycamore and in line with it, just before we get to the gum tree, we shall still go on in a perfectly straight line. We might keep that up for any distance, and travel in as straight a line as a compass can mark. Now if this country was an open one with no bogs to go around, and nothing to keep us from going straight ahead, I shouldn't need any assistance, but could go on in a straight line all day long. As it is, I must establish a long straight line, reaching as far ahead as possible, and then pick out two things in the line, one near me and one at the far end, which we can recognize again from any point. Then we'll go on by the best route we can till we come to the furthest object, and then I'll show you how to get the line again. What I want you to do is to notice the 'object trees' as we'll call them, so that we can be sure of them at any time. Notice them in starting, and as often afterward as you can see them. The appearance of trees varies with distance and point of view, and it is important that we shall be sure of our object trees and make no mistake about them."

"All right, Captain Sam," cried the boys, "pick out your object trees."

"Well," said Sam, "the big sycamore yonder will do for one, and that tall leaning pine away over there almost out of sight must do for the other. That is in our line, and what we've got to do is to get to it. It doesn't matter by how crooked a route, if we can remember the sycamore tree again and pick it out from there."

"We'll watch 'em captain, and we won't let 'em slip away from us," said Sid Russell.

"Thank you, boys," replied Sam; "I shall be so busy picking our way, that I can't watch them very well. Now then, we're ready, come on."