CHAPTER XI.
BACKWOODS GEOMETRY.
The quarrel having ended in the way described in the last chapter, theboys were compelled to find something else to talk about, as they wereunder a pledge not to refer further to that matter. They wereprepared, therefore, to take an interest in Sam's preparations forresuming the march without the assistance of a compass. Theircuriosity was great to know how he meant to proceed, and it was madegreater by what he did first.
The clouds were thick and heavy, as I have already said, so that therewas no chance to look at the sun for guidance; but Sam Hardwicke wasfull of resources. He had a good habit of observing whatever he sawand remembering it, whether he saw any reason to suppose that itmight be of use to him or not. Just now he remembered something whichhe had observed the evening before, and he proceeded at once to makeuse of it.
He cut a stick, sharpened it a little at one end, and drove it intothe ground at a spot which he had selected for the purpose. Then hewalked away twenty or thirty paces and drove another stake, sightingfrom one to the other, and taking pains to get them in line with atree which stood at a little distance from the first stake.
"What are you doing, Captain Sam?" asked Bob Sharp, unable to restrainhis 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 Iwanted to mark my map, and I sat down right here," pointing to a spotnear the first stake, "because it was shady here. The trunk of thatbig tree threw its shadow here. Now the sun does not set exactly inthe west in this latitude, but a little south of west at this time ofyear. The line of a tree's shadow, therefore, at sunset must be fromthe 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 middleof the shadow, as I remember it, so that a line from the stake to themiddle 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 Iwill go on with my work, explaining as I go."
Taking his pocket-rule he measured off twenty feet east and west fromhis first stake, and drove a stake at each point.
"Now," he said, "I have an east and west line, forty feet long, with astake 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 rightangles, and I can draw it pretty accurately with my eye, but to beexact I have measured this line as you see. Now I'll draw a line asnearly as I can straight across this one, and of precisely the samelength."
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 angleswith my first one, it runs north and south; and to find out whether ornot I have drawn it exactly, I must measure. If it is just right itwill be precisely the same distance from the south stake to the eaststake as from the south stake to the west stake; and from the eaststake to the south one will be southwest, while from the west to thesouth 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 explainhow you can help me. Our course lies exactly in a line from me throughthat big gum tree over there to the dead sycamore beyond. If we gotoward the gum, keeping it always in a line with the sycamore, weshall go perfectly straight, of course; and by choosing another treeaway beyond the sycamore and in line with it, just before we get tothe gum tree, we shall still go on in a perfectly straight line. Wemight keep that up for any distance, and travel in as straight a lineas a compass can mark. Now if this country was an open one with nobogs to go around, and nothing to keep us from going straight ahead, Ishouldn't need any assistance, but could go on in a straight line allday long. As it is, I must establish a long straight line, reaching asfar ahead as possible, and then pick out two things in the line, onenear me and one at the far end, which we can recognize again from anypoint. Then we'll go on by the best route we can till we come to thefurthest 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 callthem, so that we can be sure of them at any time. Notice them instarting, and as often afterward as you can see them. The appearanceof trees varies with distance and point of view, and it is importantthat we shall be sure of our object trees and make no mistake aboutthem."
"All right, Captain Sam," cried the boys, "pick out your objecttrees."
"Well," said Sam, "the big sycamore yonder will do for one, and thattall leaning pine away over there almost out of sight must do for theother. 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 thesycamore 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."
Captain Sam: The Boy Scouts of 1814 Page 11