"I am getting the points of the compa.s.s," 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 lat.i.tude, 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:
[Ill.u.s.tration]
"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:
[Ill.u.s.tration]
"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 compa.s.s, 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 compa.s.s 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 a.s.sistance, 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."
CHAPTER XII.
HOW TO HAVE A "LONG HEAD."
Two hours steady walking, over logs and brush, through canebrakes, across a creek, and through a tangle of vines, brought the party to the leaning pine tree. From that point the old sycamore tree looked not at all as it did from the point of starting. The boys had taken pains to watch its changes of appearance, however, and were able to point it out with certainty to Sam.
"But what"s the good of knowing it now?" asked Sid Russell, "we aint a goin" back that way agin"."
"No," said Sam, "but it is necessary to know it, nevertheless. How would you know which way to go without it, Sid?"
"Well, I"d pick out another tree ahead an" walk towards it."
"Well, but how would you know what tree to select?"
"Why I"d take one in a line with the pine."
"Well, every tree is in a line with the pine. It depends on where you stand to take sight."
"That"s so; but how"s the old sycamore to help us?"
"By giving us a point to take sight from. Let me show you. Our proper course of march is in the direction of a line drawn from the sycamore to this pine tree. What we want to do is to prolong that line, and find some tree further on that stands in it. If I stand on the line, between the sycamore and the pine and turn my face toward the pine, I"ll be looking in exactly the right direction, and can pick out the right tree to march to, by sighting on the pine. The trouble is to get in the right place to take sight from. To do that I must find the line between the sycamore and the pine. Now you go over there beyond the pine, and take sight on it at the sycamore till you get the two trees in a line with you. Then I"ll stand over here, between the two object trees, and move to the right or left as you tell me to do, till you find that I am exactly in the line between them. Then I can pick out the right tree ahead."
Sid did as he was told, the boys all looking on with great interest, and presently Sam had selected their next object tree. The boys were astonished greatly at what they thought Sam"s marvellous knowledge, but to their wondering comments Sam replied:--
"I haven"t done anything wonderful. A little knowledge of mathematics has helped me, perhaps, but there isn"t a thing in all this that isn"t perfectly simple. Any one of you might have found out all this for himself, without books and without a teacher. It only requires you to think a little and to use your eyes. Besides you"ve all done the same thing many a time."
"I"ll _bet_ I never did," said Billy Bowlegs.
"Yes you have, Billy, but you did it without thinking about it."
"When?"
"Whenever you have shot a rifle at anything."
"How?"
"By taking aim. You look through one sight over the other and at the game, and you know then that you"ve got it in a line with your eye and the sights. I"ve only been turning the thing around, and n.o.body taught me how. You"ve only got to _use_ your eyes and your head to make them worth ten times as much to you as they are now."
"Seems to me," said Sid Russell, "as if your head "n eyes, or least ways your head is a mighty oncommon good one."
"You"re right dah, Mas" Sid," said Black Joe; "you"re right for sartain. I"se dun see Mas" Sam do some mighty cur"ous things, I is. He dun make a fire wid water once, sho"s you"re born. "Sides dat, I"se dun heah de gentlemen say"s how he"s got a head more "n a yard long, and I"m blest if I don"t b"lieve it"s so."
All this was said at a little distance from Sam and beyond his hearing, but he knew very well in what estimation his companions held him, and he was anxious to impress them, not with his own superiority, but with the fact that the difference was due chiefly to his habit of thinking and observing. He wanted them to improve by a.s.sociation with him, and to that end he took pains to show them the advantage which a habit of observing everything and thinking about it gives its possessor. For this reason he took pains to make no display of his knowledge of Latin or of anything else which they had no chance to learn. He wanted them to learn to use their eyes, their ears and their heads, knowing very well that the greater as well as the better part of education comes by observation and thinking, rather than from books.
Just now he was striding forward as rapidly as he could, as it was beginning to rain.
"Keep your eye on the hind sight boys, and don"t lose it," he cried; "we must hurry or we shall be caught in a pocket to-night."
Hour after hour they marched, the rain pouring down steadily, and the ground becoming every moment softer. The walking wearied them terribly, but they pushed on in the hope that they might be able to cross the upper waters of the Nepalgah river before night. This would place them on the west bank of that stream, where Sam believed that he should find the marching tolerable. If they should fail in this, Sam feared that the water would rise during the night, and fill all the bottom lands. In that event he must continue marching down the east bank of the river; not going very far out of his way, it is true, but having to pa.s.s through what he was satisfied must be a much more difficult country than that on the other side.
Night came at last, and they were yet not within sight of the stream, notwithstanding their utmost exertions. Sam called a halt just before dark, and selected a camping place.
CHAPTER XIII.