“No, I want to be in this guessing.  The loser takes the next turn of dishwashing for each of the others.”

So Blackhawk studied the knot carefully and wrote down his guess—­Thirty-eight feet.

Sam said, “Blackhawk!  Ground’s kind of uneven.  I’d like to know the exact spot under the tree that you’d measure to.  Will you mark it with a peg?”

So Blackhawk went over and put in a white peg, at the same time unwittingly giving Woodpecker what he wanted—­a gauge, for he knew Blackhawk was something more than five feet high; judging then as he stood there Sam wrote down Thirty-five feet.

Now it was Yan’s turn to do it by “White-man’s Woodcraft,” as he called it.  He cut a pole exactly ten feet long, and choosing the smoothest ground, he walked about twenty yards from the tree, propped the pole upright, then lay down so that his eye was level with the tree base and in line with the top of the pole and the knot on the tree.  A peg marked the spot.

Now he measured from this “eye peg” to the foot of the pole; it was 31 feet.  Then from the eye peg to the peg under the tree; it was 87 feet.  Since the 10-foot pole met the line at 31 feet, then 31 is to 10 as 87 is to the tree—­or 28 feet.  Now one of the boys climbed and measured the height of the knot.  It was 29 feet, and Yan had an easy victory.

“Here, you close guessers, do you want another try, and I’ll give you odds this time, if you come within ten feet you’ll win.  I want only two feet to come and go on.”

“All right.  Pick your trees.”

“’Tisn’t a tree this time, but the distance across that pond, from this peg (H, in diagram) to that little Hemlock (D).  You put down your guesses and I’ll show you another trick.”

Sam studied it carefully and wrote Forty feet.  Wes put down Forty-five.

“Here, I want to be in this.  I’ll show you fellers how,” exclaimed Guy in his usual scornful manner, and wrote down Fifty feet.

“Let’s all try it for scalps,” said Char-less, but this was ruled too unimportant for scalps, and again the penalty of failure was dishwashing, so the other boys came and put down their guesses close to that of their Chief—­Forty-four, Forty-six and Forty-nine feet.

“Now we’ll find out exactly,” and Little Beaver, with an air of calm superiority, took three straight poles of exactly the same length and pegged them together in a triangle, leaving the pegs sticking up.  He placed this triangle on the bank at A B C, sighting the line A B for the little Hemlock D, and put three pegs in the ground exactly under the three pegs where the triangle was; moved the triangle to E F G and placed it so that F G should line with A C and E G with D.  Now A G D also must be an equilateral triangle; therefore, according to arithmetic, the line D H must be seven-eighths of A G. A G was easily measured—­70