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 feet. Seven-eighths
of 70 equals 61-1/4 feet. The width of the pond--they measured it with
tape line--was found to be 60 feet, so Yan was nearest, but Guy claimed
that 50 feet was within 10 feet of it, which was allowed. Thus there
were two winners--two who escaped dishwashing; and Hawkeye's bragging
became insufferable. He never again got so close in a guess, but no
number of fa