knowledge which the higher classes among them really possess. I have
said that they are good astronomers, and I may add that their intuitive
knowledge of geometry is remarkable. I once asked a young chief what he
considered the height of a lofty pine. It was in the afternoon, about
three o'clock. He walked to the end of the shadow thrown by the
pine-tree, and fixed his arrow in the ground, measured the length of the
arrow, and then the length of the shadow thrown by it; then measuring
the shadow of the pine, he deducted from it in the same proportion as
the difference between the length of the arrow, and the length of its
shadow, and gave me the result. He worked the Rule of Three without
knowing it.

But the most remarkable instance occurred when we were about to cross a
wide and rapid river, and required a rope to be thrown across, as a stay
to the men and horses. The question was, what was the length of the rope
required; _i.e._, what was the width of the river? An old chief stepped
his horse forward, to solve the problem, and he did it as follows:--He
went down to the side of the river, and fixed upon a spot as the centre;
then he selected two trees, on the right and left, on the other side, as
near as his eye could measure equidistant from where he stood. Having so
done, he backed his horse from the river, until he came to where his eye
told him that he had obtained the point of an equilateral triangle.
Thus, in the diagram he selected the two trees, A and B, walked back to
E, and there fixed his lance. He then fell back in the direction E D,
until he had, as nearly as he could tell, made the distance from A E
equal to that from E D, and fixed another lance. The same was repeated
to E C, when the last lance was fixed. He then had a parallelogram; and
as the distance from F to E was exactly equal to the distance from E to
G, he had but to measure the space between the bank of the river and E,
and deduct it from E G, and he obtained the width of the river required.