tactics with their own Indian mode of
warfare, one of the most singular sights is to witness the disappearance
behind their horses, after the Indian fashion, of a whole body of
perhaps five hundred horse when in full charge. The effect is most
strange; at one moment, you see the horses mounted by gallant fellows,
rushing to the conflict; at a given signal, every man has disappeared,
and the horses, in perfect line appear as if charging, without riders,
and of their own accord, upon the ranks of the enemy.

I have dwelt perhaps too long upon the manners and habits of these
people; I cannot help, however, giving my readers a proof of the
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 fro