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.

[Illustration]

I do not think that this calculation, which proved to be perfectly
correct, occupied the old chief more than three minutes; and it must be
remembered that it was done in the face of the enemy. But I resume my
own history.

CHAPTER X.

In narrating the unhappy death of the Prince, I have stated that the
Crows bore no good-will to the white men established among the
Shoshones. That feeling, however, was not confined to that tribe; it was
shared by all the others within two or three hundred miles from the
Buona Ventura river, and it was not surprising! Since our arrival, the
tribe had acquired a certain degree of tactics and unity of action which
was sufficient in itself to bear down all their enemies, independent of
the immense power they had obtained from their quantity of fire-arms and
almost inexhaustible ammunition. All the other nations were jealous of
their strength and resources, and this jealousy being now worked up to
its climax, they determined to unite and strike a great blow, not only
to destroy the ascendancy which the Shoshones had attained, but also to
possess themselves of the immense wealth which they foolishly supposed
the Europeans had brought with them to the settlement.

For a long time previous to the Crow and Umbiqua