I have said that the Shoshones threw away their bucklers at the instigation of the Prince Seravalle, who also taught them the European cavalry tactics.  They had sense enough to perceive the advantage they would gain from them, and they were immediately incorporated, as far as possible, with their own.

The Shoshones now charge in squadrons with the lance, form squares, wheel with wonderful precision, and execute many difficult manoeuvres; but as they combine our European 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 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.