SUNDAY, October 20.

All day long we have been passing through the grazing plains of Nebraska. Endless herds of cattle untrammelled by fences; the landscape a brown sea as far as the eye can reach; a rude hut now and then for a shelter to the shepherds. No wonder we export beef, for it is fed here for nothing. Horses and cattle thrive on the rich grasses as if fed on oats; no flies, no mosquitoes, nothing to disturb or annoy, while the pellucid streams which run through the ranches furnish the best of water. There can be no question that our export trade is still in its infancy. The business is now fully organized, and is subject to well-known rules. At Sherman we saw the large show-bills of the Wyoming County Cattle Raisers' Association, offering heavy rewards for offenders against these rules, and the Cheyenne Herald is filled with advertisements of the various "marks" adopted by different owners. Large profits have been made in the trade - the best assurance that it will grow - but from all I can gather it seems doubtful whether the experiment of exporting cattle alive will succeed.

We saw numerous herds of antelope to-day, but they graze among the cattle, and are altogether too finely civilized to meet our idea of "chasing the antelope over the plain;" one might as well chase a sheep. As night approaches we get higher and higher up the far-famed Rocky Mountains, and before dark reach the most elevated point, at Sherman, eight thousand feet above tide. But our preconceived notions of the Rocky Mountains, derived from pictures of Fremont a la Napoleon crossing the Alps, have received a rude shock; we only climb high plains - not a tree, nor a peak, nor a ravine; when at the top we are but on level ground - a brown prairie, "only this, and nothing more."

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