If the hunter be right-handed, and uses a pistol, he should approach upon the left side, and when nearly opposite and close upon the buffalo, deliver his shot, taking aim a little below the centre of the body, and about eight inches back of the shoulder. This will strike the vitals, and generally render another shot unnecessary. When a rifle or shot-gun is used the hunter rides up on the right side, keeping his horse well in hand, so as to be able to turn off if the beast charges upon him; this, however, never happens except with a buffalo that is wounded, when it is advisable to keep out of his reach. The buffalo has immense powers of endurance, and will run for many miles without any apparent effort or diminution in speed. The first buffalo I ever saw I followed about ten miles, and when I left him he seemed to run faster than when the chase commenced. As a long buffalo-chase is very severe labor upon a horse, I would recommend to all travelers, unless they have a good deal of surplus horse-flesh, never to expend it in running buffalo. Still-hunting, which requires no consumption of horse-flesh, and is equally successful with the other method, is recommended. In stalking on horseback, the most broken and hilly localities should be selected, as these will furnish cover to the hunter, who passes from the crest of one hill to another, examining the country carefully in all directions. When the game is discovered, if it happen to be on the lee side, the hunter should endeavor, by making a wide detour, to get upon the opposite side, as he will find it impossible to approach within rifle range with the wind. When the animal is upon a hill, or in any other position where he can not be approached without danger of disturbing him, the hunter should wait until he moves off to more favorable ground, and this will not generally require much time, as they wander about a great deal when not grazing; he then pickets his horse, and approaches cautiously, seeking to screen himself as much as possible by the undulations in the surface, or behind such other objects as may present themselves; but if the surface should offer no cover, he must crawl upon his hands and knees when near the game, and in this way he can generally get within rifle range. Should there be several animals together, and his first shot take effect, the hunter can often get several other shots before they become frightened. A Delaware Indian and myself once killed five buffaloes out of a small herd before the remainder were so much disturbed as to move away; although we were within the short distance of twenty yards, yet the reports of our rifles did not frighten them in the least, and they continued grazing during all the time we were loading and firing. The sense of smelling is exceedingly acute with the buffalo, and they will take the wind from the hunter at as great a distance as a mile.