Bat the chase on horseback was a different thing.  Its successful prosecution demanded a good horse, a bold rider, a firm seat, and perfect familiarity with weapons.  The excitement of it was intense, the dangers not to be despised, and, above all, the buffalo had a fair show for his life, or partially so, at least.  The mode of attack is easily described.

Whenever the hunters discovered a herd of buffalo, they usually got to leeward of it and quietly rode forward in a body, or stretched out in a regular skirmish line, behind the shelter of a knoll, perhaps, until they had approached the herd as closely as could be done without alarming it.  Usually the unsuspecting animals, with a confidence due more to their great numbers than anything else, would allow a party of horsemen to approach within from 200 to 400 yards of their flankers, and then they would start off on a slow trot.  The hunters then put spurs to their horses and dashed forward to overtake the herd as quickly as possible.  Once up with it, each hunter chooses the best animal within his reach, chases him until his flying steed carries him close alongside, and then the arrow or the bullet is sent into his vitals.  The fatal spot is from 12 to 18 inches in circumference, and lies immediately back of the fore leg, with its lowest point on a line with the elbow.

This, the true chase of the buffalo, was not only exciting, but dangerous.  It often happened that the hunter found himself surrounded by the flying herd, and in a cloud of dust, so that neither man nor horse could see the ground before them.  Under such circumstances fatal accidents to both men and horses were numerous.  It was not an uncommon thing for half-breeds to shoot each other in the excitement of the chase; and, while now and then a wounded bull suddenly turned upon his pursuer and overthrew him, the greatest number of casualties were from falls.

Of the dangers involved in running buffalo Colonel Dodge writes as follows:[52]

[Note 52:  Plains of the Great West, p. 127.]

“The danger is not so much from the buffalo, which rarely makes an effort to injure his pursuer, as from the fact that neither man nor horse can see the ground, which may be rough and broken, or perforated with prairie-dog or gopher holes.  This danger is so imminent, that a man who runs into a herd of buffalo may be said to take his life in his hand.  I have never known a man hurt by a buffalo in such a chase.  I have known of at least six killed, and a very great many more or less injured, some very severely, by their horses falling with them.”

On this point Catlin declares that to engage in running buffalo is “at the hazard of every bone in one’s body, to feel the fine and thrilling exhilaration of the chase for a moment, and then as often to upbraid and blame himself for his folly and imprudence.”