From the New York American.

The following letter from the last number of the Turf Register, though addressed chiefly to Sportsmen, contains a description of the mounted Indians of the West, that is eminently graphic and picturesque:

Cantonment Jesup, Lou. July 15, 1832.

Mr. Editor- The modern turf horse is said to be deficient in the power of endurance and ability to carry weight, which were so eminently possessed by the immediate descendants of the Arabian, Barb and Turkish horses, which produced the unrivalled English stock. My object is to direct the attention of America breeders to a stock of horses possessing good wind, great powers of endurance, and hardy constitutions, with fine bony, sinewy limbs. They are indigenous to our continent; and if the experiment I recommend, of crossing them with our bred horses, succeed, will preclude the necessity of recurring to the present race of horses in England, which is doubtless degenerate. I allude to the wild or prairie horse, inhabiting the southwest region of our continent, and roaming amid the immense grassy plains of that section, and to this race, partially tamed by the savage tribes of the country. No one who has seen the Osages galloping over their boundless prairies, under their fervid sun, and maintaining this gait for hours; viewed their muscular and handsome steeds, and compared his own jaded nag with the bounding and restless animals around him, but has confessed the superiority of their horses over ours. In July, 1829, the writer accompanied a party of gentlemen on a visit to Clermore's band of Osages, on the Verdigris River, a tributary of the Arkansas. A runner having been despatched to apprize them of our intention, upon arriving within two miles of the town, we halted to await their welcome. In a moment they were in commotion, and the chiefs and principal warriors (in number about a hundred) mounted, and approaching at full speed; bearing lances, and shields painted of various colors, and otherwise adorned; their heads surmounted with helmets of feathers and red and blue cloth; their arms and legs clasped by tinkling bands: some naked, with the exception of the breach clout; others clothed in the favorite dress of the Indian, a blue frock, with red collar and cuffs; and another portion with only the painted blanket streaming from their shoulders; sounding their war cry, and advancing rapidly and tumultuously; rushing in among us to give a welcome, and then wheeling their horses on the vast surrounding plain, in mimic pursuit of each other. They presented a most joyous, novel, and splendid barbaric spectacle. Here it was that my admiration of their horses was first excited; for this was the first opportunity I had to viewing their good horses. Among them were three or four, evidently of the same family; on one of which Clermore himself rode. They were of a beautiful cream color, with black manes and tails; a dark stripe along the back and dark or black legs from the knees down; not over fifteen hands in height, but of compact. A mahogany bay, of this size and form, caught my eye, as possessing a most superior walk. One brave sported a Pawnee head dress, horse, and other spoils, taken in battle. The stallion was of a very dark and peculiar iron grey, tall and slender, but a most beautiful animal. There is now at Cantonment Gibson a wild mare, caught by the Osages when on a hunt. She is white, with a neck like a stallion; finely formed in every respect; of great length of body, and having remarkably fine limbs. Every attempt has been made to break her, but with indifferent success; she having thrown, at their imminent hazard, all her riders. She has produced a likely, but small brown bay filly, by one of the worthless Cherokee ponies about the garrison. When we consider the firm, elastic soil, excellent herbage, and fervid sun of the plains over which these horses roam-the question, what advantages in soil, climate or food, the dessert or mountain Arabian horse possesses over them, naturally presents itself. They ought to possess, in an equal degree the flinty hardiness of limbs, speed, 'c. of the Arabian. But one reason can be given for the superiority of the latter, (if they be in fact superior,) viz: that the Arabs have been more careful in perpetuating a good strain and in suffering no inferior cross. But from the fact of the Osages prizing very highly their good horses,and the reluctance with which they part from them, together with my observing a particular family of horses among the chiefs, induce the conclusion that a peculiar breed exists among them; and I submit to sportsmen, whether an experiment, with a few of their stallions and mares, is unworthy a trial. Assuredly there are in our country gentlemen of fortune, enterprize, and patriotism enough,to make the experiment; and though the immediate cross with the blood horse should not evince speed enough to make first rate turf horses, yet their stamina would, by judicious crossing, produce those fine saddle and draft horses, which a late writer (Mason) asserts the Virginia turf horse of the present day rarely produces. Should the experiment be made, (and there are so many mares and stallions of every degree of excellence and blood, in Virginia and Kentucky especially that it might be conducted without bearing too onerously upon an individual sportsmen), it should not be abandoned in despair, though the first or second cross should not equal expectation. When we recollect the perseverance, repeated trials, and number of years, devoted by a Duke of Cumberland, before he succeeded in obtaining a superior stock of horses; and the pertinacity of an Earl of Oxford, in establishing the truth of a theory, by continuing a cross (of greyhounds) to the eighth removed, ere he attained the degree of perfection anticipated, we should be incited to attempt and continue our experiments. In order, Mr. Editor, that breeders may know what facilities they would meet with, and be enabled to form some idea of the expense they would have to incur, I will state the most expeditious mode of, and best season for reaching the country of the Osages.- From January to June the Arkansas has water enough for the steamboats which ply from the mouth of White River and New Orleans to ascend to Cantonment Gibson. The post is by water, about six hundred and fifty miles from the Mississippi by land, about three hundred and fifty. Clermore's village is distant from it fifty-five miles. Forty miles from the garrison is the residence of their trader, Col. A. P. Choteau, of St. Louis; a gentleman whose predilection for the sports of the turf would induce him to exert his great influence to persuade the chiefs to part with their best horses. I cannot at this moment, refer to the Indian laws, but think they prohibit any purchase from the tribes without the sanction of their agent. The agent of the Osages is Mr. Humtramck, who resides at White Hair's Town, situated on the Osage River, a tributary of the Missouri. But, upon application, doubtless the President or Secretary of War would authorize and attempt at purchase.

A SUBSCRIBER.