THE WILD WEST SHOW.—It might have been thought that "Buffalo Bill's" Wild West Show was already long and varied enough to satisfy all reasonable expectations. Two or three additions of some importance have, however, now been made to the programme. One of them illustrates the administration of lynch law in the West, a lone cowboy, who has stolen a horse, being tracked, captured, and incontinently hanged. Soldiers come up a few moments afterwards, but are too late to save him. Whether the spectacle of a human being mimicking the agonies of a slow death can be fitly included in an entertainment is a point on which grave doubts may be entertained. The same purpose would be served if the soldiery arrived in the nick of time to effect a rescue, and it may be hoped that a modification of the scene to this extent will shortly be made. The picture, as may be supposed, is realistic and vivid in the extreme, and was received last night with a round of applause apparently unqualified by any sound of dissent. Better in every respect than this is an illustration of a pioneer train of emigrants crossing the plains on a pilgrimage to the land of the Setting Sun. While preparing their meal they are set upon by a horde of savages. The old scout is seized, tortured, and hurried to the stake, but is saved from a horrible death by scouts and cowboys under the command of Buffalo Bill himself. It is understood that the wagons in this scene are those actually used by emigrants 35 years ago. Other new features in the performance are a ride round the arena by a prairie maiden, a squaw, and a Spanish girl, and a race between a Cossack, a cowboy, a Gaucho, an Indian, and a Mexican, on Spanish, Mexican, Broncho, Russian, and Indian ponies. It may be added that the other parts of the entertainment, notably the buffalo hunt, the attack on a settler's cabin, the pony express of the pre-railway and pre-telegraph days, and the capture of the Deadwood coach by the Indians, who, of course, are finally driven back by Buffalo Bill and his attendant cowboys, seem to have lost none of their power to please a mixed audience.