The interchange of circus performers between England and the United States, which has existed almost as long as circuses, has made us better acquainted in this country with the kind and quality of the performances to be witnessed in American circuses than with the manner in which they are conducted. Stickney and North were known and appreciated at Astley’s by the last generation, and the present has seen and admired, at the Holborn Amphitheatre, those inimitable gymnasts, the Brothers Hanlon, the incomparable vaulter, Kelly, and some others. Wallett, the Cookes, and many others, besides French, German, and Italian performers who have appeared in English circuses and music-halls, have found their way to America, and proved as attractive there as here. Four years ago, the Cooke family was represented in the United States by Emily Henrietta Cooke, John Henry Cooke, and George Cooke, prominent members of Stone and Murray’s company, and James E. Cooke with French’s circus. The largest circus now travelling is Barnum’s, forming a portion of the great combination advertised as the ‘Great Travelling World’s Fair.’ Barnum has long been famous in both hemispheres as the greatest showman in the world. He is certainly a man of remarkable enterprise and energy. He is quick in arriving at conclusions, and when he has resolved upon any undertaking, he exercises all his energy, and brings into force all the results of his long and varied experience, in carrying it into execution. Coup, a gentleman well known among public entertainers across the Atlantic, said to Barnum one day, ‘What do you say to putting a big show on the road?’ ‘How much will it cost?’ inquired Barnum, after a moment’s reflection. ‘Two hundred thousand dollars,’ was the reply. ‘I’ll let you know to-morrow,’ said Barnum. On the following day, he told Coup that ‘Barnum’s great show’ was a fact, and that he (Coup) was to be its manager, as he is to this day. The establishment then formed was, however, far from being the mammoth concern with which the great showman took the field in 1873. Notwithstanding the great loss which he sustained by the burning of the museum which so long attracted attention in the Broadway, New York, at the close of the preceding year, he came before the public a few months afterwards with a circus, a menagerie, a museum, a gallery of pictures and statuary, and a show of mechanical wonders and curiosities, all combined in one, and to which the public were admitted for a single payment of half-a-dollar. The address to the public with which this colossal combination of entertainments was inaugurated is so unique and characteristic that I need make no apology for inserting it entire. ‘LADIES, GENTLEMEN, FAMILIES, CHILDREN, FRIENDS: