The Genessee river rises in the Alleghany Mountains, and it is not for want of poetical names on its banks that it is not a poetical river. Its source is ten miles below _Nunda_, between the head waters of the _Owago_ and the _Cawanisque_ rivers; and it runs one hundred and fifty miles, receiving tribute from the _Canassaraga_ and _Angelica_ creeks, and the _Canesus_ and _Honcoye_ outlets. It has a great reputation for fertility; and along its valley lies the celebrated farm of Mr. Wadsworth, the agriculturist, who holds in this country the place occupied in England by Mr. Coke of Holkham—now Earl of Leicester. The Rapids of the Genessee commence a mile above the Fall at Rochester, and descend, when there is much water, with great swiftness and beauty. The first pitch of the stream is ninety-seven perpendicular feet; after which it goes sullenly on down the ravine—black, where it is not covered with foam—till, forty rods below, it takes another leap of one hundred and six feet, at a place called Carthage. We suggested to the landlord that the fall at Carthage should be called after Marius, but he did not see the propriety of it very clearly. The Genessee Fall, like Niagara, is gradually _backing up_. It is computed that the latter wears back a rood every three years—the former much less, of course. There is little doubt among the geologists, that the Genessee at one time ran directly into Lake Ontario without much of a cascade, but that, on the retreat of the lake, the surface of which has perceptibly lowered, the stream began to wear back with the attrition of the fall, and they are now three miles asunder. An aqueduct of the great Erie canal runs close across the head of the Fall at Rochester, and is built in full confidence that the cascade will continue the sobriety and order it has hitherto preserved in its retreat. If it were to take a long step up stream of a sudden, that great vein of the west would breathe more freely than is provided for by the “weirs and feeders.” This aqueduct at Rochester is a work of some pretension. It is seven hundred and fifty feet in length, and has twelve piers and eleven arches, two of which are over Mill-races. A path is railed off on the side of the canal, and it forms a picturesque promenade across the bed of the river.