Owing to the great number and variety of articles exhibited at the Fair, and owing to the want of good classification and arrangement, we must have overlooked many good things in our notices of the articles exhibited. It could not be otherwise, for the articles are never arranged in classes because the place of exhibition has always been too smal I to allow of a good arrangement. One machine of one class stood at one corner, and another machine of the same class was to be found mixed up with a totally different group. The Catalogue of the American Institute Fair has always exhibited an arrangement similar to that of a stone heap raised by a parcel of boys pitching the stones when sojourning home from school. The articles are not classified, nor does the catalogue afford the least clue to guide a visitor where to find such and such an article exhibited. We hope the managers of the Great Fair, next year, will have a good catalogue—an instructive one; they will find it a profitable speculation. BANDING PULLEYS—A most important improvement exhibited at the Fair was a circular and an upright saw for sawing scroll-work, driven by an improved method of Banding Pulleys, invented by R. W. Parker, who is now residing at 58 Dey street, this city, and for which a patent was granted on the 17th of last February. By the jower of one man at the crank, a person is enabled to saw, with either saw, through a two-inch plank; the circular saw running at 2,600 revolutions per minute, and the scroll saw 600 vibrations per minute. This was done while the writer of this turned the crank. We consider this improvement to be a most valuable one, and applicable to all machinery. For portable machines, in small shops; it is an improvement which must soon come into general use. The improvement in this method of banding pulleys consists in arranging the driving pulley in reference to two other pulleys, that the band passing over these pulleys is not only pressed with any desired force against the periphery of the driver, but is also pinched between other pulleys operating upon the band as feed rollers. FINE ARTS.—In the fine arts, some of the most beantiful bronze castings we ever saw were exhibited, J. G. Gilbert, of 216 Pearl street being the agent. A gold medal was awarded for them. These castings were made by a new process of preparing the moulds. Flowers, animals, and other objects of nature can be copied exactly, and all their bounding lines of beauty, rendered permanent as the everlasting hills in metal. ENGRAVING ON STEEL.—A gold medal was awarded to A. H. Ritchie, of the firm of Bac-hia Co., corner of Chamber and Centre street, N. Y., for a full length mezzotint steel engraving of the immortal Washington. It is the finest engraving, considering the attitude and the mass of light thrown upon the figure, we ever saw. The likeness is excellent and the whole composition of the picture is different from any other heretofore produced. We have always endeavored to notice things strictly new, useful, and beautiful; but as we said before, amid such a confused mass, many excellent things have no doubt been overlooked. We would also state that a great defect, and one injurious to exhibitors at lairs, is the absence of a full description of the nature and action of the machines exhibited. A brief and clear description should be pasted up on every machine and apparatus. We hops the managers of the fair in the New York Crystal Palace, will attend to this hint, it will make the Fair far more interesting and instructive.