The fair of the American Institute was duly opened at the Empire Stating Rink, Third avenue, between Sixty-third and Sixty-fourth streets, on the 8th inst., and although things are yet in a somewhat chaotic conditiorithe depart-nielit of machinery especiallythe signs indicate a brilliant display. The confusion is not due to ?vant of exertion on the part of the managers so much as to the dilatoriness of exhibitors. None of the machinery was cunning at the time of our going to press, though there will be no long delay. None of the departments was complete at the time of our visit ; the,',art department being specially meager. There are one or two cnayon portraits worthy of special notice, but beyond this and some excellent" photographs, there was very little ivorth seeing. The exhibition of the American Association of Wool Man-ufact"urers is undoubtedly destined to be one of the most interesting and attractive features of this fair. The following mills are already represented : The Lawrence and Pacific Mills, Lawrence, Mass.; Hamilton Woolen Co., Lo?vell, Mass.; Wm. Duncan & Son's Mills, Franklin," N. J. ; Eddy & Son's Mills, Fall River, Mass.; Lawrenceburg Woolen Mills, Law-renceburg, Ind.; Hockauum Company, Eoekville, Conn.; Harris Woolen Mill?, Woonsocket, R. I.; Weybosset Woolen Mills, Providence, B. I. ; Central Woolen Mills, Uxbridge, Mass.; Elba Woolen Mills, Providence, 11.1. ; Rock and New England Manufacturing Companies,Kockville, Conn.; American Mills, also of Rockville, Conn., Kernan and Helm, Utica, K.Y., and others whose goods viere not j'et displayed, and the ! names of which we could not learn. The goods in this department already on exhibition are such as to excite the pride of every one who has the prosperity of American iudustrv?*' heart. In the machinery department the only things wKioh were , arranged were two fine cases of saws, one fr(ji Hoe & Co., New York city, and the other from the Anirican Saw Co., , also of this city. Passing from this department we phserved a fine collection of agricultural machinery, which we will nOtice more in de-, tail hereafter. Near this collection stands a beautiful show . table of paints, exhibited by Devoe & Co., 117 Fulton street. New Yorli:. A great deal of taste is displayed in the arrange-. ment of this table, and the samples of colors exhibited are very fine. The soda-water fo-untain exhibited by John Matthews, of I this city, is one of the most beautiful designs we have ever seen. , The silk department ivill attract much attention. Although necessarily much smaller than the exhibition of woolen goods, it is, considering the comparatively recent period since the silk manufacture could be ranked as an American industry, a very remarkable display. Among the establishments represented here we notice P. G. Gimraud, Paterson, N. J. ; Frederick Bne, Schoharie, N. Y. ; Dale Manufacturing Co., Patorson, N. J.; Cheeney Bros., Hartford, Conn.; W. H. Horstmann & Sons, Philadelphia, Pa.; J. S. Shaiter, Paterson, N. J.; and the Oneida Community, of Oneida, N. Y. We shall give more detailed attention to the various dc-partmenis in future issues, and we congratulate the managers of the fair on their prospects of success. The exhibition will, undoubtedly, be one of the best ever held under the auspices of the American Institute. On Friday evening the fair was honored by a visit from President Grant, ????? was escorted through the several departments by the Hon. Orestes Cleveland, Chairman of the Board of Managers. He spent considerable time in the woolen department, and he was apparently well pleased "with the numerous beautiful products of American industry to be seen both there and in all the other departments of the fair. His presence created a great deal of enthusiasm among the large assemblage, and he was repeatedly cheered, while the band played " Hail to the Chief," and other appropriate airs.