A State Agricultural Society, numbering among its members some thousands of her foremost citizens, mainly but not wholly farmers, is one of the most commendable institutions of this great and growing commonwealth. Aided liberally by the State government, it holds an Annual Fair at some one of the chief towns of the interior, generally on the line of the Erie Canal, whereby the collection of stock and other articles for exhibition is facilitated, and the cost thereof materially lessened. Poughkeepsie, Albany, Saratoga Springs, Utica, Syracuse (twice), Auburn, Rochester (twice), and Buffalo, are the points at which these Fairs have been held within the last ten years. Recently, the railroads have transported cattle, &c., for exhibition, either at half-price, or entirely without charge, while the State's bounty and the liberal receipts for admission to the grounds have enabled the managers to stimulate competition by a very extensive award of premiums, so that almost every recurrence of the State Fair witnesses a larger and still more extensive display of choice animals. Whether the improvement in quality keeps pace with the increase in number is a point to be maturely considered. The Fair of this year was held at ROCHESTER, in a large open field about a mile south of the city, and of course near the Genesee river. Gigantic stumps scattered through it, attested how recently this whole region was covered with the primeval forest. Probably fifty thousand persons now live within sight of the Rochester steeples, though not a human being inhabited this then dense and swampy wilderness forty years ago. And here, almost wholly from a region which had less than five thousand white inhabitants in 1810, not fewer than one hundred thousand persons, two-thirds of them adult males, were drawn together expressly to witness this exhibition. The number who entered the gates on Thursday alone exceeded seventy-five thousand, while the attendance on the two preceding days and on Friday, of persons who were not present on Thursday, must have exceeded twenty-five thousand. Of course, many came with no definite purpose, no previous preparation to observe and learn, and so carried home nothing more than they brought there, save the head-ache, generated by their irregularities and excesses while absent; but thousands came qualified and resolved to profit by the practical lessons spread before them, and doubtless went away richly recompensed for the time and money expended in visiting the Fair. This Annual Exhibition is as yet the Farmers' University; they will in time have a better, but until then they do well to make the most of that which already welcomes them to its cheap, ready and practical inculcations. [Illustration: ROCHESTER.]