A correspondent of the " Memphis Eagle " says:— o' In the State of Arkansas, in the immediate vicinity of Little Rock, is as fine and good granite as is to be found anywhere in the world. I was there last fall, and saw it myself; and can say that it is not only as fine, but, if any difference, finer than that I recently saw iv. New Orleans, to which I have re-ierred to above. I was credibly informed, while at Little Rock, that, a lew miles from that city, is what is called the " Gianite Mountain "—a mountain of granite about thirteen miles long, two and three miles broad, and a quarter of a mile high. Here, then, is an almost inexhaustible quantity of this material; nor is it only here, but for miles the country is full of it. Why, then, send away to New England for it 1 Why not have it gotten here, almost, as you might say, at New_ Orleans itself, and take it right down to the city ?" The reason why these granite quarries have continued so long undisturbed, as given by this correspondent, is the difficulty of getting such a heavy material to market. This difficulty will soon, however, be entirely obviated, by the building of the Great Central Railroad from Memphis to Little Rock, which is expected to be completed within a very few years. Then the granite can be suitably prepared at the mountain, put on the cars, sent to Memphis, and thence shipped all over the western and southern country, from the Falls of St. Anthony to New Orleans. " The slate quarries of Arkansas also bid fair to be exceedingly valuable. We are now mostly supplied with slate from Wales and Pennsylvania. The Arkansas slate is found in veins about a mile wide, which cross the Arkansas river at Little Rock, and extend southwestwardly as lar as Ouachita river, and some distance in the opposite direction. Near Little Rock it is most accessible.— There the vein is seventy-five feet thick above the river bed, which, multiplied by the area of the vein belonging to a company, one hundred thousand feet, gives sevea million five hundred thousand cubic feet of slate. Should the quarry go to a depth of three hundred feet, the total yield would be thirty million cubic feet. From a cubic foot of rock it is estimated that, allowing one third for waste, a workman can split fifty good smooth slates of sufficient thickness for roofing. This gives a full aggregate of fitteen hundred millior slates, or fifteeen million squares of one hundred feet of regular size for roofing. A Cincinnati company have obtained a charter, which run's for fifty years, and have purchased a large tract of land, with a view of supplying the Cincinnati market with slate. They will undoubtedly be successful, as will other companies that will assuredly spring up. As soon as the Central Railroad is completed, Arkansas will take a start that will speedily make her one of the most prosperous and desirable states in the Union."