Since the above was written, we have been kindly favored with a copy of the following letter from Professor A. D. Bache, Superintendent Uni States Coast Survey, to our friend and townsman S. G. Fisher, Esq., concerning the recent discoveries in Mobile Bay, made by the Survey, under the immediate direction of Lieut. Com. Pattison, United States Navy. In connection with the Mobile and Ohio Railroad, these discoveries are of the highest importance, establishing conclusively, as they do, the superior advantages of Mobile Bay over any other harbor of the Gulf, as the seaboard terminus for a great system of internal improvement. Coast Sravey STATIoN, near Manchester, JV. H., Sept. 5, 1848. S. GRIFFITT's FishER, Esq., of Mobile. Dear Sir: In reply to your request, for the most recent information in regard to the changes at the entrance to Mobile Bay, and to the depth of water of 203 feet upon the bar, I send you the following extracts from a recent report by Lieut. Con. C. P. Pattison, United States Navy, the Assistant in the Coast Survey, to whom the credit is due for the excellent progress and interesting discoveries made in the hydrography of that section of the survey: 1st. The depth of water which can be carried over the bar at the entrance of Mobile Bay at mean low water, is 203 feet mean rise, and fall of tide one foot. 2d. The channel is perfectly easy, one course N.]19° W. true, going through with one or two casts on the ridge of shoalest water. 3d. Continued strong northerly winds depress the water at the extreme 2 feet below mean low water; and continued south-east and south winds elevate it 24 feet—in rare cases to an extreme of 4 feet. 4th. In heavy gales, the sea is said to break across the bar. This I have never seen, but judge it must be the case. 5th. After crossing the bar the channel varies from one-half to seven-eighths of a mile in width, averaging 7 fathoms in depth, and perfectly clear. 6th. The depth of water immediately at the end of the wharf at Fort Morgan, Mobile Point, is 63 feet; 150 yards out, there are 5 fathoms; and in mid-channel, abreast of the wharf, one third of a mile out, there are 9 fathoms. 7th. The depth of water at the anchorage of the fleet of merchant vessels in the bay, is 34 fathoms. There is perfectly secure anchorage, in any winds, for large vessels off the west end of Mobile Point, with the light-house bearing from S. E. to S. S. W. in from 8 to 10 fathoms water, and distant from the shore from one to one-tenth of a mile.8th. There is a fine harbor for small vessels drawing not over 12 feet in Navy Cove, just to the north end of Mobile Point, secure in all winds, and easy of entrance. 9th. Pelican Island in 1822 was 1,723 yards long, in 1841 it was 2,757, and in 1847 it had increased to 3,457 yards, making an increase of 1,735 yards in 25 years. The north end of this island had made a few yards further out in 1848. The shore of Dauphin Island, to the north ward of Pelican, had cut out a few yards, so keeping the distance between them nearly the Raine, 10th. The distance between the north end of Pelican Island and Dauphin Island in 1822 was 1,957 yards; in 1841, it was 788; and in 1847 it was but 383 yards. The depth through this channel has remained the same since 1822, being 13 feet at mean low water. 11th. Sand Island, upon which stands the outer light-house, was in 1822 but 131 yards across; in 1841, it was 1,542 in length; and in 1847, it had decreased to 908 yards. This island is con stantly undergoing increasing or decreasing, as the various causes of change act upon it. With in the last year, the north point has been cut off for a distance of 60 yards, and the east shore for an average width of 15; whilst the shore to the north of the light-house has made out 60 yards. A small channel 10 or 15 yards wide, and 6 feet deep, which separated the north point from a small bank dry at low water was filled during one spring ebb tide. 12th. Little Sand Island, as it is called, where was in 1822 from 3 to 10 feet water, had made up into an island in 1841 of 952 yards in length, and increased to 2,625 yards in 1847. 13th. In 1822 the greatest depth which could be taken over the bar was 17 feet; in 1841 it was 19 feet; and him 1847 it was 203 feet, each at mean low water. 14th. In 1822, the distance from the position in which Sand Island light-house now stands, to the shoalest water in the channel on the bar, was 3,446 yards; in 1841, it was 3,531; and in 1847, it was 3,724 yards. 15th. Upon a line of soundings which took over the bar in 1841 but 13 feet, in 1847 the depth was 20 feet. 16th. The changes constantly taking place cannot better he illustrated than by the frequent appearance and disappearance of Little Pelican Island, which is often several feet above water, and as often as many below it. From these facts, it appears that the islands have been on the increase since 1822, whilst the bar itself, connected with them, has passed gradually seaward, deepening as it advanced. Yours, respectfully and truly, A. D. l'AcHk, Sup’t United States Coast Survey.