July 4th. This is the eighty-seventh anniversary of our national independence–a day dear to every true American heart on account of the event it commemorates; but since no salute has been fired by us in honor of the day, and Jack looks rather crest-fallen in the phiz on that account, still we have far more and greater reasons for being of the opposite cast of countenance than we had one year ago to-day. Let us look back into the past, as long ago as a twelvemonth since, and see what was our situation and condition then, and what our prospects of success in struggles about to take place for the supremacy of our arms. By reference to the author’s remarks of what occurred on the Fourth of July, 1862, one year ago to-day, you will please note the fact that Vicksburg, although having withstood, about three weeks since, a terrific naval bombardment from our vessels, still defied our powers. Now the tables are turned; General Grant, in command of U. S. forces, has invested the place and cut off supplies reaching same for the rebel army by railroad from Jackson, Miss., and a surrender of this rebel stronghold is looked for at an early day; in fact, I must say it was not Grant, even Unconditional Surrender Grant, or any other general, who has been mainly instrumental in bringing about this condition of things, although he has performed, as I have before stated, no mean part in the programme of action, but this ship, under the superintendence of Admiral Farragut, by taking the lead of the fleet in the experiment of running the rebel batteries of Port Hudson, on the ever-to-be-remembered night of the 14th March last, and by the mercy of Almighty God, being fortunate enough to pass safely through that fiery ordeal with so little loss of life, with a gunboat (tender) lashed to her port side; also a few days afterwards, another battery of the enemy at Grand Gulf on our way up the river to Warrenton, to have communication with Major-General Grant and Acting Rear Admiral Porter, and again on our return, permitted to repass the above-mentioned battery at Grand Gulf with little loss of life and injury to ship, arriving off the mouth of Red river, which it had been previously decided upon we should blockade for the purpose of cutting off supplies from being transported by rebel steamers out of this stream to the rebel army at Port Hudson and Vicksburg, and aiding General Banks with his forces coming round from New Orleans by way of Berwick’s Bay. Alexandria, and Atchafalaya river to get in rear of Port Hudson. While Admiral Farragut has rigidly enforced the blackade of the mouth of Red river, commenced by him with but two vessels, the Hartford and Albatross soon after the passage of the rebel fortifications at Port Hudson, cutting off relief from Texas reaching them by transportation down and out of this channel, or that of their fellows at Port Hudson, and starvation is now staring them in the face, making and early surrender of both places highly probable.