On the 8th of June, the Flag Officer having received the proper authority, once more turned the Hartford towards Vicksburg, followed by the Richmond—the Brooklyn being detained, but soon followed. We anchored near sunset, alongside the U. S. steam transport Tennessee, which had got aground. During the night the Brooklyn arrived, in company with several river steamers with troops. On the following morning two steamers fastened to the Tennessee, to tow her off, while we passed on, and arrived without accident at Baton Rouge on the 10th, where we found everything going off quietly. We lay here nearly ten days, during which time the mortar schooners of Capt. Porter’s fleet had passed by us, and having left one, we on the 19th took it in tow and started for Vicksburg. We proceeded with moderate speed and success until the 21st, in the evening, when we unexpectedly ran hard aground. Our attendant steamers immediately came up to our assistance, and after laboring the entire night, succeeded in getting afloat the following morning at eleven o’clock. Continuing on we passed some high bluffs, on which we looked for rebel batteries and accordingly kept prepared for them, but we were not molested. We observe that the river is rapidly falling, having thus far receded some six feet.