After dropping back I found that the enemy had taken possession again of one of the lower hill batteries and was endeavoring to mount his guns, and had mounted a 12-pounder field piece to fire at General McArthur’s troops, which had landed a short time before at Warrenton. I sent the Mound City and Carondolet to drive him off, which they did in a few moments. I beg leave to enclose a letter from General McArthur, explaining why he did not (to use his own expression), take advantage of the results gained by the gunboats. I have since learned through General Grant that the army did assault at the right time vigorously. In the noise and smoke we could not see or hear it. The gunboats were, therefore, still fighting when the assault had proved unsuccessful. The army have terrible work before them, and are fighting as well as soldiers ever fought before. But the works are stronger than any of us dreamed of. General Grant and his soldiers are confident that the brave and energetic generals in the army will soon overcome all obstacles and carry the works. DAVID D. PORTER, Acting Rear-Admiral, Commanding Mississippi Squadron Having been repulsed with severe loss in several attempts to storm the rebel works, General Grant now determined to approach the fortifications by regular siege lines. It had been demonstrated that it was impossible to approach any point of attack, with a force equal in numbers to that with which the enemy would be prepared to resist him. General Pemberton deemed it prudent at that time, to forbid all unnecessary waste of ammunition, and thus General Grant was able to commence throwing up works and erecting forts within a short distance of the opposing line of breastworks. The firing upon the town was made only during the day, until the 26th of May, after which it was continued day and night. The mortars on the peninsula opposite Vicksburg opened fire on the 25th, and continued it until the surrender. It was estimated at Vicksburg that as many as six thousand mortar shells were thrown into the town every twenty-four hours, and on the line in the rear of the city, as many as four thousand in the same time. During about five days after the siege commenced, the troops in the city were allowed full rations. At the expiration of that time, they were gradually reduced to four ounces of flour, four ounces of bacon, one and a half ounces of rice, two ounces of peas, not eatable, and three ounces of sugar. The extent of the works, and the limited number of the Confederate troops, required every man to defend the lines, and no time was allowed to rest. Whole companies laid back of their breastworks for three weeks without leaving the line for a moment.