JACKSON, MISS., July 19, 1863.

Admiral DAVID D. PORTER, Comdg. Mississippi Fleet:

DEAR ADMIRAL: Your kind and considerate letter reached me at Clinton as we were trudging along in heat and dust after Johnston, that had been troubling us about Vicksburg during our eventful siege. We must admit these rebels out-travel us, and Johnston took refuge in the fortified town of Jackson. My heads of columns reached the place on the 9th, but the forts and lines were too respectable to venture the assault, and I began a miniature Vicksburg. The enemy was about 30,000 strong, with plenty of artillery, which he used pretty freely; some rifled 32-pounders, of too heavy metal for our heavy field-guns, but we got close up and made the invariable sap, succeeding in disabling one of the 32-pounders, knocking off a trunnion, and breaking up the carriage. We expended on the town as much of our ammunition as was prudent to expend, and a train with a re-supply reached me the very night he concluded, driving the enemy behind his earthworks, but we made no assault; indeed, I never meditated one, but I was gradually gaining round by the flank, when he departed in the night. Having numerous bridges across Pearl River, now very low, and a railroad in full operation to the rear, he succeeded in carrying off most of his material and men. Had the Pears River, now very low, and a railroad in full operation to the rear, he succeeded in carrying off most of his material and men. Had the Pearl River been a Mississippi, with a patrol of gunboats, I might have accomplished your wish in bagging the whole. As it is, we did considerable execution, have 500 prisoners, are still pursuing and breaking railroads, so that the good folks of Jackson will not soon again hear the favorite locomotive whistle. The enemy burned nearly all the handsome dwellings round about the town because they gave us shelter or to light up the ground to prevent night attacks. He also set fire to a chief block of stores in which were commissary supplies, and our men, in spite of guards, have widened the circle of fire, so that Jackson, once the pride and boats of Mississippi, is now a ruined town. State-house, Governor's mansion, and some fine dwellings, well within the lines of intrenchments, remain untouched. I have been and am yet employed in breaking up the railroad 40 miles north and 60 south; also 10 miles east. My 10-miles break west, of last May, is still untouched, so that Jackson ceases to be a place for the enemy to collect stores and men from which to threaten our great river.

The weather is awful hot, dust stifling, and were I to pursue eastward I would ruin my command, and, on a review, I think I have fulfilled all that could have been reasonably expected, and by driving Johnston out of the valley of the Mississippi we make that complete which otherwise would not have been.

I hope soon to meet you, and that we may both live long to navigate that noble channel, whose safety had absorbed our waking and sleeping thoughts so long. I trust we may sit in the shade of the awning as the steamers ply their course, not fearing the howling shell at each bend of the river or the more fatal bullet of the guerrilla at each thicket.

Last night, at the Governor's mansion, in Jackson, we had a beautiful supper and union of the generals of this army, and I assure you the "Army and Navy forever" was sung with a full and hearty chorus. To me it will ever be a source of pride that real harmony has always characterized our intercourse, and let what may arise, I will ever call upon Admiral Porter with the same confidence as I have in the past. Present my kindest remembrances to Captains Breese, Walke, McLeod, Bache, and all the gallant gentlemen who have been called about you,