While the main Army of the Tennessee was operating against Vicksburg, the enemy's forces on the WEST side of the river made unsuccessful attacks on Milliken's Bend and Lake Providence, on the 6th and 10th of June. Our loss in the former was 101 killed, 285 wounded, and 266 MISSING; loss in the latter not reported. It is represented that the colored troops in these desperate engagements fought with great bravery, and that the rebels treated this class of prisoners of war, as well as their officers, with great barbarity. It has not been possible, however, to ascertain the correctness of these representations in regard to the treatment of these prisoners.

After the capture of Vicksburg, General Grant reported that his troops were so much fatigued and worn out with forced marches and the labors of the siege as to absolutely require several weeks of repose before undertaking another campaign. Nevertheless, as the exigencies of the service seemed to require it, he sent out those who were least fatigued on several important expeditions, while the others remained at Vicksburg to put that place in a better defensible condition for a small garrison.

As soon as Vicksburg capitulated, General Sherman was sent in pursuit of Johnston's forces. The latter retreated to Jackson, MISS., which place was taken by us on the 16th of July. Our loss was about 1,000 killed, wounded, and MISSING. General Sherman captured 764 prisoners, two rifled guns, a large amount of ammunition, and destroyed the railroad, rolling stock, &c. The enemy retreated toward the Alabama line, and General Sherman returned to Vicksburg to recuperate his forces.

A military and naval force was sent to Yazoo City on the 13th. It took 300 prisoners, captured one steamer, and burned five; took 6 cannon, 250 small-arms, and some 800 horses and mules. No loss on our side reported.

Small expeditions were also sent against Canton, Pontotoc, Grenada, and Natchez, MISS. At Grenada a large amount of rolling stock was destroyed, and near Natchez General Ransom captured 5,000 head of Texas cattle, a number of prisoners and teams, and a large amount of ammunition. The other expeditions were also successful, meeting with very little opposition.

As soon as his army was supplied and rested, General Grant sent a force, under General Steele, to Helena, to co-operate with General Schofield's troops against Little Rock, and another, under Generals Ord and Herron, to New Orleans to re-enforce General Banks for such ulterior operations as he might deem proper to undertake.

Small expeditions were also sent to the Red River and to Harrisonburg and Monroe, on the Washita, to break up and destroy guerrilla bands.

After General Grant left Vicksburg to assume the general command east of the Mississippi, General McPherson moved with a part of his force to Canton, MISS., scattering the enemy's cavalry and destroying his materials and roads in the center of that State.

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All of which is respectfully submitted.

H. W. HALLECK,

General-in-Chief.

Honorable E. M. STANTON,

Secretary of War.