On the 31st, General Wilson's division of cavalry destroyed the railroad bridges over the South Anna River, after defeating the enemy's cavalry. General Sheridan, on the same day, reached Cold Harbor, and held it until relieved by the 6th corps and General Smith's command, which had just arrived, via White House, from General Butler's army.

On the 1st day of June an attack was made at five P.M. by the 6th corps and the troops under General Smith, the other corps being held in readiness to advance on the receipt of orders. This resulted in our carrying and holding the enemy's first line of works in front of the right of the 6th corps, and in front of General Smith. During the attack the enemy made repeated assaults on each of the corps not engaged in the main attack, but was repulsed with heavy loss in every instance. That night he made several assaults to regain what he had lost in the day, but failed. The 2d was spent in getting troops into position for an attack on the 3d. On the 3d of June we again assaulted the enemy's works, in the hope of driving him from his position. In this attempt our loss was heavy, while that of the enemy, I have reason to believe, was comparatively light. It was the only general attack made from the Rapidan to the James which did not inflict upon the enemy losses to compensate for our own losses. I would not be understood as saying that all previous attacks resulted in victories to our arms, or accomplished as much as I had hoped from them; but they inflicted upon the enemy severe losses, which tended, in the end, to the complete overthrow of the rebellion.

From the proximity of the enemy to his defences around Richmond, it was impossible, by any flank movement, to interpose between him and the city. I was still in a condition to either move by his left flank, and invest Richmond from the north side, or continue my move by his right flank to the south side of the James. While the former might have been better as a covering for Washington, yet a full survey of all the ground satisfied me that it would be impracticable to hold a line north and east of Richmond that would protect the Fredericksburg Railroad, a long, vulnerable line, which would exhaust much of our strength to guard, and that would have to be protected to supply the army, and would leave open to the enemy all his lines of communication on the south side of the James. My idea, from the start, had been to beat Lee's army north of Richmond, if possible. Then, after destroying his lines of communication north of the James River, to transfer the army to the south side, and besiege Lee in Richmond, or follow him south if he should retreat. After the battle of the Wilderness, it was evident that the enemy deemed it of the first importance to run no risks with the army he then had. He acted purely on the defensive, behind breastworks, or feebly on the offensive immediately in front of them, and where, in case of repulse, he could easily retire behind them. Without a greater sacrifice of life than I was willing to make, all could not be accomplished that I had designed north of Richmond. I therefore determined to continue to hold substantially the ground we then occupied, taking advantage of any favorable circumstances that might present themselves, until the cavalry could be sent to Charlottesville and Gordonsville to effectually break up the railroad connection between Richmond and the Shenandoah Valley and Lynchburg; and when the cavalry got well off, to move the army to the south side of the James River, by the enemy's right flank, where I felt I could cut off all his sources of supply, except by the canal.

On the 7th, two divisions of cavalry, under General Sheridan, got off on the expedition against the Virginia Central Railroad, with instructions to Hunter, whom I hoped he would meet near Charlottesville, to join his forces to Sheridan's, and after the work laid out for them was thoroughly done, to join the Army of the Potomac by the route laid down in Sheridan's instructions.

On the 10th of June, General Butler sent a force of infantry, under General Gillmore, and of cavalry under General Kautz, to capture Petersburg, if possible, and destroy the railroad and common bridges across the Appomattox. The cavalry carried the works on the south side, and penetrated well in towards the town, but were forced to retire. General Gillmore, finding the works which he approached very strong, and deeming an assault impracticable, returned to Bermuda Hundred without attempting one.

Attaching great importance to the possession of Petersburg, I sent back to Bermuda Hundred and City Point, General Smith's command by water, via the White House, to reach there in advance of the Army of the Potomac. This was for the express purpose of securing Petersburg before the enemy, becoming aware of our intention, could reinforce the place.

The movement from Cold Harbor commenced after dark on the evening of the 12th. One division of cavalry, under General Wilson, and the 5th corps, crossed the Chickahominy at Long Bridge, and moved out to White Oak Swamp, to cover the crossings of the other corps. The advance corps reached James River, at Wilcox's Landing and Charles City Court House, on the night of the 13th.

During three long years the Armies of the Potomac and Northern Virginia had been confronting each other. In that time they had fought more desperate battles than it probably ever before fell to the lot of two armies to fight, without materially changing the vantage ground of either. The Southern press and people, with more shrewdness than was displayed in the North, finding that they had failed to capture Washington and march on to New York, as they had boasted they would do, assumed that they only defended their Capital and Southern territory. Hence, Antietam, Gettysburg, and all the other battles that had been fought, were by them set down as failures on our part, and victories for them. Their army believed this. It produced a morale which could only be overcome by desperate and continuous hard fighting. The battles of the Wilderness, Spottsylvania, North Anna and Cold Harbor, bloody and terrible as they were on our side, were even more damaging to the enemy, and so crippled him as to make him wary ever after of taking the offensive. His losses in men were probably not so great, owing to the fact that we were, save in the Wilderness, almost invariably the attacking party; and when he did attack, it was in the open field. The details of these battles, which for endurance and bravery on the part of the soldiery, have rarely been surpassed, are given in the report of Major-General Meade, and the subordinate reports accompanying it.

During the campaign of forty-three days, from the Rapidan to the James River, the army had to be supplied from an ever-shifting base, by wagons, over narrow roads, through a densely wooded country, with a lack of wharves at each new base from which to conveniently discharge vessels. Too much credit cannot, therefore, be awarded to the quartermaster and commissary departments for the zeal and efficiency displayed by them. Under the general supervision of the chief quartermaster, Brigadier-General R. Ingalls, the trains were made to occupy all the available roads between the army and our water-base, and but little difficulty was experienced in protecting them.

The movement in the Kanawha and Shenandoah valleys, under General Sigel, commenced on the 1st of May. General Crook, who had the immediate command of the Kanawha expedition, divided his forces into two columns, giving one, composed of cavalry, to General Averell. They crossed the mountains by separate routes. Averell struck the Tennessee and Virginia Railroad, near Wytheville, on the 10th, and proceeding to New River and Christiansburg, destroyed the road, several important bridges and depots, including New River Bridge, forming a junction with Crook at Union on the 15th. General Sigel moved up the Shenandoah Valley, met the enemy at New Market on the 15th, and, after a severe engagement, was defeated with heavy loss, and retired behind Cedar Creek. Not regarding the operations of General Sigel as satisfactory, I asked his removal from command, and Major-General Hunter appointed to supersede him. His instructions were embraced in the following dispatches to Major-General H. W. Halleck, chief of staff of the army: