The following letter of instruction was addressed to Major-General B. F. Butler:

"FORT MONROE, VIRGINIA, April 2, 1864.

"GENERAL:-In the spring campaign, which it is desirable shall commence at as early a day as practicable, it is proposed to have cooperative action of all the armies in the field, as far as this object can be accomplished.

"It will not be possible to unite our armies into two or three large ones to act as so many units, owing to the absolute necessity of holding on to the territory already taken from the enemy. But, generally speaking, concentration can be practically effected by armies moving to the interior of the enemy's country from the territory they have to guard. By such movement, they interpose themselves between the enemy and the country to be guarded, thereby reducing the number necessary to guard important points, or at least occupy the attention of a part of the enemy's force, if no greater object is gained. Lee's army and Richmond being the greater objects towards which our attention must be directed in the next campaign, it is desirable to unite all the force we can against them. The necessity of covering Washington with the Army of the Potomac, and of covering your department with your army, makes it impossible to unite these forces at the beginning of any move. I propose, therefore, what comes nearest this of anything that seems practicable: The Army of the Potomac will act from its present base, Lee's army being the objective point. You will collect all the forces from your command that can be spared from garrison duty—I should say not less than twenty thousand effective men—to operate on the south side of James River, Richmond being your objective point. To the force you already have will be added about ten thousand men from South Carolina, under Major-General Gillmore, who will command them in person. Major-General W. F. Smith is ordered to report to you, to command the troops sent into the field from your own department.

"General Gillmore will be ordered to report to you at Fortress Monroe, with all the troops on transports, by the 18th instant, or as soon thereafter as practicable. Should you not receive notice by that time to move, you will make such disposition of them and your other forces as you may deem best calculated to deceive the enemy as to the real move to be made.

"When you are notified to move, take City Point with as much force as possible. Fortify, or rather intrench, at once, and concentrate all your troops for the field there as rapidly as you can. From City Point directions cannot be given at this time for your further movements.

"The fact that has already been stated—that is, that Richmond is to be your objective point, and that there is to be co-operation between your force and the Army of the Potomac—must be your guide. This indicates the necessity of your holding close to the south bank of the James River as you advance. Then, should the enemy be forced into his intrenchments in Richmond, the Army of the Potomac would follow, and by means of transports the two armies would become a unit.

"All the minor details of your advance are left entirely to your direction. If, however, you think it practicable to use your cavalry south of you, so as to cut the railroad about Hicksford, about the time of the general advance, it would be of immense advantage.

"You will please forward for my information, at the earliest practicable day, all orders, details, and instructions you may give for the execution of this order.

"U. S. GRANT, Lieutenant-General.
"MAJOR-GENERAL B. F. BUTLER."

On the 16th these instructions were substantially reiterated. On the 19th, in order to secure full co-operation between his army and that of General Meade, he was informed that I expected him to move from Fort Monroe the same day that General Meade moved from Culpeper. The exact time I was to telegraph him as soon as it was fixed, and that it would not be earlier than the 27th of April; that it was my intention to fight Lee between Culpeper and Richmond, if he would stand. Should he, however, fall back into Richmond, I would follow up and make a junction with his (General Butler's) army on the James River; that, could I be certain he would be able to invest Richmond on the south side, so as to have his left resting on the James, above the city, I would form the junction there; that circumstances might make this course advisable anyhow; that he should use every exertion to secure footing as far up the south side of the river as he could, and as soon as possible after the receipt of orders to move; that if he could not carry the city, he should at least detain as large a force there as possible.

In co-operation with the main movements against Lee and Johnston, I was desirous of using all other troops necessarily kept in departments remote from the fields of immediate operations, and also those kept in the background for the protection of our extended lines between the loyal States and the armies operating against them.

A very considerable force, under command of Major-General Sigel, was so held for the protection of West Virginia, and the frontiers of Maryland and Pennsylvania. Whilst these troops could not be withdrawn to distant fields without exposing the North to invasion by comparatively small bodies of the enemy, they could act directly to their front, and give better protection than if lying idle in garrison. By such a movement they would either compel the enemy to detach largely for the protection of his supplies and lines of communication, or he would lose them. General Sigel was therefore directed to organize all his available force into two expeditions, to move from Beverly and Charleston, under command of Generals Ord and Crook, against the East Tennessee and Virginia Railroad. Subsequently, General Ord having been relieved at his own request, General Sigel was instructed at his own suggestion, to give up the expedition by Beverly, and to form two columns, one under General Crook, on the Kanawha, numbering about ten thousand men, and one on the Shenandoah, numbering about seven thousand men. The one on the Shenandoah to assemble between Cumberland and the Shenandoah, and the infantry and artillery advanced to Cedar Creek with such cavalry as could be made available at the moment, to threaten the enemy in the Shenandoah Valley, and advance as far as possible; while General Crook would take possession of Lewisburg with part of his force and move down the Tennessee Railroad, doing as much damage as he could, destroying the New River Bridge and the salt-works, at Saltville, Va.

Owing to the weather and bad condition of the roads, operations were delayed until the 1st of May, when, everything being in readiness and the roads favorable, orders were given for a general movement of all the armies not later than the 4th of May.

My first object being to break the military power of the rebellion, and capture the enemy's important strongholds, made me desirous that General Butler should succeed in his movement against Richmond, as that would tend more than anything else, unless it were the capture of Lee's army, to accomplish this desired result in the East. If he failed, it was my determination, by hard fighting, either to compel Lee to retreat, or to so cripple him that he could not detach a large force to go north, and still retain enough for the defence of Richmond. It was well understood, by both Generals Butler and Meade, before starting on the campaign, that it was my intention to put both their armies south of the James River, in case of failure to destroy Lee without it.

Before giving General Butler his instructions, I visited him at Fort Monroe, and in conversation pointed out the apparent importance of getting possession of Petersburg, and destroying railroad communication as far south as possible. Believing, however, in the practicability of capturing Richmond unless it was reinforced, I made that the objective point of his operations. As the Army of the Potomac was to move simultaneously with him, Lee could not detach from his army with safety, and the enemy did not have troops elsewhere to bring to the defence of the city in time to meet a rapid movement from the north of James River.

I may here state that, commanding all the armies as I did, I tried, as far as possible, to leave General Meade in independent command of the Army of the Potomac. My instructions for that army were all through him, and were general in their nature, leaving all the details and the execution to him. The campaigns that followed proved him to be the right man in the right place. His commanding always in the presence of an officer superior to him in rank, has drawn from him much of that public attention that his zeal and ability entitle him to, and which he would otherwise have received.

The movement of the Army of the Potomac commenced early on the morning of the 4th of May, under the immediate direction and orders of Major-General Meade, pursuant to instructions. Before night, the whole army was across the Rapidan (the fifth and sixth corps crossing at Germania Ford, and the second corps at Ely's Ford, the cavalry, under Major-General Sheridan, moving in advance,) with the greater part of its trains, numbering about four thousand wagons, meeting with but slight opposition. The average distance travelled by the troops that day was about twelve miles. This I regarded as a great success, and it removed from my mind the most serious apprehensions I had entertained, that of crossing the river in the face of an active, large, well-appointed, and ably commanded army, and how so large a train was to be carried through a hostile country, and protected. Early on the 5th, the advance corps (the fifth, Major-General G. K. Warren commanding) met and engaged the enemy outside his intrenchments near Mine Run. The battle raged furiously all day, the whole army being brought into the fight as fast as the corps could be got upon the field, which, considering the density of the forest and narrowness of the roads, was done with commendable promptness.