[Inclosure.]

WASHINGTON, D. C., January 7, 1863.

Major-General BURNSIDE, Commanding, &c., Falmouth:

GENERAL: Your communication of the 5th was delivered to me by your aide-de-camp at 12 m. to-day. In all my communications and interviews with you since you took command of the Army of the Potomac, I have advised a forward movement across the Rappahannock. At our interview at Warrenton, i urged that you should cross by the fords above Fredericksburg rather than to fall down to that place, and when I left you at Warrenton it was understood that at least a considerable part of your army would cross by the fords, and I so represented to the President. It was this modification of the plan proposed by you that I telegraphed you had received his approval. When the attempt at Fredericksburg was abandoned, i advised you to renew the attempt at some other point, either in whole or in part, to turn the enemy's works, or to threaten their wings or communications; in other words, to keep the enemy occupied until a favorable opportunity offered to strike a decisive blow. I particularly advised you to use your cavalry and light artillery upon his communications, and attempt to cut off his supplies, and engage him at an advantage. In all our interviews I have urged that our first object was not Richmond, but the defeat or scattering of Lee's army, which threatened Washington and the line of the Upper Potomac.

i now recur to these things simply to remind you of the general views which I have expressed, and which I still hold. The circumstances of the case, however, have somewhat changed since the early part of november. The chances of an extended line of operations are now, on account of the advanced season, much less than then. But the chances are still in our favor to meet and defeat the enemy on the rappahannock if we can effect a crossing in a position where we can meet the enemy on favorable or even equal terms. I therefore still advise a movement against him.

The character of that movement, however, must depend upon circumstance, which may change every day and almost every hour. if the enemy should concentrate his forces at the place you have selected for a crossing, make it a feint and try another place. Again, the circumstance, which may change every day and almost every hour. If the enemy should concentrate his forces at the place you have selected for a crossing, make it a feint and try another place. Again, the circumstances at the time may be such as to render an attempt to cross the entire army not advisable. In that case theory suggests that, while the enemy concentrates at that point, advantages can be gained by crossing smaller r forces at other points, to cut off his lines, destroy his communications, and capture his rear guards, outposts, &c.

The great object is to occupy the enemy, to prevent his making large detachments or distant raids, and to injure him all you can with the least injury to yourself. If this can be best accomplished by feints of a general crossing and detached road crossings, take that course; if by an actual general crossing, with feints on other points, adopt that course.

There seems to me to be many reasons why a crossing at some point be attempted. it will not do to keep your large army inactive. As you yourself admit, it devolves on you to decide upon the time, place, and character of the crossing which you may attempt. I can only advise that an attempt be made, and as early as possible.

Very respectfully, your obedient servant,

H. W. HALLECK,

General-in-Chief.