ENGINEER'S OFFICE, DEPT. OF VA. AND N. CAROLINA, November 21, 1864.

Bvt. Major General J. G. BARNARD,

Chief Engineer, Armies in the Field, Va.:

GENERAL: I have the honor to report that your communication reached me late last night and beg leave to submit the following, viz:

In the event of the withdrawal of the Army of he James from its present position for operations elsewhere there will arise two cases. In both cases it will be necessary to hold the bridge-head at Deep Bottom, to insure us the navigation of the James River as far as Aiken's Landing, and the position at Cox's Hill (Fort Brady) for the advantages that will accrue to us from the probable success of Dutch Gap Canal. For these works it will require, I think, not less than 800 men for Deep Bottom and 300 men for Fort Brady in addition to their artillery, which garrisons might be reduced one-third in case they were garrisoned by excellent men with Spencer rifles.

1st. Complete evacuation. In this event it may safely be concluded that no future movement can again be made north of the James, allowing the enemy to possess the least common sense. For having shown them their mistakes previous to the present operations they will begin at once to shut up the avenues of approach on all their main roads. Occupying Camp Holly and Signal Hill with one or two strong redoubts, they will seal up the Darbytown, Long Bridge, and New Market roads, and their holding Fort Harrison will close the Varina road to us ever after. All other roads require such long flank marches to gain as to make the possibility of any future advance on this side entirely out of the question. Under these circumstances I do not think it advisable to waste labor on the destruction of any part of our present line.

2nd. Partial evacuation. This will require a force of not less than 2,500 men under excellent officers. This is a very small estimate indeed, and may be too small, but acting always on the defensive-300 men at Signal Hill, 500 at Camp Holly, 200 in the redoubt at Four-Mile Creek, 300 at Fort Brady, and the remainder distributed in the redoubts and batteries of the new line in front of Deep Bottom, could resist any determined attack, if not greater than the usual disproportionate force attacking earth-works. This arrangement it will be seen requires 1,400 men more than the first, and it is for higher authority to decide whether the advantages it gives are worth the men. The enemy may simply content themselves with occupying their old lines, throwing out a picket to watch or movements, or may select a new line below Four-Mile Church if unable to get us out of our redoubts. In regard to the present disposition of our present line in this case, I agree with you that that portion from Fort Brady to Fort Harrison need not be disturbed. The enemy will not occupy it, since their old line will be better suited for their purposes. The destruction of the gorge of the latter is advisable and could be imperfectly done night by 500 men. You will have noticed that its command is very slight, not more than five feet above the crest of the hill, but the parapet makes up in thickness. The traverse that runs through it could be used by them as a front, however, and we could not destroy it without awakening their suspicions. From Fort Harrison to the left redoubt on the Tenth Corps front (5) no labor need be expended. There are three good strong redoubts (5, 4 and 3) on this front whose gorges should be destroyed quietly by the regiments nearest them the night before leaving, and completed the day following. If this is done effectually it will necessitate them either to advance a front and two faces to each work or throw