Alexandria. I report, in this connection, that I know the fact that Colonel Taylor received that letter of instruction upon the arrival of the messenger at Alexandria, on the 5th instant, by the regular train form this place on the morning of that day. Mr. F. G. Skinner, now here, and who was on the 5th instant in Alexandria, is my authority for the above statement; and Mr. Skinner tells me that he saw that letter of instruction in the hands of Colonel Taylor, and discussed with him the purport of it prior to the movement of the troops out of Alexandria on the afternoon or evening of that day (yesterday). I this day sent by telegraph to the commanding general-in-chief a full abstract of the only letter or communication I have received from Colonel Taylor alluding to or explaining the movement of the troops out of Alexandria. Nor have I been able, form any other source, except that furnished me by the arrival of Mr. Skinner, direct from Alexandria, by the train of this morning, to learn the cause of that movement; and, so far as I am informed up to this moment, there was no proper or justifiable cause whatsoever for any such movement. After waiting for further intelligence and receiving none, and duly considering and weighing all the circumstances and bearing of that movement with the information before me, I have ordered the return of the troops, as communicated by telegram, a duplicate of which has just been transmitted to the general-in-chief.

Very respectfully, your most obedient,

PHILIP ST. GEO. COCKE,

Brigadier-General, Commanding Potomac Department.

Colonel R. S. GARNETT,

Adjutant-General, Richmond, Va.

[Inclosure.]

CULPEPER COURT-HOUSE, VA., May 5, 1861.

Colonel TAYLOR, Commanding at Alexandria, Va.:

SIR: You will not move the troops out of Alexandria unless pressed by overwhelming and irresistible numbers; and even then you should retire to Manassas Junction, to hold that point, assist in obstructing and breaking up the road between that point and Alexandria, harassing the enemy should he attempt to use the road, and not retire farther in the interior unless overpowered and forced, as a last extremity, to so retire. You will use your cavalry and infantry in this connection, and, under these orders, which I have full authority from headquarters at Richmond for giving to you, keep up your communications with the various parts in your rear, so as to call every resource to your aid and support in making a gallant and fighting retreat, should you be forced to it, and can stand at all without danger of uselessly sacrificing your command.

Very respectfully, your most obedient,

PHILIP ST. GEO. COCKE,

Brigadier-General, Commanding Potomac Department.

HEADQUARTERS POTOMAC DEPARTMENT,
Culpeper Court-House, Va., May 7, 1861.

SIR: Shall I arrest Colonel Taylor for disobedience of order and unsoldier-like conduct, in having evacuated Alexandria, under the circumstances,