From Alexandria, some twelve miles to the Westward, runs a fine turnpike road to Fairfax Court-House; thence, continuing Westward, but gradually and slightly dipping award the South, it passes through Germantown, Centreville, and Groveton, to Warrenton. This "Warrenton Pike"--as it is termed--also plays a somewhat conspicuous part, before, during, and after the Battle of Bull Run. For most of its length, from Fairfax Court-House to Warrenton, the Warrenton Pike pursues a course almost parallel with the Orange and Alexandria railroad aforesaid, while the stream of Bull Run, pursuing a South-easterly course, has a general direction almost parallel with that of the Manassas Gap railroad. We shall find that it is the diamond-shaped parallelogram, formed by the obtuse angle junction of the two railroads on the South, and the similarly obtuse-angled crossing of the stream of Bull Run by the Warrenton Pike on the North, that is destined to become the historic battle-field of the first "Bull Run," or "Manassas;" and it is in the Northern obtuse-angle of this parallelogram that the main fighting is done, upon a spot not much more than one mile square, three sides of the same being bounded respectively by the Bull Run stream, the Warrenton Pike, which crosses it on a stone bridge, and the Sudley Springs road, which crosses the Pike, at right-angles to it, near a stone house. On the 3rd of June, 1861, General McDowell, in command of the Department of North-Eastern Virginia, with head-quarters at Arlington, near Washington, receives from Colonel Townsend, Assistant Adjutant-General with Lieutenant-General Scott--who is in Chief command of all the Union Forces, with Headquarters at Washington--a brief but pregnant communication, the body of which runs thus: "General Scott desires you to submit an estimate of the number and composition of a column to be pushed toward Manassas Junction, and perhaps the Gap, say in four or five days, to favor Patterson's attack on Harper's Ferry. The rumor is that Arlington Heights will be attacked to-night."