From the editorial correspondence of the Lynchburg (Va.) Republican, of Sept. 11th, we extract the following statement with regard to the late engagement at Carnifex Ferry :

On Tuesday morning Col. McCauslin’s regiment, which had been down at Summerville as our advance, was driven in, and the enemy encamped 14 miles distant from us. We expected him to drive in our pickets on Tuesday night and attack us on Wednesday morning, but contrary to these expectation he forced his march and drove in our pickets at 2 o’cl’k Tuesday. Our line of battle was at once formed behind our breastworks, and scarcely had all our forces been placed in position, before the enemy was seen swarming in the woods from one end of our lines to the other. He approached with great deliberation and firmness, and his central column emerged from the woods and above the hills, 200 yards in front, just 16 minutes after 3 o’clock. He approached us from this point in double-quick time, evidently intending to force our works at the point of the bayonet. At the first crack of our rifles, the gallant Colonel, who led in front of his men on a splendid black charger, fell dead to the earth, while the head of his column recoiled in utter confusion. The Colonel’s horse, as if unconscious of the fall of his rider, dashed up to our embankments around them into our camp, and, from the inscriptions on the mountings of his pistols, proved to be Col. Wm. H. Lytell’s, of Cincinnati. I saw the daring officer fall from his horse, and he was certainly one of the bravest of the brave, for he sought “the bubble reputation” at the very cannon’s mouth.

A general rumor was brought down on the Central train Thursday, of renewed heavy skirmishing on our lines. From what we can learn, however, there bas been no movement of consequence, outside of the usual brushes between the pickets.

Reconnoisances of the banks of the Potomac show that the enemy have perfected a line of works from the Chain Bridge to four miles south of Alexandria, having accomplished, for a distance of about fifteen miles, a line of well-constructed earthworks.