For some time past we have understood that General Lee's headquarters are at Orange Court House, while his infantry occupies the south banks and bluffs of the Rapidan. Stuart occupies Culpepper Court House, and pickets and patrols the territory between the Rapidan and the Rappahannock, a region shaped much like an old-fashioned harrow.

September 13.—An advance of the Union army was ordered yesterday by its Chief, in which the cavalry was to take a prominent part. Orders were issued accordingly last evening, and every needed preparation made for our work. At an early hour this morning the entire cavalry corps was on the march. In order that the enemy might not be prematurely warned of our design, the several commands were ordered to make as little noise as possible. Consequently the bugle-calls were dispensed with, and commanders made use of their voices, and in some instances the orders were conveyed from rank to rank in a whisper. The three great divisions of the corps were to cross the river as follows: Gregg's, at Sulphur Springs; Buford's, at Rappahannock Bridge; and Kilpatrick's, at Kelly's Ford.

BRANDY STATION NO. 3.

At six o'clock the Harris Light plunged into the river at Kelly's Ford, leading the advance. A strong detachment of Stuart's cavalry, consisting of pickets and reserves, opposed our crossing with dogged pertinacity, but finally, yielding to our superior numbers and to the deadly accuracy of our carbines, gave way. He then advanced in the direction of Brandy Station. The farther we advanced the stronger grew the ever-accumulating force of the enemy, who disputed every inch of ground with great stubbornness. On arriving near the Station we found the enemy in strong force, with artillery posted on the surrounding hills. We saw clearly that a third cavalry fight was destined to be fought on this historic field, and we began to make preparations for the onset. It was my fortune to lead the advance company in the first charge. Three men and four horses were killed and wounded in this company by the first discharge of the enemy's artillery, whose fire was terribly accurate.

But we had not been fighting long before the other divisions joined us. At their approach great enthusiasm among our boys prevailed. Before our combined force the enemy was swept from those plains like chaff before the whirlwind. They fled in the direction of Culpepper, a naturally strong and now fortified position, where we knew we must soon encounter the Rebel chivalry en masse upon their chosen field.

FIGHT AT CULPEPPER COURT HOUSE.

From Brandy Station General Pleasonton directed Kilpatrick to make a détour viâ Stevensburg, in order to operate as a flanking column upon the enemy at the proper time. With the First and Second divisions Pleasonton pushed straight on to Culpepper, driving the enemy before him without much resistance until within about a mile of the town. Here our advance was effectually checked. A fearful duel now took place with varying fortunes. For some time the enemy baffled all our efforts to dislodge him from his strong position, and our men began to look wishfully for the flankers, when lo! Kilpatrick's flags were seen advancing from the direction of Stevensburg, and his artillery was soon thundering in the enemy's flank and rear. Under this unexpected and well-directed fire, that portion of the enemy which had kept our main column at bay fell back in confusion into the town; and, before they had time to re-form their broken lines, the Harris Light, Fifth New York, First Vermont, and First Michigan, led by General Custer, dashed upon the "Johnnies" in the streets, throwing the boast of the chivalry into a perfect rout. Many prisoners were captured, more or less material of war, and three Blakely guns. The Rebels retreated hastily in the direction of Pony Mountain and Rapidan Bridge, whither they were closely pursued by our victorious squadrons. The day following this brilliant advance Pleasonton occupied all the fords of the Rapidan, extending his pickets on our right as far forward as the Robertson and Hazel Rivers.

The way having been thus prepared by his heroic avant-couriers, General Meade advanced the Army of the Potomac across the Rappahannock, and took his temporary residence in Culpepper.

September 15.—Kilpatrick's division advanced from Culpepper to Raccoon Ford on the Rapidan. Colonel Davies' brigade supported a battery of artillery a short distance from the ford from one till four P. M. The shelling from the enemy's batteries was terrific. Their position was admirable on the high bluff south of the ford, and the range was just right for execution. Their artillery was of a heavy calibre, and supported by infantry. They were finely screened by earthworks, while our forces were almost entirely exposed, and protected only here and there by a little knoll. In the unequal duel which took place, two of our guns were dismounted and disabled, while several artillerymen and horses were killed. It was not at all practicable for us to attempt a crossing.

Before night we retired from the ford, and the divisions took up their headquarters, Gregg's, at Rappahannock Bridge; Buford's, at Stevensburg; and Kilpatrick's, on the extreme right, at James City.