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Two Battles in Virginia.

On Sunday morning, about daylight, the union troops in Eastern Virginia, under Gen. McDowell, moved forward from Fairfax C. H. and Centreville and attacked the enemy's encampment at Bull's Run, a small stream between Centreville and Manassas Gap Junction, where the main body of the rebels were entrenched. At Bulls Run the rebels were repulsed with a severe loss on both sides. — Several cannon fell into the hands of our troops. The enemy fell back towards the main encampment. Our troops followed, and encamped on the road for rest a few hours during the night. The rebels were reinforced on Sunday by a strong force under Gen Johnston. It is said that during the action at Bull's Run our men could distinctly hear the reinforcements coming in from Manassas Gap Junction, and the cheers with which they were hailed.

About daylight Monday morning the fighting was renewed, and soon became general. The force engaged is judged to be some 60,000 to 70,000 rebels and from 40,000 to 50,000 federal troops. Our army was followed by a vast number of teamsters with wagons, baggage, stones, etc., by droves of cattle, and by vast numbers of civilians who had gone down from Washington and vicinity, apparently to see the great show. Fighting continued until about 1 o'clock in the afternoon, when our troops retreated with great loss. — The numerous body of teamsters and stragglers added confusion to the scene, and our whole army was on the retreat. Some accounts say it was a complete route, but this we do not credit. The retreat was somewhat disorderly, no doubt, but considerable hard fighting was done on the retreat. One account saps the Black Horse cavalry, a southern regiment, made an attack on the rear of our retreat, when the remnant of the Fire Zouaves turned and fired, killing all but six of them.

The telegraph accounts of the battle are confused and disjointed and it is impossible to give a clear and connected narrative from the imperfect material we have.

The following regiments are reported as actively engaged in the fight, viz: 1st, 2d and 3d Connecticut; 1st regulars, composed of 2d, 3d and 8th companies of marines; the 8th and 14th N. Y. militia; 1st and 2d Rhode Island; 71st New York; 2d New Hampshire; 5th Massachusetts; 1st Minnesota; 1st Michigan; 11th and 38th New York; 2d, 4th and 5th Maine; and the 2d Vermont, besides the several batteries.

The N. Y. 71st is said to have lost about half their men. One report said the Fire Zouaves (Ellsworth's) were all killed but 200. Another said 600 of them had returned. The N. Y. 69th (Col. Corcoran's splendid Irish regiment,) is said to have a frightful list of killed and wounded. And every regiment engaged, from present accounts, was horribly cut to pieces.

Among the officers killed and wounded the following are named.

Killed — Capt. McCook, of an Ohio company, brother of Col. McCook; Capt. Gordon, Co. H, 11th Mass.; Col. Slocum, 2d N. H., and the lieutenant colonel of the Fire Zouaves.

Wounded — Col. Tompkins, N. Y. 2d; Col. Farnham, Fire Zouaves; Col. Hunter, U. S. A.; Col. Corcoran, 69th N. Y.; Col. Clark, 11th Mass.; Capt. Ricketts, of the Artillery; Col. Walcox, 1st Michigan.

The number of dead and wounded will not be known for some days, but we do not believe it is anything like the terrible report first received.

A number of our best batteries are reported to have been taken. Among them are Carlisle's, Griffen's and the West Point batteries. Gov. Sprague had his horse shot under him, and it is reported that the Rhode Islanders lost nearly all their horses. Several of our best rifled cannon were also lost.

The news received by us on Tuesday morning, and immediately issued in an extra, puts a better face on the Manassas matter, though it is bad enough at best.