At 1 A. M. the 3 companies of the New York Fifth, under Capt. Kilpatrick, reached New Market Bridge, and there waited for the main body of the Fifth, which came up at 8 A. M., when the whole regiment started forward for Little Bethel, where they arrived about daylight, and encountered a picket guard of the enemy, which was taken. Shortly after Duryea's regiment passed onward toward Little Bethel, the force from Newport News came up the road from that place, and took the road from Hampton to Bethel, not far behind the Fifth; but they left at the junction of the roads, under Col. Bendix, a rear guard of one hundred and seventy men and one field-piece, with the order to hold this position at all hazards. This order anticipated the possibility that a rebel force might get in the rear of the Federal troops and cut off the retreat. Almost immediately after, the Third N. Y. Regiment came up the Hampton road. It was still dark, and their colors could not be seen. Their approach also was over a ridge, and as General Pierce and staff, and Colonel Townsend and staff, in a body, rode in advance of their troops, and without any advance guard thrown out, as customary, to reconnoitre, they appeared from Col. Bendix's position to be a troop of cavalry. It was known that the Federal force had no cavalry, and the fire of this rear guard was poured into the advancing body, at the distance of a quarter of a mile. But the road in which the Third was marching was a little below the level of the land along the edge, and was bordered on either side by fences which served as a partial cover, and hence the fire was comparatively harmless. Ten men were wounded by it, and one killed. The Third fell back and formed upon a hill near the road, and Gen. Pierce sent a hurried message to Fortress Monroe for support, in accordance with which the N. Y. First and Second, Cols. Allen and Carr, were sent forward. Col. Duryea, admonished by the fire in his rear that something was wrong, also brought his regiment back. Daylight soon divulged the true state of the case, and the force was organized, and Brig.-Gen. Pierce of Mass. assumed the command. Gen. Pierce determined to push on in advance, and the force moved in the following order:--Col. Duryea with the N. Y. Fifth; Lieut.-Col. Washburne, with the companies from Newport News, and Greble's battery; Col. Townsend, with the N. Y. Third; Col. Allen, with the N. Y. First; and Col. Carr, with the N. Y. Second. When the fire of Col. Bendix's command was delivered, that force was stationed very near to the outlying camp of the enemy, who at once took the  alarm, and got away. Thus the rebels at Great Bethel were informed of the advance of a superior force, and sent back to their Headquarters at Yorktown for re-inforcements. When the column reached Little Bethel it was fired upon from a house which was consequently burned, and communicated its flames to several others. The Federal forces had finally reached a place in the outskirts of Great Bethel, where the road along which they moved is crossed by a marshy stream called Back River. Until recently this stream was spanned by a bridge known as the County Bridge; this had been destroyed by the rebels, and almost before its destruction was noticed, a heavy fire was opened upon the Federal troops from two masked batteries mounting rifled cannon upon the farther bank of the stream. Fortunately this first fire was not very accurate, and the missiles carried nearly a mile beyond the position the troops occupied. Then came a discharge of musketry. Thus surprised, the Federal troops were thrown into some disorder; but were soon rallied, and formed with the artillery in the centre, (upon the road,) and the infantry upon the right, and left partially covered in woods. In this position the enemy's fire was returned at a distance of one hundred yards. Under cover of this fire an attempt was made to carry the enemy's works by a charge, and Capts. Winslow, Bartlett, and Killpatrick of the Fifth, charged with their commands in front; Captain Denike, and Lieut. Duryea, (son of Col. Duryea,) and about two hundred of the Troy Rifles upon the right, Col. Townsend with his men to the left. The enemy were forced out of the first battery, all the forces were rapidly advancing, and every thing promised a speedy victory, when 250 of the Vermont men, with Lieut.-Col. Washburne, on the extreme left were mistaken for the enemy by Col. Townsend, who thereupon ordered his men to fall back. The Zouaves in front thus left unsupported also fell back, and the advantage so bravely gained was thus forfeited; upon consultation it was deemed impossible to flank the rebel position, and as after half an hour's experiment the fire of the light howitzers and musketry was found utterly ineffective against the enemy, who was well supplied with rifled cannon, the order to retreat was given, and the force was brought off in good order. Casualties in the Federal army were (as far as known)-killed, 13; wounded, 80. Several were missing. Of the wounded, 10, and of the dead, 1, were the loss by the error on the road when Col. Bendix fired into the N. Y. Third. Among the killed were Lieut. Greble, of the regular service, in command of the artillery, and Major Theodore Winthrop, aid to Gen. Butler. Of the Confederate loss, little is known. It is stated by the Charleston Miercury at 17 killed. The enemy is thought to have had at least 10 guns in battery, and is known to have had 2,200 men. The retreat of the Federal forces was necessarily very slow and tedious, many almost falling back and with difficulty made to keep their places. All expected that the rebels had flanked around into Hampton, and would fight them at the ferry. The rear of the entire force was covered by the howitzers, which charged upon the pursuing cavalry until they fell back toward the batteries. The news of the retreat arrived at Hampton long before the troops, and the ferry transports were all moored along the shore by the order of Gen. Butler, who was on the Monroe-ward side of the stream. When at last the poor soldiers came in and saw their way safe, a shout of joy sprang from the ranks and many of them sang most heartily. The wounded and dead, with a few exceptions, had been gathered up, and were carried by the weary retreating force and in the baggage wagons.--(Doc. 244.)
This evening the propeller Resolute, Capt. Budd, arrived at the Navy Yard, at Washington, together with the propeller Young America seized by the Cumberland at Old Point, and now in the service of the Government. Last Saturday night Capt. Budd, with a boat's crew of five men, went into Briton's Bay, and seizing the schooner Somerset at Leonardtown, towed her out into the Potomac, where they fired her, the schooner burning to the water's edge. On Monday morning master's-mate Fuller, with a boat's crew of four, went on board the schooner William Sampson, lying at the shore, about five miles above Acquia Creek, and burnt her also, completely destroying her. The owner and his plantation hands stood on shore at the time, but thought it prudent to say nothing. Neither of the vessels were loaded, and were in a very bad condition through want of repairs, and as it was well-known that they had been carrying provisions, &c., over to the Virginians, their fate was very soon decided.--National Intelligencer, June 13. 
Major-General Banks was detailed to the command of the Department of Annapolis, and established his Headquarters at Baltimore, Md.--N. Y. Herald, June 10.
Three battalions of the District of Columbia Volunteers passed through Georgetown, D. O., and at about the same time the Second Connecticut, First New Hampshire, and New York Ninth Regiments broke camp and proceeded by the Rock Creek Road. The two forces were to unite at Tenlytown, three miles above Georgetown. Their destination is supposed to be Edward's Ferry, on the Potomac. The latter point is about thirty miles from Georgetown, and an equal distance from Harper's Ferry and Washington. In the morning Capt. Owens proceeded with the District troops, and about forty of the Second Texas cavalry went in the same direction. In addition to camp equipage and intrenching tools, they were provisioned for twelve days. Large trains of wagons crossed into Virginia at the Government Ferry at Georgetown throughout the day, indicating, it is supposed, that one or more regiments on that side have received orders to march. One of the Ohio regiments, it is expected, will soon take up its line of march to follow Col. Stone's column.--Hon. John Cochran of New York was authorized by the Secretary of War to have mustered for immediate service, under a United States Commission, for three years, a regiment of infantry, to be commanded by himself as Colonel.--Washington Star, June 10.
The Fourth Connecticut Regiment over 1,000 strong, completely armed and equipped, left Hartford, Conn., for Jersey City on board steamers City of Hartford and Granite State. Four military companies turned out to escort them, and at least 10,000 persons witnessed their departure, which took place amid the greatest enthusiasm and firing of cannon.--(Doc. 245.)