The following is transcribed from the New York Times, dated June 14, 1861:

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CAMP HAMILTON, Near Hampton, Va., Tuesday, June 11, 1861. You have already received by telegraph accounts of the action at Bethel. The full particulars of the engagement will probably give you an idea of it very different from that which you have formed. On Sunday afternoon the orders were promulgated for an attack upon Little Bethel and Big Bethel; the latter a sort of half-way house on the road to Yorktown, a couple of miles beyond the former. The following were the orders: HEAD-QUARTERS CAMP HAMILTON, June 9, 1861. GENERAL ORDERS. No. 12 -- A plan of attack to night is here with inclosed and forwarded to Col. DURYEE, commanding Fifth Regiment New York State Troops, who will act accordingly, Col. TOWNSEND commanding Third Regiment New-York State Troops, will march his command in support of Col. DURYEE. Col. CARR commanding Second Regiment New-York Volunteers, will detach the artillery company of his regiment, with their field pieces, caissons, and a suitable supply of ammunition and take their position at the burnt bridge, near Hampton. Cols. ALLEN, CARR and MCCHESNEY, will hold their entire command in readiness, fully prepared to march at a moment's notice. All the troops will be supplied with one day's rations and each men with twenty rounds of bail cartridges. That no mistake may be made, all the troops, as they charges the enemy, will shout "Boston". Cols. ALLEN, CARR, TOWNSEND DURYEE and MCCHESNEY will take notice and accordingly. By command of Brig.-Gen. E.W. PEIRCE, R.A. PEIRCE, Brigadier-Major. Appended were notes, of which the following are the salient points: A regiment or battalion to march from Newport News. A regiment or battalion to march from Camp Hamilton -- DURYEE's. Each to be supported by sufficient reserves under arms in camp, and with advance guard out on the line of march. DURYEE to push out two pickets at 10 P.M.; one also 2 1/2 miles beyond Hampton, on the County road, but not so far as to alarm the enemy. This is important. Second picket, half as far as the first. Both pickets to keep as much out of sight as possible. No one whomsoever to be allowed to pass through their lines. Persons to be allowed to pass in ward toward Hampton, unless it appear they intent to go around about and dodge through the front. At 12 M. (midnight) Col. DURYEE will march his regiment, with twenty rounds of cartridges, on the County road toward Little Beshel. Scows will be provided to ferry them across Hampton Creek March to be rapid, but not hurried. A howitzer, with canister and schrapnel to go, and a wagon with planks and materials to repair the New Market Bridge. DURYEE to have the two hundred rifles. He will pick the men to whom they are entrusted. Rockets to be thrown up from Newport News. Notify Com. PRENDERGAST of this, to prevent general alarm. Newport News movement to be made somewhat later, as the distance is less. If we find the enemy and surprise them, we will fire a volley if desirable, not reload, and go ahead with the bayonet. As the attack is to be made by night, or gray of morning, and is two detachments, our people should have some token -- say a white rag, or nearest approach to white attainable, on left arm. Perhaps the detachments who are engaged in the expedition should be smaller than a regiment. In accordance with this, the whole of Col. DURYEE's Zouaves, except the picket and police guards, and those otherwise detailed for special duty, formed in perfect silence at 11 1/2 P.M. -- 740 strong -- on the color line, and immediately began their march. The men were all in fine spirits at the prospect of a fight. Hampton Creek was crossed in boats, and all night they continued to advance rapidly. Three companies had been thrown out in advance as skirmishers -- Capt. KILPATRICK's, Capt. BARTLETT's and Capt. SWARTWOUT's. Just at dawn one of the enemy's outposts was surprised, and one of their officers captured. The particulars of this affair and of the skirmishes of the van are set forth fully in Capt. KILPATRICK's official report, which I send you. Soon after it occurred, cannonading and the report of musketry was heard far behind us, and Col. DURYEE, supposing that the enemy had attacked the regiments which were advancing to support us, immediately turned, and as quickly as possible -- a portion of the time at a double quick step -- led his regiment back for five miles, and met the detachments from Newport News which had been sent to take part in the expedition, consisting of detachments of Col. PHELPS' (Vermont) Regiment, of the Fifth Massachusetts Regiment, and of Col. BENDIX's New York Seventh. The latter, with its artillery unlimbered, was stationed across the road, while beyond them were the other troops, drawn up in line of battle. Here we heard a melancholy story. Col. TOWNSEND's Regiment, coming from Camp Hamilton, meeting the detachment of the command of Col. BENDIX, was mistaken by the latter for the enemy to the early gray of the morning. The error was mutual. The detachment of Col. BENDIX opened a fire with artillery, and Col. TOWNSEND's men returned it. Ten of the latter were wounded -- one, perhaps, mortally. I have not heard that any of those commanded by Col. BENDIX were injured. Gen. PIERCE, who was with Col. TOWNSEND's Regiment, again ordered the Zouaves in advance, and the whole column moved rapidly forward, the men singing the "Star-Spangled Banner" and "Dixie's Land," as they went. It was 10 A.M., and the soldiers, wearied with their long and rapid march and want of sleep, were marching listlessly at the route step, when the scouts brought word that the enemy, three thousand string, were entrenched behind sand batteries, right in front, and that without waiting for an attack they were about to sally forth. It put a new spirit into the men, as the word passed down the line. They were no longer tired and sleepy. Each freshened up to his place in the ranks, and closed up in column. Each Regiment deployed into the adjoining fields, right and left, and drew up in order of battle. And here let me try to give you an idea of the place of combat. Over a small stream, twelve miles from Hampton, a bridge called County Bridge, crosses on the road to Yorktown. On the opposite bank at the bridge, and on the right of it, the enemy was posted behind sand-batteries. In front of their batteries was a broad, open field, and this side of that, on our right, was a wood, and in front and to the left, a corn field. Between the wood and the corn field ran a road connected with that by which we had advanced. Over the fence into the cornfield, Col. DURYEE's Regiment advanced, and then down the road right in the teeth of the enemies' batteries. Two twelve-pound howitzers and one six-pounder which our troops carried with them, were posted in the open held on the left of the wood. As the Zouaves advanced, both batteries opened. Right onward, at a double quick step, the regiment ran, exposed to a murderous fire. Col. DURYEE himself led the van, and after proceeding a quarter of the distance to the enemy's batteries, he commanded the men to takes the woods. There they remained for two hours and twenty minutes, under an incessant fire, which raked the position, and finally, after a gallant charge by Capt. KILPATRICK, which drove the Secessionists from one of their batteries, after our artillerists had exhausted all their ammunition and their commandant. Lieut. GREBLE of the regular army, and many others had been killed. Gen. PIERCE ordered a retreat. Col. BENDIX, with there companies of riflemen, did good service on the right of our position, and Col. TOWNSEND's Regiment, on the left, performed its part well. A barn near the enemy's line was seized, and from it many of the enemy were picked off. The action commenced at 20 minutes before 10 A.M., and ended at 20 minutes past 12 P.M. The following is. CAPT. KILPATRICK'S OFFICIAL REPORT: HEAD-QUARTERS, CAMP HAMILTON, June 11, 1861. SIR: In accordance with your orders, I have the honor to submit the following report of my command, acting as he Advance Guard, on the evening of the 9th, and a brief account of my command during the engagement on the following day, at the New County Bridge. I left camp with my command at 10 P.M., consisting of fifty men of Company H, one lieutenant, (CAMBRELLING,) four servants and four corporals; Company I, Capt. BARTLETT, the lieutenant, (YORK) four sergeants and two corporals, crossed the river at Hampton 10 1/2 P.M.; reached Newmarket Bridge at 1 A.M., throw cut scouts in all directions and waited for the main body, which arrived at 3 A.M. According to your orders, I advanced on the road to New County Bridge, the point where the enemy was reported to have made a stand. A little before daylight, when within a mile and a quarter of the Bridge, we discovered the outlying picket guard of the enemy, and were challenged, "Who comes there?" I replied, "Who stands there?" A horseman attempted to leave. Corporal ELLERSON, of Company H, sprang in advance, directing him to halt. I supposing the enemy to be in force, gave the command to fire and charge. In a moment the affair was over, twenty of thirty shots had been given and exchanged; the officer of the guard was captured and disarmed. At this time, hearing firing in the rear, and supposing that our rear guard was attacked, I returned to follow the main body under Col. DURYEE, who was advancing by forced march in direction of the firing, only to discover that by mistake our own forces coming in different directions, and supposing each to be the enemy, had fired several shots before the mistake was discovered I again advanced, and at 8 A.M. met with and drove in the picket guards of the enemy. I then detached a portion of my command, made an armed reconnoissance, and found the enemy with about from 3,000 to 5 000 men posted in a strong position on the opposite side of the bridge --three earthworks and a masked battery on the right and left; in advance of the stream thirty pieces of artillery and a large force of cavalry, all of which information I reported to you at once. I was ordered to advance and engage the enemy in throwing out skirmishers on the right and left of the road leading to the bridge. We rapidly advanced, supported by the Advance Guard of Col. DURYEE and three pieces of artillery under Lieut. GREBLE of the First Regiment United States Artillery. The enemy soon opened fire on us from the rifled cannon in front. We answered his discharges by a cheer, and continued to advance, clearing all before us, till we reached a point just on the edge of the woods, where the fire was so hot and heavy that we were compelled to halt, and there we remained as directed by Lieut.-Col. WARREN, till that gallant officer had made dispositions to turn their flanks. The enemy's fire at this time began to tell upon us with great effect. My men were falling one after another, as was the case of the rest of the command. After remaining in this position about two hours, and our object having been accomplished, numbers of our men being killed and wounded, having received a grape shot through my thigh, which tore off a portion of the rectangle on Col. DURYEE's left shoulder, passed through my leg and killed a soldier in the rear, I withdrew my men to the skirts of the wood. We managed to reach Lieut. GREBLE's battery and bring to his aid several of my men. The charge was then sounded, Lieut. GREBLE opened fire with grape and canister, within two hundred yards of the enemy's lines. Capts. WINSLOW, BARTLETT and myself charged with our commands in front, Capt. DENIKS and Lieut. DURYEE (son of Col. DURYEE,) 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 everything promised a speedy victory, when we were ordered to fall back. Where this order came from I do not know. We maintained our position till Col. TOWNSEND began to retire with his whole command. Being left thus alone and no prospects of receiving aid, we ordered the men to fall back, which they did, and in good order, forming their line of battle about one hundred and fifty yards in the rear. A few minutes afterwards orders came from Gen. PIERCE to cease firing and retire. It gives me great pleasure to mention the gallant conduct of Capt. BARTLETT, who came up with the reserve, reinforcing my line, and who was ever at the point of danger, encouraging his men. Lieut. YORK, in command of my left, and Lieut. CAMPBRELLING, in command of my light, displayed the greatest bravery. Lieut. YORK's sword was broken by a grape-shot, and he was slightly wounded in the leg. I shall ever be grateful to Capt. WINSLOW, who rescued me after our forces had left. He came to my aid, assisted by Sergeants ONDERDONK and AGNES, at the last moment, but in time to rescue me from the enemy. I would also favorably mention private WOOD, who brought me valuable information, and who fired the first shot; private JOHN DUNN, whose arm was shattered by a cannon ball, and who bore himself with the greatest bravery, and who said to Surgeon GILBERT, white amputating his arm, that he could not have lost it in a nobler cause. The whole command, men and officers, did themselves the greatest credit, and I am satisfied can conquer anything except impossibilities. Respectfully submitted, JUDSON KILPATRICK, Captain Company H. To Colonel A. DURYEE. During the fight, a Minie musket ball, evidently aimed at Col. DURYEE, who was standing with a group of officers near the outskirts of the woods, wounded two men near him. The following is Adjutant HAMBLIN's report of the killed and wounded: Fifth Regiment New-York State Volunteers. Aggregate of officers and men, June 10, 1850. Killed. GEORGE H. TIEBOUT, Company A, shot through the heart. JAMES GRIGG, Company H, killed by round shot. DAVID TIEFORTH, Company I, killed by grape shot. PATRICK WHITE, Company I, killed by a cannon ball. Wounded. JAS. L. TAYLOR, Company B, dangerously wounded in groin by a musket ball. Jos. KNOWLES, Company E, right hand shot off. JOHN DUNN, Company H, right arm shot off. HENEY E. COHEN, Company H, Corporal, shoulder dislocated. Capt. KILPATRICK, Company H, wounded in thigh by grape shot. EDWARD G. BELL, Ordnance-Sergeant, wounded in knee by spent ball. T.W. CARTWRIGHT, Company G, flesh wound in the thigh. DANIEL BRINCKERHOOF, Company C, Corporal, slightly wounded by a splinter. JOHN BROECHER, Company D, slightly wounded by a splinter. EDWARD MOORE, Company D, slightly wounded by a spent musket ball. JAMES A. COCHRANE, Company H, slightly wounded in the leg. J.H. CONWAY, Company K, slightly wounded by a musket ball. ADOLPH VINCENT, Company A, shot in the breast; dangerous. Missing. Sergt. BENJ. F. HOPPER, Company C, returned in reports as badly wounded. ALLEN DODD, Company I, Third Sergeant, as absent. The wounded are receiving excellent attention from our surgeons, Drs. GILBERT and B. ELLIS MARTIN. Lieut. THEODORE S. DUMONT was slightly wounded in the leg by a bayonet in the hands of one of the men, against which he accidentally fell while dodging a cannon ball. There were two killed, of Col. ALLEN's Regiment, and five wounded. Three of Col. BENDIX's command were killed and several wounded. Lieut. GREBLE, in command of our Artillery, was killed. The retreat was conducted in perfect order. Some of the enemy's cavalry hang on our, rear, but they were repulsed with loss. They fired on a wagon containing some of our wounded, over which there, was a flag of truce. Rev Dr. WINSLOW, our Chaplain, narrowly escaped being captured while conducting some of the wounded back to camp. He escaped through the woods. The expedition was undertaken originally with the object of cutting off a body of the enemy supposed to be near Newport News, and by a night march surprising the enemy's batteries. The engagement between bodies of our own men, in which artillery was used, by alarming the enemy and delaying our march, frustrated the surprise.

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