Fairfax Court-House, Tuesday, September 2, 1862.A battle last night, and a victory. Gen. Reno, holding with his division a position three miles this side of Centreville, and a mile to the north of the road, was attacked by part of the forces under Jackson, Ewell, and Hill, about five o'clock in the afternoon. The enemy, attempting a flank movement to put themselves, probably at Fairfax, between General Pope and Washington again, had marched with the utmost celerity across the fields north and east of the Centreville position, which had been occupied in force by Gen. Pope after the reverse of Saturday. Their artillery, therefore, which was obliged to go about by the road, had not come up; but Reno found himself at the beginning of the battle in front of a heavy force of infantry. The engagement, which began with skirmishing at five o'clock, continued for an hour between the force of Reno and the enemy before our reenforcements came. During that time, the ammunition of our troops had been exhausted, and they were obliged to give ground. Gen. Reno occupied the right, General Stevens commanding the Second division on the left. The latter moved against the enemy with determination, heading his troops in person. What might have been the result it is impossible to say, but Gen. Stevens, while leading the attack, was shot dead by a bullet through the head. His troops became disheartened by the loss of their General, and retreated in disorder. The movement of General Stevens had been intended to cover the right of Reno's other division, which was in danger of being flanked. When Stevens had been killed, and his troops driven back, there was imminent danger that the right wing would be turned, and the whole force destroyed. Unable to send forward reserves to reoccupy Stevens's position, Reno himself was falling back, and the whole line seemed likely to be lost. The enemy, fortunately, were without artillery, and unable, without a general advance, to inflict severe loss upon our troops. At this juncture Gen. Kearny, who had been ordered at two o'clock to move to Reno's support, arrived on the field with his division, and at once advanced to the relief of our exhausted troops. The retirement of Stevens's division had left an opening through which the rebels were advancing, unknown to our forces. General Kearny ordered General Birney to move his brigade still further to the left than the position which Stevens had held, and learning that the rebels were approaching on the centre, rode forward himself to make a reconnoissance of the ground and the enemy. Most unfortunately, the latter were already so far forward that Gen. Kearny suddenly found himself within their lines, and was captured before the action had fairly recommenced. Gen. Birney took command at once of the division, and sent forward his own brigade to the left, to anticipate and repel the threatened flank movement of the rebels. Randolph's battery accompanied the brigade, and opened on the enemy with great vigor and effect. It soon appeared that nearly the whole force of the rebels had been massed on the left, and the engagement was recommenced by General Birney in that position. The original line of General Reno on the right had extended to and partially held a piece of woods, against which his right wing rested. On the centre and left was a corn-field sloping down into a ravine, from which rose another hill beyond. On the crest of the latter the enemy were drawn up — at first nearly opposite our centre, afterward moving around to our left. Stevens was killed in attempting to advance through the corn-field, and his force driven back. When Birney took command, all the troops of Reno had been withdrawn from the fight, and the line was formed anew on the left. The same formation of the ground extended to the left. Birney drew up his troops at an angle with the line first held by Stevens, so as to front the rebels on the left, and sending Robinson's brigade still further in the same direction, posted Berry's brigade as a reserve, and Graham's battery near it, and himself advanced to the attack with his whole brigade. A heavy fire was kept up for half an hour. From the time when Kearny came on the field a fierce thunder-storm had been raging, and the rain fell incessantly and heavily. It was difficult to keep ammunition dry, but with the advantage of artillery, Birney continued his fire for a considerable time, and inflicted severe losses on the enemy. Finding their line at length somewhat shaken and their fire proving weaker, Gen. Birney ordered a bayonet-charge. The Mozart regiment, (Fortieth New-York,) Col. Egan; the Scott Life-Guard, (Thirty-eighth New-York,) Colonel Ward; and the First New-York, also included in Colonel Egan's command, were intrusted with this movement. The three regiments advanced with gallantry and determination, and moving down the ravine and up the opposite slope in the face of a heavy fire, almost instantly decided the contest. The rebels broke and ran, abandoned the field, and made no effort to renew the contest. The field was held by Gen. Birney all night, our dead  were buried, and the wounded removed. Gen. Berry, who had been held in reserve, occupied the field, and retained it till relieved this morning. The conduct of all the regiments engaged under General Birney is highly praised. The One Hundred and First New-York, under Colonel Gesner, was in the hardest of the fight, and lost heavily in killed and wounded. Col. Gesner, Col. Ward, of the Thirty-eighth New-York, and Col. Egan, who led the bayonet-charge, displayed great coolness and gallantry. General Birney, who is one of the few generals that have been often in battle and never defeated, won this fight with only seven regiments, after the whole division of Gen. Reno had been compelled to retire. General Reno fought cautiously and well, but could do nothing without ammunition after the advance of Stevens had been repulsed and his left had become exposed. He had no means of strengthening it till the arrival of Kearny. Most of the battle was fought in darkness and storm. The thunder was so heavy that at Centreville, three miles distant, the noise of the cannonade was wholly inaudible, and no battle was suspected to be going on. Some prisoners were taken from the enemy, but, owing to the darkness and the storm, pursuit for any distance was impossible. Among the prisoners was the Adjutant-General of General Jones, who was in command of one of the rebel divisions, and also his Chief of Ordnance. The rebel Gen. Jones was formerly Adjutant of General Heintzelman's old regiment. Major Tilden, of the Thirty-eighth New-York, was mortally wounded in the fight, and died soon after. The whole number of killed and wounded in Gen. Birney's brigade was probably not over two hundred. Of General Reno's troops the loss was not much greater. I have seen lists, but not a moment to copy them for this letter, which goes by an unexpected opportunity. Except this battle, there has been no engagement since Saturday. The enemy showed no disposition to attack Centreville in front, but endeavored to win the position by a movement on Fairfax Court-House, which was discovered and foiled by last night's contest. Centreville is abandoned. A battle is possible here, but not expected by the Generals in whose judgment most confidence is placed. Our victory is dearly bought by the death of Gen. Stevens and the capture of General Kearny. The military career of both is well known to the country. Gen. Kearny brought away from the Peninsula a very high reputation. His services are too recent to have been forgotten. Gen. Stevens's connection with the Port Royal expedition gave him less opportunity than he desired and wished for military services; but he was concerned in all of the operations in which the land forces had a share, and always showed himself the gallant soldier and able General. He has an older reputation in Mexico and Oregon, but I refer especially to his Port Royal career, because I knew him only in South-Carolina, and I wish to add to the public expression of regret at his loss, my own tribute to his gallantry and ability. I have much to say of the events of last week, the condition of this command, of generals and their conduct, and of the immediate prospects before us; but I must defer every thing till another letter, which may be sent I know not when or how. An opening cannonade closes my letter. P. S.--Gen. Kearney was shot, not captured. His body has just been brought in.
--New-York Tribune:--See Doc. 104 ante.