headquarters Army of the Potomac, South bank of the North Anna river, Wednesday, May 25--12 M.After three weeks of marching and fighting, here, then, is the Army of the Potomac, sixty miles from its starting point north of the Rapidan, safely planted south of the North Anna river, and within twenty-five miles of the objective point which, for three years, has been the goal of all the bloody struggles of this army. The hasty despatches which alone it has been possible to send amid the turmoil of action have acquainted you with the more salient facts at least in our later movements, and I shall confine these notes to the record of the operations of the past two or three days. They comprise the strategic operations employed in turning the fortified lines of Spottsylvania and the tactical operations of yesterday and to-day, in crossing the North Anna river, and the actions succeeding the passage. Taken together, they form, perhaps, the most substantial successes of the campaign, and have been gained with a gratifyingly small sacrifice of life. The experience of the two weeks we spent before the lines of Spottsylvania brought the conviction that that position could not be carried save by an expenditure of blood out of all proportion to the results of any possible victory that could be achieved there. To have been able to bring on a decisive engagement there would undoubtedly have been greatly to our advantage, for we had there a front of operations in easy distance of our proximate base, Fredericksburg, while the enemy was at a long remove from his. In these relations, a battle that would have effectually broken Lee's army would have placed us in the most advantageous position for destroying it in the retreat that would have followed. I think it was with some regret that General Grant was eventually compelled to abandon the hope of delivering such a battle. Day by day the Commanding General continued to throw out toward the left, with the hope of overlapping and breaking in the rebel right wing; and from occupying, as we did at first, a line two or three miles north, and extending five or six miles west of Spottsylvania Court-house, we finally came to hold a line running almost due east from that point and about four miles in extent, our left resting at Massaponax Church. But just in proportion as we stretched to the left, Lee extended his right to conform to our line, and intrenched himself, till finally he came to have a front practically impregnable. Nothing, in fact, can be imagined more formidable than the improvised works which each army has learnt to construct, to cover itself withal. A layer of stout logs, breast high, forms the framework on which a thick parapet of earth is thrown up; in front of this line the timber for several hundred yards is felled, making an elaborately interlaced abattis. Imagine, one, two or three such lines along the enemy's front; plant behind each a line of battle, rake the obstructed approaches with a lavish supply of artillery, and place in front of all several lines of rifle-pits, and you will form a conception, though still an inadequate one, of the nature of the task imposed upon this army when it is proposed to “move on the enemy's works.” Yet in several instances, as you know, and as all the world will some day learn with wonder, the illustrious valor of the Army of the Potomac has plucked victory from these jaws of hell, and bayoneted an unflinching foe in the very enceinte of his citadel. Advices from day to day have informed you of the different attempts that were made to carry the enemy's lines, successively on the right, the centre and the left; of the partial successes achieved, and of our not few repulses. Of our successes, the most complete was undoubtedly that won by Hancock on the morning of the twelfth instant, when his corps struck the famous salient on the right of the rebel line and captured nearly the entire division holding it. Doubtless, could we have known in advance precisely what the upshot of that attack would be, our assailing force, instead of being prepared merely with the view of carrying the position, would have been formed so as to push the success to its consequences, and the whole rebel army might then and there have been doubled up, routed and destroyed. No such golden opportunity again presented itself, and after seeking it in blood-bought reconnoissances on our right and centre, and after a sacrifice of some fifteen thousand killed and maimed men had attested the thoroughness of the effort to secure a decisive victory, the head of the army resolved to force the enemy's abandonment of his lines, with the determination of seeking elsewhere the arena for a new trial of battle. With this view, it was needful, first of all, that the army should accumulate such supplies as would allow it to cut loose from its old base, and enable it to advance far enough to open a new and more accessible one. This done, it was very certain that by simply massing on the left of our front we would so threaten Lee's communications as to compel him to evacuate his fortified line; in other words, we would effect a turning movement on the rebel right flank. True to the expectation, when the rebels on Friday discovered the corps of Hancock, which, the day before, had been feeling their extreme left, shifted over to their extreme right, Lee began to look out for his lines of retreat. On Friday night, May twenty, Hancock took up his march, advanced due east to Massaponax Church, there diverged on one of the main roads leading due southward from Fredericksburg, continued on during the night and the following day, and on Saturday evening, May twenty-first, occupied Bowling Green, with the head of his column at Milford, distant from the point of starting seventeen miles. He met no enemy. On the very same night in which Hancock started, Lee began to withdraw. In the dead of night (one o'clock A. M. of Friday-Saturday),  the rebel reveille was heard to beat, and the head of Longstreet's column, which was assigned the advance in the retreat, filed southward. Here, then, begins a grand race of the two armies, similar to that they ran from the Wilderness to Spottsylvania. A glance at the map will show us which has the better chance. It will be observed, if the examination be made with an adequate topographical map in hand, that the rebel front at Spottsylvania covers the direct and best route leading southward, namely, the telegraph road, with the roads converging on and radiating from this main line. On the other hand, it was a necessity of the proposed operation that we should beat well to the eastward. It is a recognized maxim that the party executing a flanking movement exposes his own flank. Such a manoeuvre in face of a vigilant and vigorous opponent is always a dangerous one. It had, therefore, to be done both cautiously and by a route somewhat circuitous. Lee, as we know by experience, is both vigilant and vigorous. The former quality was proved by the promptitude with which he met the advance of our flanking column by a corresponding movement to the rear; the latter was made manifest in another way the next day. Hancock (Second corps), as we have seen, had withdrawn during the night of Friday. Warren, (Fifth corps), set out early on Saturday morning, following for some distance over the same route as that pursued by Hancock. About the same time Ewell's corps of the rebel army appears to have followed Longstreet. In the meantime our old position near Spottsylvania Court-house, was still held by such portions of our front as the corps of Burnside (Ninth) and Wright (Sixth) covered. At four P. M. of Saturday, Burnside, who held position on the left of the Sixth, withdrew, and the remaining force of the rebels (Hill's corps) fancying that the Sixth also was retiring, left the works, came up directly in Wright's front and attacked. They succeeded in breaking his skirmish line in one place; but Wright opened a heavy artillery fire upon them, which checked their advance. Hill committed an error in making the attack in front, for had he crossed the river a little above, he would have struck the right flank of the Sixth corps, uncovered by the withdrawal of Warren, and would have had an enfilading fire on Wright, which it would have been difficult to withstand. In addition to this the assault was not made with much persistence, and was probably designed simply to develop our actual force left. During the night Wright withdrew; Hill did the same, and the works of Spottsylvania ceased to be the objects of either attack or defence. They remain now as parts of the series of parallels that, from the Rapidan up to our present front, stand as monuments of the most desperate campaign in history. The two armies once fairly on the march, their operations belong to the domain of strategy, which deals with the movements of armies out of sight of each other. The first obvious goal is the North Anna, north of which it was not deemed at all probable Lee would attempt to make a stand. From the first, however, it was a matter of certainty that the enemy would reach it in advance of us, for having possession of the telegraph road, he moved on an interior line. On Saturday night Hancock bivouacked at Milford. The Fifth followed the Second over the same road until striking Guinea station, when it diverged to the right (that is westward), crossed the Mattapony at Guinea bridge, and at nine P. M. bivouacked near the Old Academy, having made a march of fifteen miles. The Ninth and Sixth followed over the same general lines. The next day, Sunday, the twenty-second, the march was resumed — Warren crossing the Ta, and striking into the telegraph road, down which the rear of the columns of Longstreet and Ewell had a short time before disappeared. Here he had a skirmish with the enemy's rear guard of cavalry, consisting of Rosser's brigade, which was repulsed. Hancock advancing due westward from Milford, five miles, struck the telegraph road at Harris' store. Sunday's march brought our army forward an additional fourteen miles, and within a few miles of the North Anna. The region between Spottsylvania and the North Anna, through which the advance of Saturday and Sunday carried us, is both fair and fertile. The face of the country is beautifully undulating, nowhere bold,and the river bottoms have many large and fine plantations, all under cultivation. It was virgin ground over which we marched, showing none of those desolating traces of war that mark all Virginia north of the Rapidan. Here are fields sprouting wheat, and growing corn, and luxuriant clover; here are lowing herds, and the perfume of blossoms and the song of summer birds; here are homesteads of the Virginia planter, everything on a large and generous scale, and great ancestral English elms, dating back to the times before our fore-fathers learned to be rebels. Coming so lately from where the tread of armies for three years has made the country bare and barren as a threshing floor, the region through which we passed seemed a very Araby the Blest, and presented such a transition as is pictured by those who, having traversed the desert of Lahore, suddenly emerge upon the smiling vales of Cashmere. Resuming the advance on Monday morning, May twenty-third, a march of a few hours brought the heads of our columns so near to the North Anna, that operations passed from the domain of strategy into the tactical question of effecting the passage of the river, always a delicate and difficult one when vigorously resisted. And that it would be so resisted was natural to suppose, for the reason that if the enemy proposed making a stand on the South Anna he would wish to gain all the time possible, in order to establish himself well in his position, and also for the reason that the North Anna covers the Virginia Central railroad, which here runs  in the general direction of the stream, and but from one to three miles south of it. Even if Lee should feel that he would eventually be compelled to sacrifice this important line of communications, he would still, it was reasonably argued, attempt to hold it till all the rebel detachments that have been in the valley should be drawn in. In this anticipation we were not disappointed, and not only did he contest the passage but he made one of his fiercest assaults, with the view of crushing that portion of our army that had succeeded in crossing. The lines on which the army had been advancing brought our columns to the North Anna near the point at which the Fredericksburg and Richmond railroad crosses that stream. Hancock's column, which had the left, struck it less than one mile to the west of the railroad crossing. Warren's column, which had the right, struck it at Jericho Ford, about four miles higher up. By an opposite fortune Warren was able to effect the passage without any resistance, but was savagely assailed on the other side, while Hancock had to fight on the north side for a passage, but once over, has thus far found little to bar his progress. The head of the column of the Fifth corps, Griffin's division leading, reached the North Anna at one P. M., on Monday, and within ten minutes after the time of its arrival began to cross. The river at this point is fordable, but has a very rocky bed, with precipitous banks, and the men had to wade it waist deep. The rebels appear not to have expected that the passage would be made so high up the stream, and hence had no great force in the immediate vicinity. In fact they had no time to bring up much force, as the rear of Hill's corps was arriving almost at the same time with the head of Warren's column. Immediately on crossing, Griffin's division was formed in line of battle, the Second brigade (Sweitzer's), having the advance, while Ayres took position on his left, and Bartlett was held in reserve in the centre of the line. Cutler's division formed on the right of Griffin, and Crawford's (Pennsylvania Reserves), on his left. Moving rapidly up across an open space of six or eight hundred yards, Griffin took position in the woods, where a heavy skirmish line was soon met. At first the only rebel troops in the neighborhood consisted of McGowan's brigade, of Wilcox's division (Hill's corps), under command of Colonel Brown, of the Fourteenth South Carolina. But he was presently reinforced by the other three brigades of Wilcox's division — namely, those of Scales, Gordon and Thomas; while Heath's division joined on to the right of Wilcox, and prisoners say that Breckinridge's division afterward came up. The skirmish line which was all our advance at first met, had been easily driven back, and the command had taken up its position in the woods, and had just received orders to intrench, the first preparations for which it was just taking, when Griffin's division, at five fifteen P. M., was furiously assailed by the rebel force above enumerated, which suddenly developed in two lines of battle, with a heavy skirmish line in front. Volley after volley, fierce and sharp, was poured in, and the enemy opened from three batteries a very heavy cannonade. Griffin's division, however, without works, successfully resisted the attack, and repulsed it with great slaughter. Our men, in fact, served them with the same treatment they had themselves received in the numerous attacks they had been compelled to make, and illustrated afresh the enormous advantage the defensive has in such a country as this: that is, they lay low, covered themselves well, allowed the rebels to approach and when the whites of their eyes were visible, raked their line with a withering volley. Finding that he was gaining nothing and losing very heavily, it appears that the rebel commander, while continuing to hold three of his brigades on Griffin's front, detached Colonel Brown's South Carolina brigade to effect a detour and make an assault in flank. The mode in which he made this I have from Colonel Brown himself, who, not half an hour afterward, was a prisoner in our hands. Marching by column up the railroad for some distance, he wheeled by right into line of battle, and fell upon Cutler, who, as we have seen, was formed on the right of Griffin. Cutler's division had not yet gotten into position when Brown attacked with much vigor: its left gave way, and the whole command was considerably broken and thrown into much confusion. This, of course, uncovered the right of Griffin's line, held, as we have seen, by Ayer's brigade, and exposed him to imminent danger of having his flank turned. To avoid this the right was refused somewhat, and General Griffin threw forward three regiments of Bartlett's brigade, which arrived just in time to save the exposed flank from being turned, and reestablished the line. In the execution of this manoeuvre, occurred one of those odd rencounters which occasionally happen in the complicated actions of battle. One of Bartlett's regiments, the Eighty-third Pennsylvania, Lieutenant-Colonel McCoy commanding, in marching up by the flank (that is, in column, not in line of battle), ran plump against Brown's line, which was moving to follow up its success against our right. It was one of those critical situations which a moment will decide, the decision, in fact, depending on who should gain the advantage of the first volley. Rapid as a flash McCoy flung his forward companies into line, and got the first fire. One of McCoy's men seized the rebel commander by the collar and dragged him in; the Eighty-third poured in a volley on the enemy's flank and rear, and the whole rebel brigade made off in disorder. The repulse of the rebels was most complete, and during the engagement and the following morning, not less than one thousand prisoners were taken. In addition to this the rebel loss in killed and wounded was very heavy, though its precise extent could not be ascertained, as during the night the enemy made a forcible attack  upon our pickets, and under cover of this succeeded in carrying off their dead and wounded. Our own loss was inconsiderable: Griffin's division, which bore the brunt of the attack, may have lost two hundred; Cutler about one hundred and thirty, while the loss of Crawford's division, which held the left, and whose skirmish line alone was engaged, was but trifling. All things considered this may justly be regarded as one of the most beautiful detached engagements of the campaign; and taking into account the very important results hanging upon it, it fully merits the praise accorded to it by the Commanding General in a despatch sent to General Warren immediately after the action, in which General Meade “congratulated him and his gallant corps upon the handsome manner in which the enemy's attack was repulsed.” Although the Commanding General extends praise to the whole corps, the other divisions will willingly acknowledge that it belongs more particularly to the First division (Griffin's), which received and repulsed the main attack of the enemy. Especial credit is due to the Second brigade of this division, commanded by Colonel Sweitzer, though equal eulogy is claimed by the brigade of Bartlett, which so promptly checkmated the flanking manoeuvre of Brown. Passing now from the position of Warren, on the right, to that of Hancock, on the left, we find his corps engaged at the same time with the Fifth, though unlike Warren, who passed the river unopposed, he had to carry his crossing against severe opposition. As I have already mentioned, Hancock's point of passage was the Chesterfied or county bridge, half a mile above the railroad bridge. Here the rebels had a strong position and a tete-de-pont, which had to be taken before the passage could be effected. Six or eight hundred yards north of the Anna is Long creek, which runs parallel with the river, and empties into it east of the railroad bridge. The two streams, therefore, form a species of island, and here the rebels had a prepared position to oppose any crossing. Near the bridge-head is an extended redan, with a wet ditch in front, the gorge swept by rifle-pits in the rear. On the opposite, or southern bank of the river, is a similar work and other rifle-pits, while the southern bank commands the northern, and was swept by rebel artillery. These works were built a year ago, immediately after the battle of Chancellorsville. The island is a perfectly flat and bare plain, and across this it was necessary to advance in order to carry the bridge. The position was held by McLaws' division of Longstreet's corps. To General Birney's division of Hancock's corps was assigned the gloriously perilous task of carrying it. On the left was the brigade of Colonel Egan; on his right Pierce's brigade, and General Mott's brigade on the right of Pierce. The Fourth brigade (the Excelsior, commanded by Colonel Blaisdell, of the Eleventh Massachusetts), came up partly in rear, its left to the right of the redan. To cover the assault, three sections of artillery were put in position, and replied to the artillery fire of the enemy. On the left of Birney's division was Barlow's division, the left of which connected with the right of Gibbon's division, while Tyler's heavy artillery division was held in reserve. An hour before sundown of Monday, the assault was begun and most brilliantly executed by Birney's command, which swept across the open space at double-quick, under a storm of artillery and volleys of musketry. Two regiments of the Excelsior brigade (the Seventy-first and Seventy-second New York), first reached the redan, the garrison of which ran precipitately as the menacing line of fixed bayonets came sweeping along. Making foot-hold in the parapet with their muskets, the brave fellows clambered up and simultaneously planted their colors on the rebel stronghold. Thirty rebels, unable to get away in time, were captured in the ditch. The total loss in this brilliant exploit — the very rapidity and daring of which astonished and paralyzed the rebels — did not exceed a hundred men, and secured us the possession of the bridge, across which a portion of Hancock's corps immediately crossed, and held the bridge-head during the night. The work of Monday, therefore, had secured us the passage of the North Anna at two different points, and night found the whole of the Fifth corps crossed at Jericho ford, and a portion of the Second corps across at Chester-field bridge. Yesterday, Tuesday, twenty-fourth, was mainly employed in passing over the rest of the army and pushing out our lines and securing our position. That held by General Warren was happily one of great strength — being a point at which the Anna makes a bend in the form of a horse-shoe, thus affording a secure point d'appui for both flanks. Early yesterday the whole of the Sixth corps (Wright's) filed over at this point, took position in rear of the Fifth, and a portion of it in the afternoon relieved part of Warren's front. Hancock, on his front, was not able to make such rapid progress. Noon found only such portions of the command as had forced the passage the previous night across the river. The rebels still held the works, rifle-pits and commanding heights on the southern bank. In the afternoon, however, Crawford's division of Warren's corps extended to the left, to make a diversion in his favor, engaged the enemy, and enabled the whole of Birney's division to pass over. The remainder of the Second corps speedily followed. Meanwhile Burnside's corps still remained on the north bank of the river; but the operations of yesterday afternoon having swept the rebels from our whole front, the Ninth corps was able this morning to make the passage at Oxford, midway between the points of crossing of Hancock and Warren. During Monday night Hancock's left extended to the railroad bridge, we holding the northern end  and the enemy the southern. The rebels, however, had prepared it for burning, and during the night it was set fire to and destroyed. This is no loss, as there appears to be no present intention to use the Fredericksburg and Richmond railroad--Port Royal, on the Rappahannock, having been to-day opened as a new base. The water transportation of the army is now all there, and a long train, with our wounded was this morning sent across under escort to that point. This morning finds our advance pushed out three miles south of the North Anna, and across the Virginia Central railroad, which has been effectually destroyed. No engagement has, up to this hour, taken place. The main body of the rebels appear to have drawn back to the South Anna, which is a line they have long been preparing, and mean to defend to the last. Their advance line rests along Long creek, one mile north of the South Anna. General Grant's plans, with reference to this position, have not yet been developed, and though a study of the ground affords an anticipation of the nature of the operation that will next be made, I refrain, as yet, from recording even speculations. The heat, during the past four days of marching and fighting, has been excessive, and the work has been a most severe strain on the physical and moral powers of men and officers; but there is nothing which buoys an army up like success, and the determination of the Army of the Potomac abates not a jot or a tittle of the purpose with which it set out. I need not say that purpose is the capture of the rebel capital and the destruction of the rebel army.