The Washington Star, from its correspondent at Fredericksburg, furnishes an account of the battle of Saturday, which is very interesting. We give it in full to show how the Yankees were led to believe that "to-morrow" (Sunday) would relieve their losses:

The occupation of Fredericksburg having been successfully accomplished, the next move was to drive the rebels from their strongholds in the rear of the city. The lines of the rebels, which extended in the form of a semi-circle from Port Royal to a point about six miles above Fredericksburg, were strongly fortified and protected by a range of high hills. Stonewall Jackson occupied the right wing, extending from Port Royal to Guinney's station, (a station on the Richmond and Fredericksburg Railroad,) Gen. Longstreet the centre, extending to the telegraph road, and Generals Lee and Stuart the left west of Massaponax creek, while General A P Hill's corps acted as a reserve. Lee's reason for occupying the left was because he could be on his guard against Sigel, who threatened to outflank him by way of Culpeper. The entire rebel force is estimated at 200,000 men, and occupied a front of not less than twenty miles. The troops were for the most part veterans who had fought through all the peninsular campaign, while the officers were the ablest that the South could produce. It was no mean enemy we had to contend with, I assure you.

The disposition of the Union forces occupied the whole of Friday night and Saturday morning, and, as General Burnside was anxious to commence the attack at an early hour as possible, there was not much chance for the troops to rest themselves. A few stragglers, it is true, managed to sneak away for the purpose of pillaging; but the great mass of the soldiers were constantly under arms. General Burnside was in the city all night, personally inspecting the troops and dissecting their movement. It was arranged that General Franklin's corps should cross the river two miles below the city, with the view of turning the enemy's position on Massaponax creek, while Hooker would engage the rebels nearer the centre, and Sumner would turn their right. By this arrangement it will be soon that Franklin was opposed to Stonewall Jackson, while Hooks and Sumner attacked the centre and the left of the rebels under Longstreet and Lee.

The eventful morning came, and with it a dense fog which obscured the movements of the enemy. The balloon was sent up just before daylight, but in consequence of the fog no observations could be had. However, the disposition of the Union forces had been made and Gen. Burnside determined to commence operations, fog or no fog.

Franklin moved his column, consisting of the First and Sixth corps, just before sunrise, his right resting on the outskirts of the city, his centre advanced a mile or so from the river, and his left resting on the Rappahannock about three miles below, Skirmishing commenced a few minutes after daylight on the extreme left. A rebel battery opened on our troops, and the fire became so annoying that the 9th regiment New York State Militia were ordered to charge and take the cannon at the point of the bayonet. The order was obeyed with alacrity, but after a fierce struggle the charging party were compelled to fall back. At this critical moment, Gen. Tyler perceiving the disorder into which the 9th New York were thrown, came to their aid with a brigade. The 9th were quickly rallied, and, assisted by Tyler's brigade, another attempt was made to storm the rebel batteries, but without success. The fight now became general on the extreme left, and another desperate effort was made to capture the rebel battery by Gen Tyler's brigade; but the fire of the rebels was so withering in its effect that our brave fellows were unable to gain any advantage. Each charge thinned the ranks at a fearful rate, and the chances of capturing that much coveted battery appeared no better than at first.

By noon the whole of Franklin's corps was engaged with the enemy, and a desperate effort was made to turn the enemy's position on the Massaponax and drive him beyond the creek. Gen. Franklin commanded the movement in person, and handled his troops with remarkable judgment. The rebels maintained possession of some small hills with their usual stubbornness, but gradually fell back as the Union troops evinced a determination to go forward. During the afternoon the rebels came to a stand, and for a time assumed the offensive; but as they advanced to meet us they were bravely met and repulsed with heavy loss. It was at this time that some three hundred of Hill's command well into our hands and were conducted to the rear as prisoners. Still the enemy contested every foot of ground, and it was only by dint of the hardest kind of fighting that he could be compelled to change his position.

It was during the heat of this engagement that the gallant Bayard was mortally wounded. He was conversing with Gen. Franklin when a cannon ball struck him in the hip and threw him clean out of the saddle. Poor Bayard, he never dreamt of danger in the thickest of the battle, and never lost his courage, even when his leg was amputated. The Surgeons say that he cannot survive many days, and that the operations they have performed can only prolong his agony a short while. But I am digressing from main facts.

The obstinacy with which the rebels held possession of their ground rendered Gen. Franklin's task a very difficult one indeed. He had to cope with Stonewall Jackson and the veterans of Cedar Mountain, Bull Run and Antietam — troops who understood their business thoroughly, and were not to be scared by trifles. Hence the task of turning the rebels' position on the Massaponax was no ordinary one. Still, the Union commander was not discouraged; he had driven the enemy back several rods and was determined to drive them further.--Old Stonewall had met his match this time, and, notwithstanding his troops fought with their usual bravery, they were gradually pushed southward. At sundown Franklin had succeeded in driving the enemy nearly a mile and his troops occupied the field during the remainder of the night. The movement on the left was a complete success, although to-morrow is required for finishing up the job. The casualties on both sides were very numerous as the list of killed and wounded which I have forwarded to you will show Among those who were wounded were Captain Hendrickson, commanding the Ninth New York State Militia and Captain Hart, Assistant Surgeon General to General Tyler.

Reynolds's corps advanced ere the dense fog had lifted itself from the river banks, and about 9 o'clock the enemy's infantry were engaged. The opposing columns had fairly got to work when the rebel artillery commenced playing upon us through the fog. The shots were all aimed at random, however, and produced but little effect. Notwithstanding the view was so obscured, the rebel artillerist kept up the cannonade for several hours, and, as peal after peal rang through the air, the effect was terribly sublime. The fire was returned by our batteries in gallant style, and for hours nothing but the destining roar of artillery could be heard on all sides. Up to noon, when the fog cleared off, and the balloonist were enabled to get a glance at the enemy's works, the fight was an artillery one, and productive of no very important result on either side. As soon as the sunshine showed itself, however, the infantry were brought into play, and the work commenced in real earnest. Generals Mead and Gibbon's division encountered the right of Gen A. P. Hill's command and Longstreet's veterans.

The fight raged furiously during the entire day, and our troops suffered terribly from the enemy's artillery. The enemy were posted behind hills in great strength, and at one time it seemed impossible to dislodge them. About noon Gen. Gibbon was relieved by Gen. Doubleday's command.--Gen. Mead, who was fighting against superior odds, was also reinforced by Gen. Stoneman's command, which had the effect of checking the rebels and driving them back a short distance. It was in the midst of this struggle that Gen Gibbon was wounded and partially disabled. He kept the field, however, during the remainder of the day, and won many laurels by his brilliant conduct. Gen, McClellan's endorsement of Gibbon's dash and ability has been fully borne out by the result of the day's fighting. During the afternoon Gen. Newton's division was moved up to the left of the centre, when the firing, which had ceased in that part of the field, broke out with redoubled fury. Our troops were here exposed to a plunging fire from the enemy's artillery, which was posted on the neighboring hills and for a short time the Union soldiers were exposed to a destructive fire. Our artillery returned the fire with deadly effect, and immortalized themselves by their accuracy of aim and unwavering courage.

The right, consisting of the 7th and 9th corps, under General Sumner, earned imperishable honors, and, as the list of the killed and wounded will testify, the laurels were won at a fearful cost. The action on the right commenced about ten o'clock, and aged furiously all day long. The enemy occupied the wood and the hills in the rear of the city, and in point of advantage the odds were decidedly in their favor. The courage of the Union troops was unbounded, however and every inch of the ground was hotly contested. It soon became evident that the first ridge of the hills on which the enemy were posted behind earthworks could not be carried except at the point of the bayonet, and accordingly General Sumner ordered French's division to charge upon the batteries.--General Howard's division acted as a support, and the troops sprang forward to obey the order with much enthusiasm. By this time the atmosphere was clear, except from the smoke of artillery, and a good view could be had of the rebel position and the adjoining country. It was a grand sight to see the devoted column,

Seeking the bubble reputation even at the cannon's mouth.

Steadily they marched across the plain, and never faltered until they were within a dozen yards of the ridge, when suddenly they were met by a ga fire from the rebel infantry, who were posted behind a stone wall. For a few moments the head of the column exhibited some confusion; but, quickly forming into line they retired back to a ravine within musket shot of the enemy. Here the Union troops were reinforced by a fresh body of infantry, who advanced to the assistance of their comrades in splendid style, notwithstanding large gaps were made in their ranks at every step. The reinforcements having arrived, and the line of assault being again formed, the order "double quick, with fixed bayonets!" was given, and once more the column advanced to dislodge the rebel artillery.

From the moment the storming party left the ravine up to the time they reached the foot of the hills, they were exposed to the hottest fire of the enemy. The concentrated fire of Lee's artillery and infantry rained upon their devoted heads in a manner truly terrific. No troops, however disciplined and brave, could withstand the shock, and after suffering terribly our soldiers were thrown into disorder and brought to a sudden halt. At this juncture the centre of the column gave way and fled in dismay, but they were afterwards rallied and brought back. A second and third attempt was made to dislodge the rebel artillerists, but in vain, and at each attempt the ranks of the storming party grew thinner and thinner. Sumner now brought all his available artillery into play, hoping to shell the rebels out, and from that time until dark the roar of cannon was incessant. The rebels, who had been driven back a short distance during the day, returned to their original position when night came, so that we were unable to remove our dead. Several attempts were made to remove the bodies during the night, but the enemy opened upon us with their infantry and compelled us to desist. All of our wounded were removed however, and such of the dead as were not within musket range of the rebels were burled.

Among the wounded is Gen. Meagher, of the Irish Brigade, and Col. Nugent, of the 69th New York Volunteers. The latter is said to be badly injured, but will probably recover. A large number of the officers of Meagher's brigade were wounded, and many of them killed.

The Third and Fifth Army Corps, under General Hooker, formed the centre and co-operated with Sumner's column during the battle. Gen. Burnside was anxious that a movement should be made as early as possible, and, accordingly, at the break of day the troops commenced to move towards the enemy's earthworks. The men were full of hope and confident of success and they filed out of the city in splendid order. Skirmishing commenced shortly after daylight, and in a short time afterwards the rebel artillery commenced playing upon us through the fog. The firing was so inaccurate, however, that our troops paid but little attention to it, and kept pressing on, regardless of the deadly missiles which were flying through the air. By and by our artillery responded, and for hours a most terrific cannonade was kept up on both sides. The enemy's position was one of exceeding strength, and appeared to be invulnerable to our artillery, notwithstanding our guns were excellently handled.

About noon the infantry, who had been waiting for the fog to clear off, advanced for the purpose of storming the enemy's position on the hill. Confident of victory, the troops marched steadily up to within shot of the batteries; but a murderous fire from the rebel riflemen, added to the fury of the cannonade, compelled our man to fall back with heavy loss. The attempt to carry the rebel batteries was repeated again in the afternoon, and the attacking party, strongly reinforced, started on the "double-quick;" but the enemy, who was also heavily reinforced, proved too much for us. All along the line the battle raged with unusual fierceness, and when night came it was hard to say who were the victors. Of the killed and wounded there were probably as many on the side of the rebels as on ours. No correct estimate can be formed of the loss in Hooker's corps, but it was pretty heavy. The firing of musketry ceased about half-past 5 o'clock, but the rebels continued to cannonade the city until long after dark. They evidently intended to shell us out of our position in Fredericksburg, but thus far they have been unsuccessful.

The result of the day's fight proves conclusively enough that the enemy's position is one of great strength, and that it will require a desperate effort on the part of Gen. Burnside to drive him from his stronghold General Franklin appears to have been the only one who has effected any important result, and to-morrow he may succeed in turning Stonewall Jackson's position on the Massaponax--General Burnside is confident of success, and is busily engaged in making arrangements for a renewal of the battle to-morrow. During the fight nothing was seen of General D. H. Hill's command, and much anxiety is created as to his whereabouts. It is supposed by many that Hill has gone to intercept Sigel, who is probably on his way to Culpeper, and by others that he may be working around in our rear.

In addition to the officers already mentioned as being killed and wounded, I learn the following were among the unfortunate ones:

General Jackson, of the Pa Reserves, and Lieut. Col. Dickinson, 4th U. S. artillery, were both killed. Gens. Vinton, Kimball, Caldwell, and Campbell were wounded, but none of them seriously. --Major Jennings, of the 26th New York Volunteers, and Col. Sinclair, of the Pa. Reserves, are also among the wounded.

All the wounded are being properly cared for, and to-night the surgeons are indefatigable in their efforts to relieve the sufferers.

--The great battle has not yet come off; but before the setting of tomorrow's sun it will, beyond much doubt, be known whether we are to occupy Richmond this winter or not.

The slight resistance that General Lee offered to the crossing of the Rappahannock seems to have been designed, and not a matter altogether of necessity, as many were led to suppose yesterday.--It seems to have been ascertained to-day beyond much doubt that Jackson did not effect a junction with Lee until last night, and that the quiet reception of our terrific cannonading was simply to save ammunition and draw us nearer to their formidable line of fortifications.

Gen Lee's army is now nearly, if not quite, 130,000 strong, with 200 pieces of artillery. If he stands at all he will fight the most bloody battle of the war. This position is a stronger one than at Antietam, and if a panic is created in our ranks the Rappahannock will be a difficult steam to recross. Ball's Bluff, repeated upon a most gigantic scale, will be our fate. But it is useless to speculate when the telegraph will have announced before this reaches you the result of the struggle.

I have spent the day in this city. I have several times described what Fredericksburg was; what Fredericksburg is you have also learned by telegraph in advance of the mall. The city has not only been in part burned, but ruined beyond almost all hope of recovery. All who passed through the village of Sharpsburg two days after the battle of Antietam thought it would be almost impossible to make a town look more desolate and forsaken, but the appearance of Sharpsburg, as compared with that of Fredericksburg, is comely and pleasant.

The Washington correspondent of the New York Times writes:

The Washington Star, of the 13th, says:

Wounded officers who have arrived here from Fredericksburg express the opinion that the enemy has yet much the best of the situation at Fredericksburg, as they are in position where they can only be dislodged at much sacrifice of life, and in the meantime they are capable of doing us much more injury than we can them.

The version of General Burnside's dispatch to the President, bearing date yesterday at 4 A. M., which some of our city contemporaries have published, embraces a very grave mistake. He did not state therein that he had, on Saturday, carried the first line of the enemy's works, but the ridge opposite the town. On this ridge, if we are not mistaken, the enemy had made rifle pits.

Information has been received here from Fredericksburg up to 1 P. M. to-day. The artillery firing there this afternoon was wholly on the part of the rebels, our guns not replying, as theirs did us no harm. It soon ceased, however.

A general officer who left there this forenoon states that the most careful estimates so far made reduce our casualties in the battle of Saturday below ten thousand, it having been thought yesterday forenoon that they were largely in excess of those figures.

The Yankee papers, under date of the 13th, have the following dispatch from Nashville. How the prophecies have been realized our readers best know:

Skirmishing in front for the last week or ten days has invariably been with the rebel cavalry. No infantry force this side of Murfreesboro'.

No doubt the rebels will fall back on our advance to a line beyond Dusk river, where they may dispute the crossing.

It was rumored here that General Halleck had ordered a simultaneous advance here and on the Potomac.

Gov. Johnson publishes the following proclamation in to-morrow's Union.

Executive Office, Dec. 13, 1862.

Whereas, there are many helpless widows, wives, and children in the city and scenery, who have been reduced to poverty and wretchedness in consequence of their husbands, sons and fathers having been forced into the armies by this unholy and un- furious rebellion, and their necessities having become greatly manifest, and their wants of the necessaries of life so urgent, that law, justice and humanity would be grimly violated unless something be done to relieve their suffering condition, the following assessment is therefore ordered in behalf of the suffering families from those who contributed directly or indirectly to bring about this unfortunate state of affairs.

The amount annexed to each name may be paid in five months, by instalments, the first payment to be made on or before the 23rd day of December.--All persons called upon under this notice will pay the amount required to the Comptroller of State, and it will be applied in such manner as may be prescribed for the purpose for which it was collected.

Among the names ssed are the following:--John Overton, $2,500; W. G. Harding, $1,000; Stokely Donalson, $500; Hon. Wash. Barrow, $500; Nell S. Brown, $500; Chatham Family, $500; McNairy, $500; McGavock Estate, $750, Miss Wilson and Mrs. Brownlash, $500. The total amount reaches $50,000.

Gen. Rosecrans has addressed a letter to Gen. Bragg, complaining that the rebels stole overcoats from the prisoners at Hartsville; also, that the cartel had been violated in returning prisoners by flag of truce to this point instead of to Vicksburg and Alken's Landing.

Morgan was last night within twelve miles of Carthage, Tenn.