Now York, May 5, The Times and Ilerald contain long and intercsting accounts of proccedings of Hooker's army. The Times1 correspondent states that after tbree days skirniishiog on both sides the rebels on gaturday afternoon and evening, attacked our right flank, Jackson with his whole corps of 40,000 men throwing himself impetuously on Howard's Eloventh Corps, but the movement was only partially successful, and reinforeements being promptly sent by Hooker, the rebels were handsoinelv checked Howard's corps consisted of Schurz's, Steinwehr's aud Diveu's divis ions The Tim-cs' correspondent states t'ia this oorps disgracefuüy abandoned tbeir position behind their breastvrorks and ruslied panicstrickeu towards headquar ters. Our right was thus completely turned and the rebels in a fair way of doubling u3 up. Hooker was immodiately in the saddle and turtiing to the commander of his own old corps, Berry, shouted, " General, throw your men iuto' ;he breach and receive the eoeuiy on your bayo.iets Dun't fire a shot. They can't see you." They rushed gloriouïly at doublequiek to tho rescuospressnig forward a horrid array of elittering steef. Tlie enemy worc oheeked aud retired to tbeir breastworks, just abandoned by Howard's corps. . Batteries irumediately massed on the crest of the Lili, pouring in n terrific fire until far into the night. Gen. Pleasanton also checked a flying battery of a dozen pieces, and drew up his little brigade of cavalry with drawn sabres to protect the guns. He had thein doublé shotled with cannister and swept tho enemy's position mürderonsly. In tliis charge of the rebels they took from the " cuwardly Dutchraen," as the Times' correspoudent styles thein, twelve pieces of cannon. The Germans fled past Hooker's headquarters in -paiïic, many members of the staff, with pistols and sabres, vainly endeavoring to stay their flight. Sykes' regulars aro pioking tbem up. I lio arhllery eombat continued til] niiduigkt. Geueral Hooker and staff were s 11 Ihe timo undei' tha severeat ñre, and the correspondeut of lbo Times, diiting Sunday evening, says, it is reportod frouj Howard's front that lbo rebels had been engaged all Friday niglit iu cuttiug a road past his right, but not mucb attentiüa was paid to tlie faot. On the tiftcruoon cf Saturday it was raported by picke's on the right of Slocuin's frout, that wagons were seeu moving all day in a westerly direetion. Siekles, with a heavy ioroe, was sent to reoöDuoitre, when the ádranos feil in with the rear of JaokfcOn's army. - Siekles immediately pushed on to cheekmato Jackson, and soon cnptured the entire Twen ty-third Georgia Regtmeut, 400 uien, including oiEcers. ïhis movcment of Siekles eut Jackson's foree in two, and Oen Willinma comraenoed a flank tnovenient ou the enemy's rigbt, with goi;d prospect of success. It was supposud that Howards :orps, foimerly Sigei's would saooessfally resist Jaekson'.s movement, but the first división assailed Cari Schurz's, who aliaost iustautly gavo way, thousanda throwing away their guns tnd streaming towards headquartfirs. Gen. Diven's división by uemoralization of others, was utiable to stand against the rfcbels, and Diven was the second time wounded in tho foot, whilo endeavoring to rally hm men. Howard, with all his daring and resolution, could not stem the tido, and tho brigades of Colonels Bushbeek and Mc Lean remained figluiug ns loiiff as possible, retiring in good order. Of courso th is disaster eompkiled thu reoall of Siekles, wLo had beeu vigorously at work. Gon. Williams' división returned to ünd a portion of Lie works oceupied by :he onemy, Sickled could not communicatc with the whole of his army by tbo route he caino, and Hoeker ordered a niglit attack to restore coranmnication. Ward's brig:ide, aided bj Best's Báttery, made the attaok at 11 o'clock aéttight, wbieli was entirely succrssful, and in a charge runda by the brigade a portion of the artillery lost by Hownrd was gallantly rctaken. 'i ho uiemy was dr i ven back uearly u inile. That night (Saturday) our men slept on their arms. Sunday, at 5 o'oloek in the DJorMUg, the rebels could be liiinly seen on the plank road, about a di i le and a half froni Hooker's hoadquarters at Ohancellor House, which house had been penetrated the eveuing previou.-i b_y a shell. Our line of battlo was immediatelyfonuod, nnd in half an hour our advauee bocaine engaged. Soon battalion atter battalion becarne engaged, the aucmy advancing his ínfiiutry in overwhelmiDg nunibera, seemiug determinad to erush ours. Siokles' and Slocum's brave men, however, held theni in check, inüicting dreadful slaughter upon theni. Frooch's división was sent in on our right flank and soon crushed tliat portion of the enetny'a line, and at 8 o'clock Frcnch sent lus eonipliinents to Mooker, stating ha had chargod the rebels aud was driving them before him. Five vvlio'e rebel divisions were tbrown upou öickles, but he and his gallant soldiers held the traitor.s in check, taking, uuring the day, an aggregate of 2,000 prisoners The fight was u desperate band to hand conflict and the carnage perfectly frightful. Officers say the dead and wouüded rebels covered the ground in beaps, t ie rebels literally throwitig themselves upon the muzzles of our guas. Mott's brigade made fifteen distiuct eliarges, and eaptured soven stand of rebel eolors. The Seventh New Jersey alone eaptured tour stand of eolors aud 500 prisoners. Part of Coueh's Seoond Corps was present, nnd Hancock ga'hintly going to the relief, hard pressed Sickles. The pgagement lasted f rom 5.30 to 8.45 A. M., TÍien, báiug out of amuauaition, our furces held their position for an hour at the point of the bayonet. Upon Leing resuppiied they feil back in goud order to Chancellor House, wliere the contest was again maiutained with great havoo to the enemy and considerable loss to ourselves. The viciuity of Chaicelor House was now the theatre of the fight, and Hookcr maintained his headquarters tbere till 10 o'clook, when it was burned by a rebel shell. In the meantime Hookcr esiablished anew line, our forces were withdrawn to that front, aud at 11:30 musketry fiïing ceat-od. 'i'ho engagement lasted six hours and was the most terrifio of the war. Our artillery literally slaughtered the enemy. Our batteries lost heavily, but the guus were all saved. The enemy are uow no longer in our rear, but directly in our front between us and our forces in Fredericksburg. We are occupying a fortifled and entreuchod position. The euetny gained some grouud but at a sacrifico to five of bis seven divisiona. Suudiiy anemoon the rebels made several attempta to foree our linea, several of his batieriea and regiment being actually dcstroyed in attempts to can-y the apex of our position noar Chancellur House, where a large quautity of our artillar; ia masscd. Our present position is impregnable. General Lee ordered our lines to be broken at all hazards - but the rebels will only destroy themselves by their attaeks. Our troops are perfectly cool and confident. The rebel Gen. Hill is reponed killed. Gen. Berry was killed while leading his brave men. New York, May 5. A Falmouth letter, Snnday, lOo'elock in the eveuing, states that Sedgwiok attaeked the hoightsat Predeneksbnrg galluntly carried by storm, cnpturing the Sixteeuth and thej Eighteeiuh Mississippi regiinents, one company of New Urleans, the Washington artillery, of eight guns, and over 1,000 prisoners. General. Gibbon planted the Stars and Stripes over the rebel works. Our loss moderate. Scdgwiek aftetwaids drove the rebels back, and at 6 P. M. on Sunday had advanced to the briok churcli, 4 1-2 uiile3 towards Chanoelloryille, on tbe plank road and here had a severo fight with Earl's (rebel) división, reinforcecl by Lee, but repulsed them taking a lot of prisoners. Th o enemy now faemmcd in between Hookerand Hedgwick. The advautago deeidedly with us. The Iïerald says our loss in storming the heights of Fredericksburg was about one thousaud killed and wouuded. The WorWs correspondent says the battle was resumed on Monday and was a inost desperate affair. The rebils made a series of superhurnan attaeks at all points, but were repulsed with torrific jlaughter, Our forces have destroyed the bridgea in the rear of the rebels icross Matapony, thus completely cutting Jlf all retreat to Richmond.