We continue our details of Grant's movement on Richmond, taking up the ;hread of the narrative by giving an account of tíunday's battle, fronj a corres üondent of the New York Hcrald, which s as follnws : Headqüarters, 5th Armt Coeps, ) May 8th, 1864. J And the work of war still eoes on. - This corps ha? again been heavily engaeed to-day. The closest and severest contest of the day haa just ended. Our column marched all night. It was the last to leave the intrenchments where the battles of the Wilderness were f.ught; and, first in the fight there, was firat also in the fight here Taking the Brook road, by way of Todd's tavern, and moving separate from trainï, our march was unobs'ructed and rapid. It waa not known, of course, where we would meet the enemy. A rumor prevailed that only Ewell's corps was staying behind, and that the rest of the rebel army was hurrying, with all possiblo speed, to resist the advnnce of Gen. Buller's forc(s on Richmond. The day's events developed a different state of affairs. There had been a cavairy fight in front of us, and a report carne to Gen. Warren that only cavairy and some artillery had boen seen, and prisoners aid there was infantry near us. The resultsliowed the statement to be incorrect Advancing from Todd's tavern, on the road to öpottsylvunia Court House, four regiments of Gen. Bartlett's brigade, of Gen. Griffin's división - the lst Michigan, 44th New York, 83d Pennsylvania and 18th Massachuselts regiments - were sent ahead as skirmishers As we passed down the road shells were hurled at us with great rapidity. Gen. Warren and staff were advaucing down the same road. Gen. Warren had bis horse disabled by a piece of shell. Lieut. Col. Locke, hie Assistaut Adjutant General, was hit in the cheek by a fragment of a shell, inflicting a severe but not dangerous wound The General and staff, however, marched on, regardless of the dangerous missiles falliug about them furiously and fast. Several casualties occurred among the troops by the shelling. Afl we advanced the enemy feil, makne only shght resistaneo. Reacbing wíiat is ealled Állsop's Farm, we carae nto a clearing of about a kundred acres, and triangular in form. The rebel artilery had been stationed in this clearing. To the rear of the clearing is Ny Run, a small streatn, affording no obstacle to the advance of troops. The woods are a mixture of pine, cedar aud oak, but nol so dense as the scène of our late battlea Tl'e wooded ground rises beyond the Run and is ridgy. At the opening into the clearing the road forks, both leadinj to Spottsylvania Court House, some th.ee miles distant from this poiut. The battle line as formed comprised General Griffin's división ou the right, and Gen. Robiuson's, on the left The enemy's ar tillery was now located in a small clear ing on the ridge fronting us. Captain Mnrtins, Company C, ?d Massachnsett battery, and Lieut. Rittenbouse, Co. D Fifth United States artillery, were sta tioned on the right fork of tbe road anc conimandiug the rebel battories. They sent back counter shells. The line of battle advanoed through the clearing. - Having driveu the enemy up to this point two miles into the woods fronting us, our forces pushed theru ; and now began the serious opening of the day's work. Our troops ran oq to three lines of the enewy, the last behind earthworks. Two corps of the enemy - Ewcll's and Longstreefs - as was afterwards ascertaiued, were here awaiting us. The fight was terrible. The remainiug divisions oí the corps - Gen. Crawford's and Gren. Wadsworth's, the latter now couunanded by Gen. Butler - were hurried iorward lapidly. The flght became general and lasted four hours. Our troops behaved raagnificently, keeping at bay moie than treble their number. It will bo understood that the romainiug corps of the army, which had taken the roaa by way of Ohancellorsville íot thifi póint., were still behind. It would not do to be drivon back, and our men fought with a desperation, showing not only thelr usual firm courage, but fullest appreoiation of the position of affairs aud the importance of holding their ground. This opening fibt commcnced about eight a. M. In tho aftor noon there was a fuccession of other battles, the 5th still being engaged. Just before night one brigade of the Gth corps went to the assistance of the 5th corps and, with this excepción, the 6th did all the day's Sghting. The closing struggle of the day was, if anything, more des perate than the one of the morning. The fiercest effort was made by the enemy to drive us back and get on our flanks ; but the coolness and courage of our men repelled every effort. We have beaten the enemy ; but it has been a most costly victory. Our iossea are set down at 1.300 - killed, missing and frounded. Tonight our división is commanded by a Colonel. Brigades have lost their commanders, and 1 know of one the 4th Michigr.n - that is comnianded by a lst Lieutenant. Gen. Robinson, early in the enga gementof liis división, was shot through the knee. The bone is thought to be shattered, nnd that the limb will have to be amputated. Col. Coulter now commands the división. Colonel Deunison, commanding the 3d Brigade of the 4th División, is wounded in the arm. Capt. Martin is slightly wounded in the neck, His battery lost two killed and seven wounded. Among the killed is Colonel Ryan, 104th New York. He was formerly assistant Adjutant General of Gen. Sykes, was a gradúate of West Point, aud a young and most promisins; officer. Maj Stark, of his regiment, was also killed. But I cannot particulariza thï killed and wounded at the time of sonding this dispatch, which I have to close abruptly, to avail myself of a possible prospect of getting it through, Several regiinents have suffered terribly. The lst Michigan, which went with nearly two hundred men, came out at the end of the closing fight with only twenty-threo men L-ft. The 32d Massachusetts regiment, Colonel Prescott captured the 6ih Alabama regimental flag. At half-past five p. ir., both Lieut. Gen. Grant and General Meado visited tte scène of action. Thoy rode directly to the front. Not only did the troops not eogaged cheer them lustily, but the men in buttle, knowing their presence, fought with more determined desperation. The weather has been intensely hot, nd thero have been during the day many suu strokes of our exhausted soliers. TIIE BATTLE OF TÜESDAT. Headquarters Army of tbe Potoniao, Jattle Field nenr Spottsylvania, May l-8o'clock, A. M. The ba'.tlea of the Wiiderness were ontinucd yeaterday in the most s..nguinry of the six bloody engagements whieh have distinguished Uiis campaign. The army was disposiid at early tnorning as follows, shghtly in advance of the position ooeupied the previous day. The Seeond corps on the right, west of the Rieer Po, and nearly in a lino with the road running from Shad}7 Grove (Jhurch lo Spottsylvania Court House ; tho Fifth corps in center east of the river and faciüg southwestward of Spott ylvania, and the Sixth corps on the left, facing toward Spottsylvitnia. Batteries were posted in rear at all available points - Burns's, Arnold's Slceper's Rodgers's, and Ayell'8 batteries supporting tho right and prolecting the bridge across the Po river, formed of three pontoons Meade'a and Stewart's batteries wore disposed toward the left of the Fifth corps in front of a wood. The country is quite as wretched and barbarous for fighting purposes as that bevond tho oli Wilderuess tavern on tho Germauia plank road. There are a few scattered openings across which our Unes of battle could be seen at Dtervala, but the main position of our owii artny and that of the eneiuy was concealed as heretofore by the dense "orest which made the battle almost a mystery. Desultory figbting began ear[y in the day. Our artiüery at from ei"ht o'clook a m , uutil after dark, was never silent. Froiu every position whcrever the enemy's lines were at all exposed the guns belched forlh upon theoi a tempest of shrieking shot and shell. Mink's bitter}-, attached to the Pifth corps, and posted on the edge oí the forest mentioned, evidently did terrible execution ; aud about eleven o clock ra the dny a charge of the eneuiy, iuteuded to cflfect its oaptura, was repulsed.- Musketry firing by sharpshooters and fieroe skirinishca continued at different points during tho forenoon. The enomy had evidently massod the greater portion of hia troops on bis left and left center. It having been determined to assault hia center, the divisions of Gibbons and Birney, belonging to the Second corps, wcre withdrawn across the Po rivar to assist the attaek. The first brigade, Robinson's, and the SeeoDcl brigade of Cutter's división, Fifth corps, General Rice, eommenned the fighting. GrifEn's división and the main portioa of the Fifth corps, and Gibbous's división of the Second, then advanoed, driving the enemy into their riflo pits after several hours of battle, during which the roar of musketry was louder and moro continuous than at Gettysburg. The works wero not taken. General Rice was killed early in the fight, while getting bis column iuto position. Meanwhile, Barlow's división of the Second corps, lelt aoross the Po river, and faeing in a line cearly perpendicular to our general lino, was attacked by a heavy body of the enemy in flank, and forced to tíwircg rouDa. A secoüd charge of the rebels ia óverwbelxning föree drove tlio right of the división still further around, ita rear in line with the river. - Holding its own for a time, it finally withdrew across the bridge, still fighting. Officors returning from the right aggerated the occurrcnce into a position very dangerous to srmy headquarter?, tents, &c, whieh were suddenly struok, and the forco evacuatod at doublé quiok. The loss in all this fightiug was very severe, both in tnen atid officers. General Barlow, being still pressed af ter retiring across the river, kept on fighting until dark. Meapwhile the dispssitions for a general assault by our vvhole line, whieh had been made in the afternoon to take place at 5 o'clock, were postponed uutil nearly dark. At 6 o'elock a withcring fire upon the enemy's lines was opeued by all our batteries in position ; the roar and shrieking of.shell and grape phot was awful. Generáis Grant and Meado, with their staffs, took poaition on a hill overlooking tbe woods. but from which very little of tlio battle itself could be seen.