BATTLE OF BAPAUME.--_January 3rd._--General Faidherbe had brought his forces close up to the position which covered the investment of Peronne. His four Divisions consisted of fifty-seven battalions, which were opposed by only seventeen German battalions. He decided on the 3rd to push on in four columns to Grevillers and Biefvillers, on the high road, and to Favreuil on the east. But General von Goeben was not inclined to give up his position at Bapaume. Under cover of a force in occupation of Favreuil, General von Kummer in the morning assembled the 30th Brigade in front of Bapaume, and behind it the 29th, of which, however, three battalions were left in the villages to left and to right. A reserve was established further to the rear at Tronsloy, whither the 8th Rifle Battalion, with two batteries, was detached; and General von Barnekow received orders to hold three battalions and the 2nd Foot Detachment in readiness at Sailly Saillisel, without raising the blockade. Finally the detachment under Prince Albrecht, jun.--three battalions, eight squadrons, and three batteries--advanced on Bertincourt, near to the subsequent battle-field. In this disposition, in bitterly cold and sullen weather, the attack of the French was awaited. General Count von der Groeben had already sent the 7th Cavalry Brigade against the enemy's right flank, but it did not succeed in forcing its way through the villages occupied by the hostile infantry. On the right wing the Division Robin was at Beugnatre met by so sharp a fire from two battalions of the 65th Regiment and two horse batteries which had joined them from Transloy, that it withdrew again on Mory. The garrison of Favreuil was reinforced by two battalions and two batteries against the approach of the Division Payen, which was marching by the high road to the eastward of that place. The first French gun moving out from Sapignies was immediately destroyed, but several batteries soon became engaged on both sides, and the French forced their way into Favreuil and St. Aubin. The 40th Regiment advanced on these places at noon from Bertincourt, and after a lively action re-occupied them; but had to evacuate Favreuil again, and took up a position alongside of the 2nd Guard Uhlan regiment and a horse battery sideward of Fremicourt, which secured the right flank of the Division. On the left, the Division Bessol had driven the weak garrison out of Biefvillers. The 1st Battalion of the 33rd Regiment, which moved forward to retake that place, became hotly engaged; it lost all but three of its officers, and had to retire upon Avesnes. The Division Derroja also took part in this fight. The French now brought up a strong force of artillery, and extended their firing-line to the south nearly as far as the road to Albert.