General Bourbaki informed his Government that he had taken Montbeliard, it was true without the castle, had occupied the villages on the west bank of the Lisaine, and that he would attack on the 16th. He had learned from General Billot that the German right wing extended considerably beyond Mont Vaudois, whence he inferred that important reinforcements had reached the enemy, whose strength he estimated at 80,000 to 100,000 men. Nevertheless he anticipated a fortunate issue for the outflanking operation by fetching a yet wider compass to the left. _January 16th._--At half-past six on the morning of the 16th the Germans again stood to arms in the positions of the previous day. The French again began the attack with their right wing. From the loopholed houses they fired on the Landwehr company holding the castle of Montbeliard, causing some loss among the latter as well as among the gunners. The summons to surrender was disregarded, and the fire of the fortress artillery was used to such good purpose against two batteries which showed themselves on the neighbouring height, that these were obliged to retire, leaving behind them two guns. Neither could they advance from a new position they had taken up at the farm of Mont Chevis, and where they had been reinforced by three batteries, against the fire from La Grange Dame, although the cannonade continued until dark. No attempt was made from Montbeliard to pierce the German line. Further to the left the reinforced 1st Division of the French XVth Corps advanced on Bethoncourt. At one o'clock the fire of its artillery from Mont Chevis and Byans obliged a Baden battery to limber up, and it was then directed on the village. Large bodies had been massed in the neighbouring forest, from out which at three o'clock they advanced. General Gluemer had meantime despatched reinforcements to the threatened front. Two determined attempts pushed close up to the village were frustrated by the destructive artillery and rifle fire of the defenders. A third attack made with a whole brigade at four o'clock, was not permitted even to approach. The losses on the French side were considerable, and the snowy field was strewn with the fallen. Some unwounded prisoners were also taken.