At 1 A. M. a second deputation from General Beauregard conveyed to Fort Sumter the message that if Major Anderson would name the time when he would evacuate, and would agree not to fire in the mean time upon the batteries unless they fired upon him, no fire would be opened upon Fort Sumter. To this Major Anderson replied that he would evacuate at noon on the 15th, if not previously otherwise ordered, or not supplied, and that he would not in the mean time open his fire unless compelled by some hostile act against his fort or the flag of his Government. At 3.30 A. M. the officers who received this answer notified Major Anderson that the batteries under command of General Beauregard would open on Fort Sumter in one hour, and immediately left. The sentinels in Sumter were then ordered from the parapets, the posterns were closed, and the men ordered not to leave the bombproofs until summoned by the drum. At 4.30 A. M. fire was opened upon Fort Sumter from Fort Moultrie, and soon after from the batteries on Mount Pleasant, Cummings' Point, and the floating battery; in all 17 mortars and 30 large guns for shot — mostly columbiads. Meantime the garrison of Sumter took breakfast quietly at their regular hour, were then divided into three reliefs, each of which was to work the guns for four hours; and the fire of Sumter was opened at 7 A. M. from the lower tier of guns, upon Fort Moultrie, the iron battery on Cummings' Point, two batteries on Sullivan's Island, and the floating battery simultaneously. When the first relief went to work, the enthusiasm of the men was so great that the second and third reliefs could not be kept from the guns. As the fire of the enemy became warm, it was found that there was no portion of the fort not exposed to the fire of mortars. Shells from every direction burst against the various walls. Cartridges soon run out; there were no cartridge bags, and men were set to make them out of shirts. There was no instrument to weigh powder, and this, with the absence of breech-sides and other implements necessary to point guns, rendered an accurate fire impossible. Fire broke out in the barracks three times, and and was extinguished. Meals were served at the guns. At 6 P. M. the fire from Sumter ceased. Fire was kept up from the enemy's batteries all night, at intervals of twenty minutes.--Tribune, Times, and Herald, April 13, 14, 15.