On the 13th of September the rebel advance reached Munfordsville, where it was met by Colonel J. T. Wilder. Again the Sabbath sun looked down on one of the fearful contests of this dreadful war; and it may here be mentioned, how frequent during the war for the Union, battles of great moment to the country were fought upon the Sabbath day. With the first light of Sunday morning, the advance of Bragg’s army, under General Chalmers, made a fierce attack on Munfordsville. The rebels had conceived an idea that the Federals had fled, and came rushing on to what they anticipated as certain victory, when the patriots, making no sign till the enemy was close upon them, opened a sudden and furious fire from their well-aimed guns. Utterly confounded, the rebels reeled back before the unlooked-for shower of death, and fled to the woods in great confusion. A similarly fierce attack had been made on the right, while the above was made on the left; and under the dreadful fire of the rebels, the Union flag was pierced with one hundred and forty bullets. The enemy was completely repulsed, and, at a little before ten, they ceased firing. No more fighting ensued during that day. In the mean time, a reinforcement of six companies had been sent to Colonel Wilder; and dispatches for more had been sent to Louisville and Bowling Green. But Louisville was in great trouble, and could spare no troops; and for reasons utterly inexplicable, General Buell did not send any assistance, though his entire army was stationed at Bowling Green. On Monday the battle was renewed fiercely, and kept up during the day. Evening came, and with it General Bragg and the bulk of his army. On Wednesday morning, the place was surrendered by Colonel C. L. Dunham, who had arrived with his regiment, and then had command. The troops surrendered consisted of the Seventeenth, Sixtieth, Sixty-seventh, Sixty-eighth, Sixty-ninth Indiana, a company of Louisville cavalry, a part of the Fourth Ohio, and a section of the Thirteenth Indiana battery; amounting in all to about four thousand five hundred men, and ten guns. Both officers and men were at once paroled. General Bragg, unmolested by General Buell, continued his march northward, and before reaching Louisville, turned his troops toward the centre of Kentucky. General Buell marched straight to Louisville, where, having encamped, he left Bragg in the heart of the State, to despoil it, and pick up everything in the way of supplies that could in the future be of value to him. BATTLE OF PERRYVILLE, KY. OCTOBER 8, 1862.