On Monday morning the city became comparatively quiet. In the evening Generals Buell and Mitchell arrived in Edgefield, and understanding that the authorities had appointed a committee, consisting of the Mayor and several of the leading citizens, he sent a message requesting an interview. The hour of the interview was fixed at eleven o’clock, A. M. on Tuesday. In the mean time General Nelson arrived in the city about eight o’clock, A. M., in command of a fleet, consisting of one gunboat, the Cairo, and eight transports. Transports continued to arrive during the day, and at night the number reached eighteen or twenty. A large portion of this army disembarked during the morning, and occupied the public square, encamping in the vicinity at night. At eleven o’clock, the committee of citizens were conveyed by order of General Buell to Edgefield, on the steamer Hillman. They were met at the landing by Generals Nelson and Mitchell, and escorted to General Buell’s headquarters. The interview was an amicable one, General Buell giving assurance that the personal liberty and property of all citizens would be fully protected, and no State institutions of any kind interfered with. The first business of General Buell, after having thus established a cordial understanding with the officers of the city, was to inaugurate his military authority by the appointment of a Provost-Marshal, to preserve order, and regulate the intercourse of the Union troops with the citizens. Colonel Stanley Matthews, a highly respected and well-known gentleman, conservative in politics, was selected for this responsible position, an appointment which was greeted with satisfaction by the citizens. The post-office was continued in the hands of Colonel J. H. Markland, a native Kentuckian, and a gentleman of high character and social standing.