"The tabular statement shows the position of the several regiments. The camp at Nolin is at the present extremity of the Nashville Railroad. This force was thrown forward to meet the advance of Buckner's army, which then fell back to Green River, twenty-three miles beyond. These regiments were substantially without means of transportation, other than the railroad, which is guarded at all dangerous points, yet is liable to interruption at any moment, by the tearing up of a rail by the disaffected inhabitants or a hired enemy. These regiments are composed of good materials, but devoid of company officers of experience, and have been put under thorough drill since being in camp. They are generally well clad, and provided for. Beyond Green River, the enemy has masked his forces, and it is very difficult to ascertain even the approximate numbers. No pains have been spared to ascertain them, but without success, and it is well known that they far out-number us. Depending, however, on the railroads to their rear for transportation, they have not thus far advanced this side of Green River, except in marauding parties. This is the proper line of advance, but will require a very large force, certainly fifty thousand men, as their railroad facilities South enable them to concentrate at Munfordsville the entire strength of the South. General McCook's Command is divided into four brigades, under Generals Wood, R. W. Johnson, Rousseau and Negley. "General Thomas's line of operations is from Lexington, toward Cumberland Gap and Ford, which are occupied by a force of Rebel Tennesseeans, under the command of Zollicoffer. Thomas occupies the position at London, in front of two roads, which lead to the fertile part of Kentucky, the one by Richmond, and the other by Crab Orchard, with his reserve at Camp Dick Robinson, eight miles south of the Kentucky River. His provisions and stores go by railroad from Cincinnati to Nicholasville, and thence in wagons to his several regiments. He is forced to hire transportation. "Brigadier-General Nelson is operating by the line from Olympian Springs, east of Paris, on the Covington and Lexington Railroad, toward Prestonburg, in the valley of the Big Sandy, where is assembled a force of from twenty-five to thirty-five hundred Rebel Kentuckians waiting reinforcements from Virginia. My last report from him was to October 28th, at which time he had Colonel Harris's Ohio Second, nine hundred strong; Colonel Norton's Twenty-first Ohio, one thousand; and Colonel Sill's Thirty-third Ohio, seven hundred and fifty strong; with two irregular Kentucky regiments, Colonels Marshall and Matcalf. The troops were on the road near Hazel Green and West Liberty, advancing toward Prestonburg. [Illustration: GEN. THOMAS' BIVOUAC AFTER THE FIRST DAY'S BATTLE.]