General Price and Jackson were employed in raising all the turbulent elements of the State, and rallying followers to their standard. They were also greatly inspirited in their labors by the rumor that Ben. McCulloch was approaching with eight or ten thousand men to aid them in the overthrow of the government. On the 3d of July, General Lyon left Booneville with two thousand men, for the south-west. General Sweeney, who was in command of the south-west expedition, at Springfield, published a proclamation to the people, inviting them to remain loyal, and warning all rebels to disperse, take the oath of allegiance, and escape the penalties of their lawless career. BATTLE OF CARTHAGE. JULY 4, 1861. Colonel Siegel arrived at Springfield on the 23d of June, and there learned that the rebel troops, under Jackson, were making their way southwardly through Cedar county. He immediately proceeded with his command, numbering over a thousand men, and a small field battery, towards Mount Vernon, for the purpose of intercepting him. On arriving at that point, he learned that General Price, in command of one thousand two hundred of the State troops, was encamped at Neosho, the county seat of Newton county, situated in the south-west corner of the State. His object there was to prevent Jackson going south, or Price going north. He appears to have decided to move southwardly and capture Price if possible, and afterwards attend to the Governor. As he neared Neosho, on the 30th, the reports began to come in of the strength of Price, until his force was swelled to thirty-five hundred men, including Arkansas volunteers. The inhabitants expressed their welcome for Colonel Siegel, and detailed the most pitiable accounts of the oppression of the rebel soldiers. On the 1st of July, the entire force entered the town without opposition, and encamped there, the enemy having retreated. On the 2d, Colonel Siegel, learning that the forces of Price, Rains and Jackson had united at Dry Fork Creek, eight miles from Carthage, and having communicated with and received orders from Brig.-Gen. Sweeney, proceeded at once to attack them. He took up his line of march on the 3d, and on the morning of the 4th came upon the enemy, who were in great force. The Federal command was about one thousand two hundred strong, including part of Colonel Salomon’s regiment. They met the enemy in camp on an open prairie, three miles beyond Dry Fork, and after approaching within eight hundred yards, took position. The artillery was placed in the front; two six-pounders on the left, two six and two twelve-pounders in the centre, and two six-pounders on the right. The fight commenced about half-past nine, the balls and shells of the enemy flying over the Union troops, and exploding in the open prairie.