Rome during our advance, and of striking the flank of the enemy whenever an opportunity affords, or breaking their communications. Colonel Murray's command will be assigned to duty on the left, and will endeavor to keep up constant communication between the advance of the Armies of the Cumberland and Tennessee, and will also have one regiment detailed daily as advance guard and flankers for the main infantry column now advancing on the Rome road. Particular pains will be taken to find out all about the roads, the practicability of moving troops over them,in order that the wings of the army many co-operate. Also find out everything possible relating to the movements of the enemy. The command is now moving, and they will take the first opportunity to get into the respective positions on the right and left flanks.

In the Field, near McGuire's, Ga.

II. The march of the Army of the Tennessee will be directed toward Adairsville to-morrow morning. Major-General Logan, commanding Fifteenth Army Corps, will move his command from its present position by the most practicable routes to the road running from McGuire's to Adairsville, and thence toward the latter place, looking out well for the protection of his trains from the direction of Rome.

Brigadier-General Dodge will move his command from the position [in] which it is encamped to-night directly toward Adairsville. His trains will be kept well to the rear, bringing most of his fighting material to the front. The pioneer companies of the respective corps will repair the roads to-night in the immediate vicinity of the troops. The march will commence at 6 a.m.

By order of Major General James B. McPherson:

WM. T. CLARK,

Assistant Adjutant-General.

ADAIRSVILLE, GA., May 18, 1864.

(Received 10.15 a.m. 19th.)

Major General H. W. HALLECK,

Washington, D. C.:

Johnston passed last night here. We overtook him at sundown yesterday, and skirmished heavily with his rear till dark. In the morning he was gone and we are after him. By to-night all the heads of columns will be near Kingston, whiter Johnston is moving. Whether he proposes to fight there or not we cannot tell, but to-morrow will know, for I propose to attack him wherever he may be. Our cavalry has not yet succeeded in breaking the railroad to his rear. I now have four heads of columns, all directed on Kingston, with orders to be within four miles by night. Weather fine, roads good, and the country more open and less mountains.

W. T. SHERMAN,

Major-General.

ADAIRSVILLE, GA., May 18, 1864-11 a.m.

(Received 11 a.m. 19th.)

Major THOMAS T. ECKERT,

Washington, D. C.:

Army reached here at 10 a.m. to-day. Met rebels three miles from here yesterday and Howard's corps was sharply engaged for two hours,