LEXINGTON, July 4, 1863-6 a. m.

General BURNSIDE:

Following dispatches * from Judah explain themselves. I warned the force at Jamestown yesterday afternoon to be watchful toward Columbia, and I have just notified Carter of their movement, directing him to co-operate immediately. Have sent to Colonel Byrn to proceed immediately with his whole disposable force, including Ninth Michigan, from Stanford, toward Columbia, via Liberty, and to act from Liberally in accordance with the information he obtains there; if gets none, to push on to Columbia. Here are the two massages from Judah:

[HARTSUFF.]

[Inclosure.]

MARROWBONE, [July 3,] 1863-2.45 p. m.

Evidence within the hour is positive that the rebel mounted force of from 1,500 to 2,000 have gone toward Columbia. Not knowing what disposition ordered Shackelford immediately, by a shorter route than that upon the map, to proceed to Columbia. Ia have added the Twelfth Kentucky Cavalry to his command. I also ordered at once from 800 to 1,000 of Manson's cavalry to proceed at once to Glasgow, from which point if it does not receive contrary orders, it will push to Greensburg and co-operate with Shackelford, Carper, or any other United States forces sent out in pursuit of or to intercept the enemy in his probable attempt to strike the railroad at our south of Munfordville. I think it necessary to act promptly, and have done so, as I hope, for the best. I do not think it prudent to remove the infantry and artillery from this point or Tompkinsville. I may leave inthe morning for Glasgow. Shackelford will have a force of 1,800 men.

H. M. JUDAN.

LEXINGTON, July 4, 1863-8 a. m.

(Received 8.45 a. m.)

General BURNSIDE:

Following just received:

The development of the past two hours verifies my conjecture, and the movements I ordered toward Columbia and Greensburg. The Eighth Kentucky Cavalry has been in Burkesville. no enemy in my front. I have arranged to have Manson's brigade in Glasgow by a forced march some time to-morrow night. Cavalry entire to precede infantry and artillery, and go on to Greensburg. Hobson's brigade I have ordered to follow up Shackelford. You will perceive the necessity for the different movements of the two brigades. Morgan's while force, from 4,000 to 5,000, has advanced toward Columbia. If Carter can check until my force can come, all will be well. I think it will, anyhow. bacon Creek Brigade will be the point struck, I believe, just above Munfordville. I think Morgan may now be remanently disposed of, by checking him beyond Columbia until I can get at him and partly behind him. I will be in Glasgow to-morrow, and, unless I receive country orders continue to direct Shackelford's movements, as well as those my division. Force at Russeville and Rowling Green should be returned, and surplus concentrated at Munfordville.

H. M. JUDAH.

Have informed General Boyle,and told him he could order the Twentieth Kentucky to Manfordville, and make any other disposition os his forces he thought best, making arrangements to destroy stores at Munfordville,

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* But one found.

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