NASHVILLE, January 29, 1864.

The ADJUTANT-GENERAL OF THE ARMY:

GENERAL: In my communication of the 27th instant, written by order of the Court of Inquiry instituted by Special Orders, No. 13, of 1864, I asked for all reports on file in the War Department nearing on the conduct of Major-Generals McCook, Crittenden, and Negley, at the battle of Chickamauga. I am now directed to ask particularly for the following:

Certified copies of the official reports of the battle of Chickamauga, made by Brigadier-Generals Wood, Brannan,and Davis, and Colonel Harker (Wood's divisions); also the supplementary report an papers appended, which Major-General Negley forwarded October 9, 1863, at the request of and through Major-General Rosecrans; the same being required by Major-General Negley in his letter of 22nd January. Please send them to the Galt House, Louisville.

Very respectfully,&c.,

ED. SCHRIVER,

Inspector-General, Recorder.

The Court here desired Major-General Crittenden to furnish the recorder, from time to time, as far as possible, a list of the witnesses whose evidence he may wish to submit to the Court.

A recess of half an hour was taken, and subsequently an adjournment till 7 p.m. was ordered.

7 p.m.

The Court met pursuant to adjournment.

Present, Major-Generals Hunter and Cadwalader, Brigadier-General Wadsworth and Colonel Schriver, recorder, and Major-General Crittenden.

Captain THOMAS C. WILLIAMS, Nineteenth U. S. Infantry, aide-de-camp to General Rousseau, being duly sworn, says to questions

By the COURT:

Question. Please stat what you know about the conduct of General Crittenden at the battle of Chickamauga and the position of his troops.

Answer. I did not see General Crittenden at the battle of Chickamauga. Two of his division reported to General Thomas on Saturday or Sunday; my impression is on Saturday. They behaved with great gallantry,and were amount the last to leave the field on Sunday night.

Question. Do you know under whose orders those divisions reported to General Thomas?

Answer. About 2 to 3 p.m., on Sunday, General Garfield (General Rosecrans' chief of staff) and Colonel Thruston (chief of General McCook's staff) reported to General Thomas, but I do not know under whose orders the divisions reported.

Question. How many divisions were in General Crittenden's corps?

Answer. I think there were three.

Question. When General Garfield and Colonel Thruston reported to General Thomas, was it with two divisions alluded to?

Answer. No.the two divisions were there before.

Question. Do you know where the remaining division of General Crittenden's command was at the time General Garfield and Colonel Thruston reported?

Answer. I do not.

By General CRITTENDEN:

Question. Do you know the names of the commanders of the divisions that reported to General Thomas?

Answer. General Wood and General Palmer.