By General TYLER:

Question. You do not mean to say, general, that their army, man for man, was superior to ours?

The material of our army is as good or superior to that of the rebel.

Commission adjourned to meet on December 13, 1862,at 10 a.m.

NASHVILLE, December 13, 1862-10 a.m.

The Commission met pursuant to adjournment. All the members present; also the judge-advocate and General Buell.

Colonel SHOEMAKER (a witness for the Government), having been duly sworn by the judge-advocate, testified as follows:

By the JUDGE-ADVOCATE:

Question. What is your position in the service of the United States?

Colonel, commanding the Thirteenth Michigan Volunteers.

Question. State, if you please, to the court what you know of General Bragg crossing the Cumberland River at the point they crossed and all about it.

I was at Hartsville, at Dixon's Springs, on the night of the 8th of September; left there on the morning of the 9th; passed through Carthage; crossed the Cumberland River at that point; saw Generals Bragg and Hardee on the south bank of the Cumberland on the afternoon of the 9th; saw a portion of the army of General Bragg on the south side of the Cumberland on that day.

Question. What were they doing, colonel?

They were mostly bivouacking. I saw some marching. It was toward evening I saw most of them, and they had apparently just gone into camp; many of them were moving. I saw many of them next day,many troops and wagons, and I saw scattering parties through to Sparta, but no body of forces. I also saw at Dixon's Springs some cavalry, said to be the advance of General Cheatham.

Question. I propose, Mr. President, to ask a question over which we have had some discussion,and which I presume General Buell will again object to. What do you know of the size of the invading army at that point, as gathered from your own observation and what the rebel officers informed you?

General BUELL. I object to that portion of the question which proposes to take as evidence the statements of the officers of General Bragg's army in regard to its strength.

General Buell and Colonel Shoemaker retired, during which the Commission unanimously-

Resolved, While the Commission is not disposed to deny the position of General Buell as to the inadmissibility of purely hearsay evidence on a trial of an accused party it will not sustain the objection now offered, but will place the answers of the witness on its record and be governed in its opinions according to the weight which collateral testimony may give to such answers.

Colonel SHOEMAKER. I saw what I judged to be a division of General Bragg's army on the road as we were passing along.

General TYLER. Can you locate them?

They were within 6 miles of the river, on south side of the Cumberland River. I also saw some cavalry at Dixon's Springs on the morning of the 9th of September, commanded by General Wheeler, and said to be the advance of General Cheatham's portion of the army.