SATURDAY AFTERNOON, December 20, 1862.

Colonel WILDER'S examination continued.

Cross-examination by General BUELL.

Question. At what hour Tuesday were you summoned to surrender?

At 5 o'clock in the evening.

Question. Was the rebel force in position around your post before that hour?

One the south side of the river they were, and just coming around on the north side. They had not got all their artillery in position then; probably not more than four batteries.

Question. When you sent your messenger to me did you know of the position and strength of the force of the rebel army that was threatening you?

At that time I was pretty well aware that the whole force of the rebels was on the way, but did not believe that more than 7,000 were threatening me then; the balance was back, coming on, and were between Munfordville and Glasgow; part of them were not yet arrived at Glasgow.

Question. In what way did your informant arrive at the strength of the regiments of Bragg's army?

I was informed by a great many persons. Some of them arrived at it by counting the regiments in some of the divisions and learned from men belonging to them what the force was. There was one man who had a relative in the advanced cavalry who told him what the force was; and there had been parties of rebel cavalry scouting the country for two weeks before, some of whom represented the force to be as high as 60,000; but taking all the information I could get I think it was about 40,000. The community about Munfordville are largely loyal, and have a good many relatives in the Southern army, who would come in from a distance to within 10 or 12 miles to see their friends, and from these I obtained information of the strength of the rebel army. I also obtained it from deserters.

Question. Which of these sources of information would represent the minimum strength?

Those who counted. Reports went through the country that they had as high as 75,000, but I gave no credence to them.

Question. Would what is called the effective strength of the forces according to returns be represented by the number of men found in the ranks?

My experience is that the paper showing is always in excess of that you can get in line for action.

Question. And particularly is it not in excess of the number that would appear in the ranks on the march, where this kind of information would be obtained?

The ranks in a regiment on the march would count for generally much smaller than when in camp. There are always stragglers and details for wagon guards in every army.

Question. So is it not likely that the information of those who have actually counted the strength of a corps on the march would fall short of its actual strength?

Very much so.

MORROW P. ARMSTRONG (a witness for the Government), being duly sworn by the judge-advocate, testified as follows:

By the JUDGE-ADVOCATE:

Question. State, if you please, your name and position in the service,