in his official report of the battle of Stone's River; facts gathered from prisoners, deserters, scouts, and refugees, and from rebel newspapers. After the battle, he consolidated many of his decimated regiments and irregular organizations, and at the time of his sending re-enforcements to johnston his army had reached its great effective strength. It consisted of five divisions of infantry, composed of ninety-four regiments and two independent battalions of sharpshooters - say, ninety-five regiments. By a law of the Confederate Congress, regiments are consolidated when their effective strength falls below 250. Even the regiments formed by such consolidation, which may reasonably be regarded as the fullest, must fall below 500 men. I am satisfied that 400 is a large estimate of the average strength. The force would then be -

Infantry, ninety-five regiments, 400 each................. 38,000

Cavalry, thirty-five regiments, say, 500 each............. 17,500

Artillery, twenty-six batteries, say, 100 each............ 2,600

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Total..................................................... 58,100

This force has been reduced by detachments to Johnston. It is as well known as we can ever expect to ascertain such facts that three brigades have gone from McCown's division an two or three from Breckinridge's (say, two). It is clear that there are now but four infantry divisions in Bragg's army, the fourth being composed of fragments of McCown's and Breckinridge's divisions, and must be much smaller than the average. Deducting the five brigades, and supposing them composed of only four regiments each, which is below the general average, it gives an infantry reduction of twenty regiments (400 each, 8,000), leaving a remainder of 30,000. It is clearly ascertained that at least two brigades of cavalry have been sent from Van Dorn's command to Mississippi, and it is asserted in the Chattanooga Rebel of June 11 that General Morgan's command has been permanently detached and sent to Eastern Kentucky. It is not certainly known how large his division is, but it is known to contain at least two brigades. Taking this minimum as the fact, and we have a reduction of four brigades. Taking the lowest estimate - four regiments to the brigade - and we have a reduction, by detachment, of sixteen regiments (500 each), 8,000, leaving his effective cavalry force 9,500. With the nine brigades of the two arms thus detached, it will be safe to say there have six batteries (80 men each, 480), laving him twenty batteries (2,120), making a total reduction of 16,480, leaving of the three arms a total of 41,680.

In this estimate I have placed all doubts in Bragg's favor, and I have no doubt it is considerably beyond the truth. General Sheridan, who has taken great to collect evidence on this point, places it considerably below these figures. But assuming these to be correct, and granting, what is still more improbable, that Bragg would abandon all his rear posts, and entirely neglect his communications, and old bring his last man into battle, I next ask what have we to oppose to him?

The last official report of affective strength now on file in the office of the assistant adjutant-general is dated June 11 instant, and shows that we have in this department, omitting all officers and enlisted men attached to department, corps, division, and brigade headquarters: First. Infantry - one hundred and seventy-three and seventy-three regiments; ten battalions sharpshooters, four battalions pioneers, over regiment engineers and mechanics, with a total effective strength of 70,918. Second. Cavalry - twenty-seven regiments and one unattached company, 11,813. Third. Forty-seven and a half batteries field artillery, consisting of 292 guns