I have this moment received your dispatch. I intend a column of 12,000 men, with three batteries, for East Tennessee; but, as I have telegraphed you, it is impossible to fix a time for it to be there, so much depends on the circumstances which may arise in the mean time.

My unavoidable advance to Green River has througly started the enemy and he is strengthening himself in men an position rapidly. C. F. Smith telegraphs me that two brigades, with twelve guns, say 6,000 men, were ordered from Camp Beauregard to be at Bowling Green yesterday, and I have information that Floyd's division, say 6,000, arrived last Thursday. I have information also of the arrival 10,000 men from Mississippi; but they may be those that Smith tells me of, though my information is that they came through Nashville, which would make it somewhat doubtful. At all events there are doubtless 30,000 men now at Bowling Green; and unless checked by strong demonstrations and attacks on Columbus and the Tennessee and Cumberland Rivers, the number can easily be increased to 50,000 or even 60,000 before I can get there. These facts make the co-operation I have in former letters mentioned as important quite essential now to any great success. It is quite essential, too, that the success, should be speedy, or otherwise the enemy will be so strong in West Tennessee and Kentucky from Bowling Green to Columbus as to increase our work vastly. It is my conviction that all the force that can possibly be collected should be brought to bear on that front of which Columbus and Bowling Green may be said to be flanks. The center, that is, the Cumberland and Tennessee where the railroad crosses them, is now the most vulnerable point. I regard it as the most important strategical point in the whole field or operations. The possession of it secures their force and gives access through the two revivers to the very center of their power. While they hold it, at least two-thirds of the whole force on that front may safely be considered available for any one point that is threatened. This I am satisfied you have sen, and that you perceive the importance of co-operation against the center and flanks.

The movement on East Tennessee attacks their rear, and, if properly supported, promises great results. The first 12,000 must probably be followed by others, particularly as is will be unsafe, if not absolutely impossible, to carry along the outfit for 10,000 men. With it the column would employ some 1,200 teams of all descriptions and occupy a stretch of road that the troops could not protect, to say nothing of the difficulty of foraging so many animals in a country which affords but scanty supplies. These armies must therefore be taken in by installments, or strongly protected at depots, where the volunteers can be organized to receive them. In any event I must tell you what I have been unwilling to do all along, that you will require more troops in Kentucky. Don't acknowledge, this, however, but act on it.

Let me stop for to-night. It is 3 o'clock, and I have to get up at 5 to go to Green River, where McCook telegraphs me he is threatened by a strong force.

Truly, yours,

D. C. BUELL.

DECEMBER 29, 1861.

General McCOOK, Munfordville:

How far on the other side of the river would it be necessary for you to go to secure a strong position or prevent the enemy from taking one?

D. C. BUELL,

Brigadier-General.