HEADQUARTERS, June 9, 1862.

General MITCHELL, Huntsville;

Your two dispatches of yesterday are received. I, too, think it bad to fall back from a point once taken unless you have effected the object, but if have advanced without an attainable object you may have to retire of necessity or policy. In this case it ought to depend on your ability to hold your position and at the same time guard against an advance on Nashville. I apprehend that Negley's position is a wrong one in both respects if the enemy can command the force you suppose, which I am ready to believe. Is he not liable to be penned up in the sharp bend of the river opposite Chattanooga or have his retreat cut off by a force crossing below from the railroad? If this is so, the alternative you have is to withdraw him to some point which will threaten a force advancing either from Kingston or Chattanooga, or else hold the position, and concentrate all the force you can spare at such a point. McMinnville and some strong mountain position not far in advance of that, within supporting distance, between Dunlap and McMinnville, would be a good position if you have time to take it. The road to McMinnville should immediately be put in order. The choice of the alternatives depends on the force of the enemy.

D. C. BUELL.

HEADQUARTERS DEPARTMENT OF THE MISSISSIPPI, Corinth, June 12, 1862.

Major-General BUELL, Commanding,&c.:

GENERAL; I have just been shown a letter from General Nelson to Colonel Kelton, complaining that newspapers have done him injustice in stating that the troops of General Pope and some of the troops of General Sherman were the first in Corinth. In my reports to the Secretary of War I stated precisely what was officially reported to me and in the order of time as reported. General Sherman was the first to report to me that this his troops were inside of the enemy's intrenchments; next General Pope, stating the exact hour and minute his men raised the flag on the court-house in Corinth; next, but some time after, came General Nelson's report, indorsed by you. All these were sent to the Secretary of War in the order in which they were received. I never inquired nor do I now know who was first in Corinth nor have I ever attempted to decide upon the conflicting claims. Probably if the question is one of any importance it can be determined when all the official reports have been received. Certainly General Nelson can have no cause to think that I have done him any injustice by sending to Washington the several reports, his among others, immediately on my receiving them. His insinuation that my headquarters furnish newspaper articles is a gross injustice to my staff. The explanation of the substance of telegraphic dispatches and reports getting into the newspapers is very plain. All officers are well aware that the substance of such dispatches and reports, when of interest as news which it is proper to publish, is posted up on a bulletin-board, where any one who chooses can copy and send them to the newspapers. No newspapers reporter has ever been harbored in my camp and no one has been permitted to obtain news at my headquarters which was not public for all who wished it.

It has also been reported to me that General McCook felt aggrieved