CHATTANOOGA, TENN., June 28, 1863.

In General Bragg's report of the battle of Murfreesborough I find the following:

The failure of General McCown to execute during the night an order for a slight change in the line of his division, and which had to be done in the morning, caused some day delay in the general and vigorous assault by Lieutenant-General Hardee, but about 7 o'clock the rattle of musketry and the roar of artillery announced the beginning of the conflict.

This passage coveys to the mind of the reader that I had failed to execute an order, thereby delaying the attack, and that the attack commenced at 7 o'clock. Neither proposition is sustained by the facts in the case. Upon reading General Bragg's report, I applied to him to correct this error, in a communication addressed to his chief of staff, in which I say:

I received an order on the night of the 30th from General Bragg to change the position of Rains' brigade. The change was made during the night. I also received an order from Lieutenant-General Hardee to change the position of McNair's brigade. General Cheatham was to point out the now position, which he did. The brigade was placed accurately upon the ground indicated by General Cheatham before I left for General Bragg's headquarters. As to the hour of attack, I have to say the attack commenced at 6 o'clock. This fact is sustained by the reports of my subordinates.

I forward inclosed a copy of this application,marked A, together with a copy of the reply thereto, marked B, in which reply General Bragg refuses me the justice to which I am entitled, and, by some strange misapprehension on his part, he bases that refusal on the ground that my application and the certificates therein inclosed sustain his report. This mistake is singular and palpable. He says in his report that I failed to execute an order, whereby the attack was delayed. This statement I deny in my application and sustain the denial by proof. In General Bragg's reply he assumes that this denial constitutes and admission of the fact. His report places the beginning of the conflict at 7 o'clock. My application places it at 6 [o'clock], and the evidence therewith offered proves my statement correct; yet General Bragg in his reply assumes that my application and certificates "fully" sustain his report in this respect, notwithstanding they differ an hour as to the time of the beginning of the attack. When the rules of logic are so far reversed as to make a positive denial an admission of a fact, and when the laws of nature are so far changed as to make 6 [o'clock] in the morning and 7 o'clock one and the name thing, then General Bragg's assumption that my application for a correction of his report sustains the report itself will be comprehensible, and not until then. His report and my application are the reverse of each other, both as to my failure to execute an order and as to the time of attack. General Bragg's reply says that on these points they agree.

General Bragg further says, in his reply, that the statement in his report which I asked him to correct was based on the following paragraph in General Hardee's report:

Major-General McCown having failed to get McNair's brigade on the line of battle Tuesday night, as directed by me, the brigade was moved into position next morning.

I would respectfully state that I am at a loss to understand how General Bragg could have base a statement in his report of February 23, 1863, on a paragraph in the report of General Hardee, dated February 28, 1863, five days after General Bragg's report.

I deem it proper here to relate clearly the facts in the case. Near sundown on the evening of December 30, 1862, Lieutenant-General Hardee came to the left of and assumed command, and requested General