An extract from a letter from Colonel Arthur T. Reeve, who commanded the 55th Colored Infantry in this fight, reads:

"Our (the Federal) command having been moved up on double-quick—a distance of about five miles—immediately before their arrival on the field and the consequent fact that this arm of our force went into the engagement very seriously blown, in fact, very nearly exhausted by heat and fatigue, with their ranks very much drawn out, were whipped in detail and overwhelmed by the very brilliant and vigorous assaults of your forces. When the engagement first began I was at the rear of the Federal column, in command of the train guard, and hence passed over the ground on the way to the battle-field after the balance of the army had passed, and am able to speak advisedly of the extreme exhaustion of the infantry, as I passed large numbers entirely prostrated by heat and fatigue, who did not reach the field of battle and must have fallen into your hands after the engagement."

[General Sturgis' Report, No. 2.]

"Memphis, Tenn., June 24, 1864.

"Sir: I have the honor to submit the following report of the operations of the expedition which marched from near La Fayette, Tenn., under my command on the 2nd instant. This expedition was organized and fitted out under the supervision of the major general commanding the District of West Tennessee and I assumed command of it on the morning of the 2nd of June, near the town of La Fayette, Tenn., in pursuance of Special Orders, No. 38, dated Headquarters, District of West Tennessee, Memphis, May 31, 1864, and which were received by me on the 1st inst. The strength of the command in round numbers was about 8,000 men,' (which included the following Phalanx regiments: 59th Regt., 61st Regt., 68th Regt., Battery I, 2nd Artillery, (Light,) 2 pieces.)

"My supply train, carrying rations for 18 days, consisted of 181 wagons, which with the regimental wagons made up a train of some 250 wagons. My instructions were substantially as follows, viz: To proceed to Corinth, Mississippi by way of Salem and Ruckersville, capture any force that might be there, then proceed south, destroying the Mobile and Ohio Railroad to Tupelo and Okolona and as far as possible towards Macon and Columbus with a portion of my force, thence to Grenada and back to Memphis. A discretion was allowed me as to the details of the movement where circumstances might arise which could not have been anticipated in my instructions. Owing to some misunderstanding on the part of the quartermaster, as to the point on the Memphis and Charleston Railroad at which some forage was to have been deposited from the cars, there was some little delay occasioned in getting the column in motion.

"The following incidents of the march are taken from the journal kept from day to day by one of my staff, Capt. W. C. Rawolle, A. D. C. and A. A. A. G.:

"'Wednesday, June 1st.—Expedition started from Memphis and White's Station toward La Fayette.

"'Thursday, June 2nd.—The general and staff left Memphis on the 5 o'clock a. m. train and established headquarters at Leaks' House, near La Fayette, and assumed command. Cavalry moved to the intersection of State line and Early Grove roads, six miles from La Fayette. It rained at intervals all day and part of the night.

"'Friday, June 3rd.—Ordered the cavalry to move to within three four miles of Salem. Infantry marched to Lamar, 18 miles from La Fayette. Owing to the heavy rains during the day and the bad condition of the roads and bridges, the train could only move to within four miles of Lamar, and did not get into park until 11 o'clock p. m., the colored brigade remaining with the train as a guard.