I arrived per the steamer Louisiana, with the fleet, Saturday morning, January 10, at a point about 2 miles east of the post, and debarked two sections of my battery, consisting of four 6-pounder brass pieces, in the immediate vicinity of the landing occupied by the First Division, and at 1 p.m. marched with that division until 8 p.m., arriving within 1 mile of the enemy's fortifications, when by your order I encamped for the night and reported to Brigadier-General Osterhaus for instructions.

Sunday morning, by direction of General Osterhaus, I advanced with the troops composing his division, and at about 12 o'clock occupied a position within about 300 yards in a northeasterly direction from the main fortification, at which place I went into battery and commenced firing and continued in action during the entire engagement, firing 165 rounds in all, of which 125 were spherical case and 35 solid shot, most of which I have reason to suppose proved effective. Our elevation was 1 to 1/2, our shot exploding at 1 1/2 to 2, the latter varying with the different position of our guns.

I succeeded in dismounting a battery of three Parrott guns, located within the main fortifications, which were bearing directly upon my position; also destroying the roofs of several buildings from which riflemen were annoying the infantry in front of me, completely silencing their fire in that direction. I then changed the direction of my fire along the line of the enemy's rifle-pits and batteries outside the main works, doing considerable damage to both. My position enabled me to fire diagonally through the lines in rear of their earthworks, and also to observe quite accurately its effect.

During the entire engagement our guns were unprotected by front works and were exposed to plain view of the enemy, who were pouring a deadly fire upon the infantry skirmishers in our front, over whom we were compelled to throw our shot.

I have to report but few casualties. William Gardner, gunner of squad Numbers 6., was wounded in his right leg by the explosion of a shot from the enemy, causing quite a severe flesh wound, leaving a fragment buried in the flesh, from which he is still suffering; he is on board the steamer J. C. Snow, in charge of surgeons. Four of my horses received wounds from musketry, rendering three of them unfit for service. The amount of damage to ordnance and loss of stores I am unable to give as yet. It is not, however, very great, as we suffered but little confusion.

This is the first engagement of the battery. I take pleasure in noticing implicit compliance with orders of every man connected with my command, not one shrinking from his place of duty notwithstanding our dangerous position.

The right section of my battery, consisting of two 3-inch rifled pieces, was detached, under command of Colonel Lindsey, of the Second Division, and debarked at Fletcher's Landing Friday night, January 9, for an expedition up the east side of the river to some point above the fort, a report of which I have not as yet received.

Very respectfully, your obedient servant,

CHAS. G. COOLEY,

Captain, Commanding Chicago Mercantile Battery.

Brigadier General A. J. SMITH,

Commanding First Div., First Army Corps, Army of the Miss.