No. 35. Report of Captain Jeremiah McCarthy, Battery C, First Pennsylvania Light Artillery.

OPPOSITE FREDERICKSBURG, VA., December 19, 1862.

SIR: The following is my report of the operations of my battery during the late engagements:

The battery was placed upon a commanding elevation, opposite a small stream, called Deep Run, on the night of December 10, with instructions to fire upon any person or body of men who should interfere or obstruct the throwing across of pontoon bridges, and to protect the passage of our troops across them.

Just before the completion of the bridges, the enemy, numbering about 300, appeared in a ravine on the opposite side, firing occasional shots among those who were constructing the bridges. A few shots from my battery, in connection with several other batteries, caused them to retire. The distance from my battery being about 1,300 yards, the projectiles used were case shot and percussion shells, the effect being very satisfactory.

Friday, December 12, according to instructions, opened on the enemy's batteries on the opposite hills, the distance being about 2 1/2 miles. The projectiles used were percussion shell and case shot, only a few of which reached the desired point.

During Saturday, Sunday, and Monday I fired occasional shots.

The following is the number of rounds fired in the above engagements: Spherical case shot, 52 rounds; percussion shell, 20 rounds; total, 72.

During the firing I noticed that about 8 rounds of the case shot did not explode.

I have the honor to be, your most obedient servant,

JEREMIAH McCARTHY,

Captain, Commanding Battery.

Major TRUMBULL,

Commanding Left Center Batteries.

No. 36. Report of Captain Michael Hall, Battery D, First Pennsylvania Light Artillery.

OPPOSITE FREDERICKSBURG, VA., December 19, 1862.

SIR: I have the honor to submit the following report of the part taken by my battery in the late engagement of the 12th to the 15th instant:

The battery was in position on a commanding eminence, with orders to fire on any body of troops that made their appearance on the opposite side. We fired principally spherical case, at a distance of 1,200 yards, and during the crossing of the troops kept up a steady fire. We fired several rounds at long range, which failed to explode. The amount of ammunition expended was 103 case shot and 14 rounds of percussion shell.

I am, sir, very respectfully, your obedient servant,

MICHAEL HALL,

Captain, Commanding Battery D.

Major TRUMBULL,

Commanding Left Center Batteries.