I believe this is the Georgia artillery battery you have interest in. The Pulaski Artillery of Georgia was formed in late 1861 from Company K of the 10th Georgia Infantry Regiment. The battery was from Pulaski county Georgia. The first commander was Capt. John Read who commanded the battery until the spring of 1863. The battery served in the Dept of South Carolina and Georgia from the fall of 1861 to the spring of 1862. It moved to Virginia and the forces of General J E Johnston and Robert E Lee. The battery had 72 men and two six pounder field guns and two 12 pounder field howitzers. It was sent for a brief time to the Dept of North Carolina, the battery soon returned to Virginia and rejoined the Army of Northern Virginia. This time, the battery was still a four gun battery but a 10 pound Parrott replaced one of the 12 pounder field howitzers. The battery continued in service with the ANVA but in the spring of 1863, Captain Read was promoted and Capt J C Fraser replaced him. The battery now had 63 men and one ten pound Parrott rifle and two 3" rifles. Capt Fraser was killed on July 2nd, 1863 at the Battle of Gettysburg. Capt Morgan Callaway assumed command of the battery and the battery continued service with the Army of Northern Virginia until the end of the war. When the battery surrendered in April 1865, it had only four men present for duty. In late 1864, the battery was armed with four 12 pounder Napoleons field guns. The battery is mentioned often in the book "The Long Arm of Lee" by Jennings Cropper Wise, the story of the artillery in Virginia. The book is out of print so use a on-line book search if you want it.
Hope this helps.