The monument to the Branch Artillery is south of Gettysburg on South Confederate Avenue. (South Confederate Avenue tour map) The battery was commanded at the battle of Gettysburg by Captain Alexander C. Latham.
The two 10 pounder Parrotts that the marker talks about being substituted on July 2nd were captured from the Fourth New York Independent Battery during fighting at the Devils Den.
From the marker:
July 2. Took position here 4 P. M. and actively engaged until night. The Howitzer and Bronze gun were disabled and two captured 10 pounder Parrotts substituted.
July 3. Engaged in firing upon the Union lines within range. About 5 P. M. aided in repelling cavalry under Brig. Gen. Farnsworth which had charged into the valley between this point and Round Top.
July 4. Occupied position near by and west of this until 6 P. M. Then withdrew from the field.
See more on the history of Latham’s Battery (Branch Artillery) in the Civil War.