RD
In the Alexander Papers, I found the following references to an artillery battalion being organized. This would be several days before the infantry moved from Crystall Hill to Camp Hope [later Camp Nelson]. Don't know if the artillery made that move along with the infantry or not.

7/21/62 S O Army of the South West #40
Major Rundell [sp?] will assume command of the Bn of Arty composed of Woodruff‘s Btry, Pratt’s Btry, Daniels’ Btry & Hart’s Btry & set up camp of instruction

8/2/62 HQs Army of the South West to McRae cdg-The Major Gen cdg directs that you at once detail from your command thirty seven men, to report to Maj. C. H. Rundell, cdg Bn at this place to form a part of Capt. Hart’s Btry. The men will be detailed from the Ark troops. They will bring with them their small arms and accoutrements complete. Each man will be furnished with a descriptive roll by his Company in proper form approved by his Regimental and Bgde cdr.

8/2/62 Hindman to Col Nelson cdg Bgde-detail men from the Ark troops Of your command 40 men to report to Maj Rundell cdg Arty Bn to form a part of Hart’s Btry

In the CSR's at Fold3, I found this regarding Maj Rundell:
Major C H Rundell signs for pay rec’d from Capt [J H] Hynson AQM of 1st Bn Arty as Maj of Arty from 7/21/62 [date of appointment] to 8/16/62 [date of resignation]