I have an Archaball (note spelling) who was born Aug. 10, 1874 that was the son of Joseph (Aug 11, 1836) and Mary Ann Dealy/Deely (Dec. 4, 1838). Archaball was the brother to William, my great-grandfather. If you email me at
judithakies@aol.com, I would be happy to share the information I have. Joseph's parents are John Ax and Elizabeth Irwin.
I was surprised (delighted) to find that they belonged to the Church of the Latter Day Saints, which is where I have been able to find much of my information (
www.familysearch.org). Archaball is also listed on their website.