Last night I ran a search on Ancestry for the military records of my great-great-grandfather William H. Wiggins. This is what I found:
Admittedly, grandfather's handwriting was atrocious; however, I could make out the G for company G followed by 9th NY Heavy Arty. Ancestry didn't see it that way, this is their interpretation:
Just look at Grandfather's regiment! And he was retired, not rehired, good grief.