Catherine,
OOOOOH. This is an exciting find. That gives me a lot to work with. I had no siblings for William, and in my searches for James and Mary I was throwing in a +/-10 years on a guestimated age just to narrow down my results to more relevant listings. One thing that always caught my eye were any potential listing for families with any names that William used for his kids. The census record you found has one: Jane. Common name, but its enough to give food for thought. I know that census takers have never been 100% reliable so I consider John vs James to be close enough to investigate. I'm going to cross reference that family with the records I kept of the Albany city directories. I made a table to compare every William Armstrong listing.
I sometimes set up a private tree for pure speculation just to see what "shaky leaves" show up that will help me find descendants that might rule them out. I set it up as private so no one will come along and copy my speculation as fact.
Thank you so much for your assistance. I don't know why that never game up on any of my familysearch research. Before I got the death certificate and learned the parents names, all I had to search for was William H. Armstrong and I thought I had found every single one there was.
Rick