I am the GGGrandaughter of James Bankhead Speirs and I'm betting he and William were brothers. James was born on Cape Breton Island in 1834 to James Speirs and Janet/Janette Bankhead. I'm having great difficulty getting information about James Speirs and his Scottish roots, though I know he was born there. He and Janet were married in Glasgow. I understand they came to America around 1834. I have a fair amount of information on the line through James Bankhead Speirs. They were mostly in W.Va. In re-reading a genealogy chart I have here, I see a William Speirs, brother of James, but it doesn't give his middle name. This might be a hit for you - according to this he was born in Maryland...I don't have a year. He married an Ellen Bailey of W.Va. If I'm reading this old info correctly, they had the following children: Sam,Isin of Troy, W. Va. and Matthew of Gallipolis, Ohio. I hope this gives you a lot to work with. If this is your line and you can get past James Speirs, Williams father, I'd sure like to hear about it.
Cousin (?) Juanita Speirs