Still no dates or places on which to search Cindy. It's tricky when we have no idea about what years to look around. It's always better to give as much detailed information as possible, otherwise it's impossible to start searching anything.
Quote:
'I have a baptism record for Wm. Peters (3rd. g-grandfather) born to Henry and Mary Peters in England at the right time.'
What date is this, and where in England?
Have you done any research into this family in England?
Does the William Peters you've found appear in following records in a marriage or burial in the area?
If you find him in subsequent records. then he obviously can't be the one who emigrated.
If there's no sign of him, its POSSIBLE it could be him. Of course he could just have moved to another part of England, so it doesn't prove it is him, but if you do find him, that's that avenue cut off.
Do you know if the Henry Peters, the possible father, had any brothers and sisters?
Have you traced him on the UK Censuses? If so, you will know his parents' names.
Have you looked for a will for Henry's father?, or Henry's father's brothers and sisters?
They might just mention members of the family who have emigrated.
What about William's brothers and sisters?
Did any of them remain in the uk?
If so when did they die, and did they leave any wills?
Again you don't give this information in your post, but what year did they emigrate?
It sounds as though Henry was the first of the family to do so.
Have you searched for the death of the possible Henry's father, and for an obituary in the local newspapers? Again, family members might be mentioned.