Hi again,
I have been searching for a William with dau Elizabeth fitting the ages you give but none come close.
William constantly gives Fen stanton as place as birth on the 61, 71, 81 and interestingly Fen stanton is mentioned as Huntingdonshire I wonder if its one of those annoying boarder town on an old map I found Fenstanton is classed as Huntingdonshire.... But it doesn't explain why he isn't with his daughter ither in Doddington or Chatteris.. (the 2 places of birth she gives) I tried the variations of ball, bell, bill and boll but nothing seems to show up... Very strange. I couldn't find any William with dau Elizabeth in the whole of Cambs.
It seems likely that they should be in Chatteris as they remained there for the next few census.
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Births Dec 1842
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BULL Elizabeth North Witchford 14 115
North Witchford district covers Chatteris so this looks like the birth record of Elizabeth. If you were to get her birth cert it will let you know her mother and her full name.... Possible that if her mother died after giving birth to her that Elizabeth could have been with relatives whilst daddy was working...
I know I'm rambling too much... I just don't understand why they wouldn't be on the 1851.
Sorry I can't find them for you and forgive my ramblings. I have been searching for any clues that I could and thats the best I could find I'm afraid.
Hope you are able to find out more about your Elizabeth and her father.
All the best Angela.