I have come across the info pasted below which may help as I searched William Oliver. I understood an Elizabeth (Oliver) might reside here and found a marriage 1824 I think (sorry, my browser crashes when I flit from tab to tab) for an Elizabeth Oliver and Thomas Shaw. William's grandson George (b circa 1842) was a packer and there were other transferers and potters' assistants whatever. It was however a common trade around Rawmarsh/Swinton/Kilnhurst. But just maybe one of our families has a piece of info that can decide one way or the other. I know a (newly found) relative of mine has searched this long and hard and we have both arrived at similar ancestors via different dates (slightly).
All the best:}
Name William Oliver
Census Date 1841
Wath Upon Dearne,Yorkshire West Riding, England Residence Swinton
Gender Male Aged 80-84 Birth Year (Estimated to be) 1761-1765
Birthplace Yorkshire Rotherham
Book Number 11
Parish of Wath Upon Dearne
County Yorkshire West Riding
Page Number 11
Registration Number HO107
Piece/Folio 1329/25
Thomas Shaw M 35-39 Yorkshire
Elizabeth Shaw F 40-44 Yorkshire
Ann Shaw F 15-19 Yorkshire
William Shaw M 12 Yorkshire
Alfred Shaw M 7 Yorkshire
William Oliver M 80-84 Yorkshire
