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The same family in 1861..

Is this the same William and Frances that the Genealogist has cast doubt on? If so, why do they think it is the wrong family?

Name: William Burrows
Age: 3
Estimated Birth Year: abt 1858
Relation: Son
Father's Name: William
Mother's Name: Frances
Gender: Male
Where born: Nottingham, Nottinghamshire, England

Civil Parish: Codnor and Loscoe
Ecclesiastical parish: St James
County/Island: Nottinghamshire
Country: England

Street address:

Occupation:

Condition as to marriage: View Image

Registration district: Basford
Sub registration district: Greasley
ED, institution, or vessel: 21
Neighbors: View others on page
Household schedule number: 250
Household Members: Name Age
John Bassendine 49
Frances Burrows 35
George Burrows 12
John Burrows 14
Robert Burrows 7
Walter Burrows 10
William Burrows 39
William Burrows 3

A possibility in 1871?

Name: William Burrows
Age: 13
Estimated Birth Year: abt 1858
Relation: Son
Father's Name: William
Mother's Name: Fanny
Gender: Male
Where born: Nottinghamshire, England
Civil Parish: Codnor and Loscoe
Ecclesiastical parish: Codnor
Town: Codnor
County/Island: Derbyshire
Country: England
Street address:

Occupation:

Condition as to marriage:

Disability: View Image
Registration district: Basford
Sub registration district: Greasley
ED, institution, or vessel: 3a
Neighbors: View others on page
Household schedule number: 475
Household Members: Name Age
Fanny Burrows 45
Fanny Burrows 9
George Burrows 22
John Burrows 24
Mary A Burrows 4
Robert Burrows 17
William Burrows 49
William Burrows 13
Charlotte Foster 17

Gt.Grandfather in 1891, for reference purposes...

Name: William Burrows
Age: 33
Estimated Birth Year: abt 1858
Relation: Head
Spouse's Name: Annie
Gender: Male
Where born: Nottinghamshire, England

Civil Parish: Melton Mowbray
Ecclesiastical parish: Melton Mowbray
Town: Melton Mowbray
County/Island: Leicestershire
Country: England

Street address:

Occupation:
Condition as to marriage:
Education:
Employment status: View Image

Registration district: Melton Mowbray
Sub registration district: Melton Mowbray
ED, institution, or vessel: 1
Neighbors: View others on page
Household Members: Name Age
William Burrows 33
Annie Burrows 23
William Burrows 13
Annie Burrows 11
Harriet Burrows 4
Gertrude Burrows 4/12

Please can anyone help me, I am trying to trace my gt.gt.grandfather named William Burrows I know that his occupation was a Framework Knitter in 1889,as it states this on my gt.grandfathers marriage cert.His name was William also and he married Annie Caunt in Bottesford .I have traced Gt grandfather in the 1891 census living in Melton Mowbray aged 33 with 4 children and in the 1901 census living in Nile Street Nottingham aged 43 with 8 children.The family I thought was his William & Frances from East Bridgeford has been given doubt by a Geneologist I paid to search my tree as I am back to square one I was hoping someone could help me as I have been searching for about 5 years now