The census records confirm James was born Turton, and wife Betty in Edgworth.

There is a baptism for Joseph, son of James and Ann, but this is another from Little Bolton.  Turton (Walmsey) baptism records are missing.

Aged 52 in 1851, born Turton (and wife Betty Edgworth)
Aged 63 in 1861
Aged 83 in 1881 (died)

Probate: Under £2,000
The Will and Codicil of Joseph Mather formerly of Turton but late of Breightmet in the parish of Bolton, both in the County of Lancaster, Gentleman who died 27 February 1881 at Breightmet was proved at Manchester by Andrew Mather of Wrexham-street Mold in the County of Flint Publican and Joseph Mather and James Mather both of Wood's Court, Bolton in the County of Lancaster Wholesale Provision Merchants, the sons, the Executors.

Aged 49 in 1851, born Edgworth
Aged 57 in 1861, born Edgworth
Aged 66 in 1871, born Edgworth
Aged 69 in 1873 when died, Turton


Name:    Betty Cooper
Event Type:    Baptism
Baptism Date:    19 Jun 1803
Baptism Place:    Turton, St Anne, Lancashire, England
Father:    William Cooper
Mother:    Ann Cooper
Reference Number:    GB127.L98/1/2/3

Lancashire Death indexes for the years: 1873
MATHER    Betty    69    Turton    TUR/9/10

Age 15 (rounded), born 1826 according to 1841 census
Age 34 in 1861
Age 44 in 1871

Name:    Charles Mather
Gender:    Male
Birth Date:    14 Oct 1825
Baptism Date:    1 Jan 1826
Baptism Place:    Independent,Edgworth,Lancashire,England
Father:    Joseph Mather
Mother:    Betty
FHL Film Number:    0560880 (RG4 1038)

Deaths Mar 1889   (>99%)
Mather     Charles     64     Ashton     8d, 387

Death recorded at Ashton-under-Lyne which is near Droylsden, Lancashire, where the family were living.

Name:    Charles Mather
Gender:    M (Male)
Birth Date:    1826
Birth Place:    Droylsden, Metropolitan Borough of Tameside, Greater Manchester, England
Death Date:    1 Jan 1889
Death Place:    Egerton, Metropolitan Borough of Bolton, Greater Manchester, England
Cemetery:    United Reform Churchyard
Burial or Cremation Place:    Egerton, Metropolitan Borough of Bolton, Greater Manchester, England
Has Bio?:    N
Spouse:    Betty Mather
Children:    Sarah Mather, Alice Mather, Betsy Jane Mather
URL:    https://www.findagrave.com/mem...

Age 14 in 1841
Aged 44 in 1871, born Edgworth

It seems Elizabeth wasnt baptised. There is no Elizabeth (or Betty) Mather baptised at the Edgworth Independant.

Name:    Elizabeth Roscoe
Death Date:    6 Oct 1900
Death Place:    Lancashire, England
Probate Date:    3 Nov 1912
Registry:    Manchester, England

ROSCOE Elizabeth or 323 Darwen Road, Bromley Cross, Bolton Lancashire (wife of Thomas Roscoe) died 6 Oct 1900.
Administration Manchester. 13 Nov to the said Thomas Roscoe Engineer. Effects £235 2s 8d.

Age 12, birth:  25 MAR 1829   
Christening:  31 MAY 1829   Independent, Edgworth, Lancashire

Not on 1841 census, but there was a Sophia born 1849, which is probably an error and is same person.

1881 census: Born Breightmet, Lancashire, England

Name:    Sophia Isherwood
Estimated Birth Year:    abt 1829
Registration Year:    1896
Registration Quarter:    Apr-May-Jun
Age at Death:    67
Registration district:    Bolton, Lancashire
Volume:    8c
Page:    240

Probate:
Name:    Sophia Isherwood
Death Date:    23 Jun 1896
Death Place:    Lancashire, England
Probate Date:    13 Nov 1912
Registry:    Manchester, England

Age 10, born 1831 according to 1841 census
Aged 30 in 1861, born Edgworth

Name:    Frances Mather
Birth Date:    3 Apr 1831
Birth Place:    Edgworth, Lancashire, England
Gender:    Female
Event Type:    Baptism
Father:    Joseph Mather
Mother:    Betty Mather
Baptism Date:    12 Jun 1831
Baptism Place:    Edgworth, Lancashire, England
Denomination:    Independent
Piece Title:    Piece 1038: Edgworth (Independent), 1807-1837

Name:    Frances Mather
Estimated Birth Year:    abt 1831
Registration Year:    1885
Registration Quarter:    Oct-Nov-Dec
Age at Death:    54
Registration district:    Bolton
Volume:    8c
Page:    241

Age 8, born 1833 according to 1841 census

Name:    Andrew Mather
Gender:    Male
Birth Date:    30 Jan 1833
Baptism Date:    10 May 1833
Baptism Place:    Independent,Edgworth,Lancashire,England
Father:    Joseph Mather
Mother:    Betty
FHL Film Number:    0560880 (RG4 1038)
Abode: Edgworth

Missing on 1851 census, but alive in 1861

Name:    Andrew Mather
Estimated birth year:    abt 1833
Registration Year:    1897
Registration Quarter:    Jan-Feb-Mar
Age at Death:    64
Registration district:    Holywell, Flintshire
Volume:    11b
Page:    177

Name    Andrew Mather
Birth Date    1833
Death Date    11 Feb 1897
Cemetery    Mold Cemetery
Burial or Cremation Place    Mold, Flintshire, Wales
Has Bio?    N

In Loving memory of Andrew Mather of Bowling Green Hotel, Mold who departed this life Feb 11th 1897 aged 84 years.

Age 6, born 1835 according to 1841 census

Name:    Alice Mather
Birth Date:    24 Jan 1835
Birth Place:    Edgworth, Lancashire, England
Event Type:    Baptism
Father:    Joseph Mather
Mother:    Betty Mather
Baptism Date:    29 Mar 1835
Baptism Place:    Edgworth, Lancashire, England
Denomination:    Independent
Piece Title:    Piece 1038: Edgworth (Independent), 1807-1837

Alice was still alive in 1911, in South Manchester

Name:    Alice Chadwick
Death Date:    16 Nov 1913
Death Place:    Manchester, England
Probate Date:    18 Dec 1913
Registry:    London, England
CHADWICK Alice of 39 Withington Road, Whalley Range Manchester Widow died 16 Nov 1913. Probate London 18 Dec to Annie Chadwick spinster Effects £1845 4s 10d

Born after June 1, before Sep 1837

Aged 4 in 1841
Aged 24 in 1861
Aged 44 in 1881 (married to Daniel, 64)

Aged 2 in 1841
Aged 22 in 1861

MATHER, JOHN        COOPER 
GRO Reference: 1839  M Quarter in BOLTON UNION 
Volume 21  Page 137

MATHER John £2,190 - 2 Jan 1884
The will of John Mather late of the "Railway" Hotel, Bromley Cross, Turton near Bolton in the County of Lancaster, Publican who died 29 October 1883 at the "Railway" Hotel was proved at Manchester by Mary Mather of the "Railway" Hotel, Widow, the Relict the sole Executrix.

5 mo in 1841

MATHER, JOSEPH        COOPER 
GRO Reference: 1840  D Quarter in BOLTON UNION 
Volume 21  Page 126

Lancashire Birth indexes for the years: 1840
MATHER    Joseph    COOPER        Edgworth        EDG/1/339

Name:    Joseph Mather
Estimated Birth Year:    abt 1841
Registration Year:    1913
Registration Quarter:    Oct-Nov-Dec
Age at Death:    72
Registration district:    Ormskirk, Lancashire
Volume:    8b
Page:    1004


Name:    Joseph Mather
Death Date:    26 Apr 1913
Death Place:    Lancashire, England
Probate Date:    2 Jul 1913
Registry:    Lancashire, England

Probate:
MATHER Joseph of Italia, Lancaster Road, Birkdale, Southport Lancashire died 5 Oct 1913.  Probate London 1 Nov to Annie Mather widow Joseph Henry Mather medical student and James Balmer Mather manufacturer.  Effects £47961 11s 6d.

Aged 18 in 1861


Name:    James Mather
Registration Year:    1843
Registration Quarter:    Jan-Feb-Mar
Registration district:    Bolton, Lancashire
Volume:    21
Page:    133

Name:    James Mather
Estimated Birth Year:    abt 1843
Registration Year:    1891
Registration Quarter:    Oct-Nov-Dec
Age at Death:    48
Registration district:    West Derby, Lancashire
Volume:    8b
Page:    397

Probate:
Name    James Mather
Death Date    23 Nov 1891
Death Place    Liverpool, Lancashire, England
Probate Date    12 Feb 1892
Registry    Liverpool, England

MATHER James of Wellington Villa, Waterloo near Liverpool provision merchant died 23 Nov 1891. Probate Liverpool 12 Feb to Robert Chadwick cloth finisher, Robert Latham hosier, and George Barnes picture dealer.
Effects £6,751 3s 11d
Resworn April 1893 £8,068 17s 10d

Aged 5 in 1851
Aged 15 in 1861
Aged 35 in 1881, born Turton
Aged 45 in 1891, widow
Aged 70 when died

MATHER, SARAH  ANN      COOPER 
GRO Reference: 1845  J Quarter in BOLTON UNION 
Volume 21  Page 167

Name:    Sarah A Cunliffe
Estimated Birth Year:    abt 1845
Registration Year:    1915
Registration Quarter:    Oct-Nov-Dec
Age at Death:    70
Registration district:    Lancaster, Lancashire
Volume:    8e
Page:    1021

Name:    Sarah Ann Cunliffe
Death Date:    27 Nov 1915
Death Place:    Lancashire, England
Probate Date:    1 Jul 1919
Registry:    Lancashire, England

CUNLIFFE Sarah Ann of Silverdale, Lancashire Widow died 27 Nov 1915. Probate Lancaster 1 July to Annie Kitchen (wife of Thomas Kitchen). Effects £1235 8s 6d