Age 35 in 1841 (rounded)
Age 47 in 1851, born Ringley
Age 66 in 1861, born Ringley (assume age an error)

Born: Ringley, Lancashire, England (1851 census)

Ringley is 4 miles SE of Bolton, 2 miles south of Little Lever, and near Kearsley.

There are no baptisms in Ringley (or Lancashire) for a Sarah Bayley, even though we have confirmed her maiden name from her father bieng John Bayley, a Calco Printer.

Did Sarah divorce James Brooks, or did she die?  There are two matching death record for Bury between 1860 and 1865 (when James remarried), both in 1864.

Deaths Jun 1864   (>99%)
BROOKS     Sarah          Bury     8c, 291

Actually, she probably died in June (see Ainsworth burial)

Name:    Sarah Brooks
Gender:    Female
Burial Date:    24 Jun 1864
Burial Place:    Middleton, Ainsworth, Lancaster, England
FHL Film Number:    1545704
Reference ID:    item 2a p 99

Was aged 16 months when died, so born about May 1837 (just before the civil BMD register started).

Deaths Sep 1838   (>99%)
Mather  Alice     Bolton  21 66

Burial Record:
Name: Alice, daughter of Sarah Mather
Abode: Little Bolton
When Buried: 9 Sep 1838
Age: 16 Months
Performed by: Hughes(?), Curate

Burial: 9 Sep 1838 St Peter, Bolton, Lancs.
Alice Mather - Daughter of Sarah Mather
    Age: 16 months
    Abode: Little Bolton
    Buried by: M Argles Curate
    Register: Burials 1838 - 1840, Page 10, Entry 80
    Source: LDS Film 1966471

Note: Sarah recorded the death, as husband William had recently died.

Aged 1 at 1841 census, so born after Mar 1839.  Father had died by Sep 1838, so if concieved before Aug, must be born Apr 1839 or earlier.  Therefore, born April 1839.

Aged 1 in 1841
Aged 10 in 1851 census (born Little Bolton)
Aged 20 in 1861 census (born Bolton)
Aged 44 in 1881 census (born Bolton)

MATHER, JOHN        - 
GRO Reference: 1840  J Quarter in BOLTON UNION 
Volume 21  Page 107

Name    John Mather
Baptism Date    26 Jul 1840
Parish    Bolton-le-Moors, Lancashire, England
Mother    Sarah Mather
Register Type    Bishop's Transcripts
Reference Number    Drm/2/26a
Son of Sarah Mather, Spinster of Little Bolton

Lancashire Birth indexes for the years: 1840
MATHER John Little Bolton MATHER LB/4/428 

18 weeks on June 1841 census