William was alive in April 1833 to record the death of his son James, but it was Sarah (widow) to report Alice died 5-Sep-1838, aged 16 months, so died 1833-1838.
James and Alice both Buried at St. Peters, with abode Sharples, so the following is a perfect match:
Burial: 8 Dec 1833 St Peter, Bolton, Lancs. William Mather - Age: 22 yrs. Abode: Sharples Buried by: Chas. Agar Hunt Curate Register: Burials 1831 - 1834, Page 250, Entry 1998 Source: LDS Film 1966471
General Notes
In 1832, William married Sarah Bayley. His witness was Henry Isherwood (who may have married his sister Mary Mather 30-Jan-1831 at Kearsley and lived at Hacking Lane in 1841).
After Sarah's husband William Mather died (in 1837), Sarah was a neighbour of Samuel and Alice Mather in 1841, living a few doors away at Waterloo Rd, Little Bolton. Its tempting to think that William is the son of Samuel and Alice but if they baptised him 21 July 1811 then that is too soon after Isaac's birth of 13 Oct 1810.
Sarah's husband must have died after 1837, as they had a child Alice (who died 1838), and John in 1839.
According to baptism of James, William was a Spinner from Shaprles.
Occupation Details
From 1832 William's occupation was Cotton Spinner in Sharples.4
William and Sarah were married in a religious ceremony on January 23rd, 1832 at St. Peter's (Bolton) by Vicar J Slade and witnessed by Henry Isherwood & James Liptrot.6
Marriage/Union Notes
WILLIAM MATHER m. SARAH BAYLEY 23 JAN 1832 Saint Peter, Bolton Le Moors, Lancashire, England
Marriage: 23 Jan 1832 St Peter, Bolton, Lancashire, England William Mather - of This parish Sarah Bayley - of This parish
Name: James Mather Baptism Date: 27 Jan 1833 Baptism Place: Bolton-le-Moors, St Peter, Lancashire, England Father: William Mather Mother: Sarah Mather Reference Number: GB127.L243/1/3/10
James, son of William & Sarah Mather of Sharpes, Spinner
Name: George Mather Birth Date: 29 Apr 1833 Father: William Mathes Mother: Mary Telford Baptism Date: 28 May 1833 Baptism Place: Sunderland, Durham, England Denomination: Presbyterian Piece Title: Piece 0484: Sunderland, Spring Garden Lane Chapel (Presbyterian), 1825-1837
or
Name: George Mather Gender: Male Baptism Date: 29 Jul 1832 Baptism Place: Newcastle-upon-Tyne, Northumberland, England Father: William Mather Mother: Margaret FHL Film Number: 1068963 Reference ID: item 2 p 150
Name: George Mather Gender: Male Age: 14 Birth Date: 1833 Burial Date: 15 Nov 1847 Burial Place: Bolton-Le-Moors, Lancashire, England Father: William Mather Mother: FHL Film Number: 1545454 Reference ID: it 4 p 270 rn 2154