The 1851 and 1871 census shows William is from Hindley.
7 May 1843, William of Bradshawgate a carder, son of John Mather a Spinner married Sarah Hine of Little Bolton. There is a Bradshawgate in Bolton and Leigh. Sarah's father was John Hine, a mason.
In 1847, Susannah was born, the only MATHER+HINE birth.
In 1861, William and Sarah (40 & 41) were at Little Heaton with daughter Susannah (14) and two boarders, Eli and Jane Gramshaw (29 & 20) from Hyde.
In 1871, William and Sarah (49 & 50) were loghers with David and Susannah Anderson (i.e. their daughter). William was a grinder in the Cotton Mill.