Joseph Mather was an illegitimate son of Ann Mather, and probably not George's son (as father not named on marriage).
In 1861, Joseph Mather (3) was living with his single mother Ann and grandparents.
In 1871, Joseph (15) was son of Ann and George Warburton at Egerton.
In 1881, Joseph Warburton (26, unmarried), a Carter was living with his parents at 2 School Court.
In 1881, Joseph Warburton (illegitimate son of Ann Mather) was a carter, living with his parents George and Ann Warburton at 2 School Court, Turton. John and Jane Warburton and their son William were living at 4 School Court.
15 Dec 1888, Joseph Mather (30), a stoker, married Elizabeth (Eliza) Warburton at Walmsley Christ Church
In 1891, Joseph and Eliza (32 & 31) were at 4 School Court, Turton with son Robert (2).
In 1901, Joseph and Eliza (both 42) were at 4 School Court, Turton with son Robert (2).
In 1911, Joseph Mather, a fireman at the Bleach works had been married to Elizabeth 22 years and had 1 child (still alive). Both were 52, living at 4 School Court, Egerton.