Joseph's birth was registered in 2q 1866 Bury 8c 484. He is only known otherwise from the 1871 census entry which shows him as a grandson of John (by my reading; he is son of John according to Ancestry). Lancashire BMD shows his mother's maiden name as Warburton so he is assumed to be Sarah's illegitimate son. He appears in no other censuses so it is uncertain whether he died (there is a death registered in 2q 1875, aged 10) or adopted a different name.