James may be the son of Isaac "Mathers" and Esther Kershaw who married at Manchester in 1838. There is no other marriage in the 10y prior to James being born..
Jame's birth was registered Q4 1846. There were 5 James Mathers born in Bolton 1846-47.
In 1861, there are no census records for a James son of Isaac or son of Esther. However, in 1870, there is James of correct age, son of Isaac at Rhode Island, USA.
Occupation Details
From 1838 James' occupation was Overlooker in Manchester.2