I have these details for Josiah Caldwell but have been unable to find him (nor any of his immediate family) on the 1851 census.
1812 birth: Aldwark Derbyshire (census; christened Bradbourne, IGI)
1835 marriage: in Brassington (IGI) To Hannah Torr b. 1810 Brassington Derbyshire.
1836 birth of William: Brassington
1841 census: Brassington (with wife and children)
1845 birth of Joseph: Cromford (census)
1847 birth of George: Brassington (census)
1851 census: not found
1851 Dec birth of Josiah: 6 Upper Bland Street, Newington [Southwark]
1861 census: East End, Manchester-Ashton under Lyne New Road, Droyslden (with wife and children, and granddaughter)
1871 census: Clayton Street, Droylsden (with wife and children, and granddaughters)
1881 census: 1 William Street, Droylsden (with wife and son Josiah and his family)
If anyone is able to check relevant areas of the 1851 census I would be very grateful.
Many thanks
Nell