Whilst this does not match what is written as occupation, Joseph's address in 1841 is Furnace Road Brough Bridge, Stoke upon Trent, Staffordshire, England.
A daughter Mary baptised 23rd February 1840 abode Furnace Road, father's occupation Potter
CARNALL, MARY       mmn WARRILOW  
GRO Reference: 1840  M Quarter in STOKE UPON TRENT  Volume 17  Page 174
The above digital £3 gro image for Mary's birth may well give a different occupation
A son born to them in 1846 called Enoch Richard Carnall, his father Joseph occupation "Potter" abode furnace road.
SS