Sue
There is only one baptism in Sheffield for Eliza Cartwright born between 1809 and 1811. That is in 1811 at the parish church, mother Alathea Cartwright, spinster.
Note that GRO index has Alethea Thornton b 1849 Sheffield, mmn CartWright.
Dave
Alethea went on to marry a cutler called Joseph Sheldon.
In the 1841 census they're on Green St - FMP have transcribed her as Habatha, and she was aged 47.
BTW their son Austin Sheldon married my gt-gt grandpa's sister.
Small world!