My 2nd great grandmother Grace Martin Wills was born on 8 Feb 1849 at Carnarton and christened on 8 Apr 1849 at Tuckingmill which is between Camborne and Illogan in Cornwall. Her father George was a Labourer.
In the 1851 Census their household was enumerated at Carnarton (in the ecclesiastical district of Tuckingmill, in the parish of Illogan) with her father George's occupation given as Rail Labourer.
I have not been able to locate Carnarton but at http://www.old-maps.co.uk/ I searched for Tuckingmill and not far to its south east, I located Carn Arthen and other place names like Carnarthen Farm.
Would this be the same location?