The 1881 says he was born in Breage, Cornwall.
An unmarried daughter Joanna, born 1846 Sithney is with him and his wife Jane.
This looks like Joanna's birth record
WILLIAMS, JOANNA MITCHELL
GRO Reference: 1845 D Quarter in HELSTON Volume 09 Page 115
Sithney is in the Helston registration district.
1871 living here Wheal Crofty Road Tolgarrack House, Camborne, Redruth, Cornwall
Registration district Redruth
Archive reference RG10
Piece number 2325
Folio 31
Page 1