Hi Allison
If you want to go further back, FreeREG and BathBMD are good sources for Bath records.
BathBMD gives the registration of Austin and Janet, showing that their mother's maiden name was Careley.
Bath Birth indexes for the years: 1854
Surname Forename(s) Sub-District Registers At Mother's Maiden Name Reference
KIRKHAM Austin Abbey Bath CARELERY ABB/11/346
KIRKHAM Mary Jeannette Abbey Bath CARELEY ABB/11/347
There were two Francis's registered around 1848/9
Bath Birth indexes for the years: 1848
Surname Forename(s) Sub-District Registers At Mother's Maiden Name Reference
KIRKHAM Francis Bathwick Bath HIGGINSON BWK/4/119
Bath Birth indexes for the years: 1849
Surname Forename(s) Sub-District Registers At Mother's Maiden Name Reference
KIRKHAM Francis Xavier Bathwick Bath CARELEY BWK/4/280
The second has the same mother, and it fits with your Francis having second name Xavier.
There are no earlier births registered at Bath to the same couple, and no sign of Agnes Kirkham c1843 anywhere in the country. There's something odd going on there, could the older children be from a different marriage, or illegitimate? Have you found the family in 1841?
This looks like William, baptised in 1816 but 8 years old, and with father a lodging house keeper.
http://www.freereg.org.uk/cgi/SearchResults.pl?RecordType=Baptisms&RecordID=6656478The father had three wives, trace him further with FreeREG.
David