Can't find William & Rhoda on the 1861, but found
daughter Fanny aged 23, unmarried, working as a
waitress at the Bath Hotel, Bournemouth, Hampshire.
What caught my eye was that there was also a
visitor by the name of Jane Fall aged 61, unmarried,
born Jersey, Channel Islands.
Don't know if there is a connection thou.

1861 ref: RG9/666 Folio 21
Sue