I thought the Jane=Kate theory had been based on the fact that Jane had been found in London in 1871 and until this thread Kate had not, so it was thought/hoped they might be one and the same?
On the other hand, a Jane Adams marries John McAuley, Dec qtr 1873 Medway, and turns up in subsequent Kent censuses with him showing a birthplace of Melksham c1847-9, and a clutch of children with mmn Richards.
E.g. Mary Alice McCauley, mmn Richards, Sep qtr 1874 Medway.
So I take it all back 
. Looks entirely possible that Kate was really the daugher Jane belonging to that Melksham family, and Florence was their granddaughter rather than their niece.
No doubt the 1873 marriage certificate would be illuminating as to who her father was.
Mega sleuth! I was holding some info back because I didn't want to overcomplicate things, but I'll lay all my cards on the table as you're catching up to me.
I've spoken to another descendent of Jane/Kate, and she believes after William died Jane remarried the McCauley chap and moved to Kent (apparently she's listed as a widow on the marriage cert), and Florence was sent to Melksham. I didn't buy it, because I couldn't find evidence that Kate & William were ever together; but as you've all debunked that, the other descendent could be right.
With regards to the Janes: there is a Thomas Richards (older brother of Henry) who also has a daughter called Jane, born within a couple of years of Henry's Jane. At the moment, I believe Thomas is Florence's grandad... but I'm ready to be proved wrong again!
Just to complicate things even more, though, I recently discovered there were TWO Richards families in Melksham, and both had sons called Henry... so I think I need to go through all those parish records with a fine tooth comb to confirm that Thomas is the brother of the Henry that was Florence's uncle.
(And for anyone who's interested, I've pieced together Florence's life from 1881 onwards: 1881, living with the Richards in Melksham; 1891, working at Wiltshire Lunatic Asylum; 1892, gets engaged to another colleague at the Lunatic asylum, but then calls it off on her Uncle Henry's advice, so the jilted lover goes and murders her uncle in revenge(!); moves to Portsmouth and works as a barmaid; meets George Staniforth who is in the Royal Marines and they marry; 1899, family moves to Hull.)
I really appreciate all the help you're all offering me!
