I didn't know what this was, so I emailed the Victoria and Albert. This is the reply I received:
The instrument you took a photograph of is an undated Baryton of about
1720 by Jacques Sainprae, a French Huguenot who settled in Berlin some
time at the end of the 17th century. Its museum number is 1444-1870.
Barytons were played like a 'cello, but the thumb of the left hand often
plucked a series of strings at the back of the neck while the
the right hand played with a bow. Haydn was perhaps the greatest
baryton composer and his patron was Prince Esterhazy, a bit of a prima
donna (perhaps?) who insisted that the easy parts should be most
prominent and reserved for him, while the professional musicians
struggled with the harder parts.