Jon, if the focal length of the lens is 24" and the width only 3in, it can be no faster than 24/3 - or f:8. Petzvals are typically about as long as the focal length.
The serial number list in Thiele starts with 27450 as 1884, so it has to be a little before that. Does it say "in Wien" or "Wien & Braunschweig"? Anyway it has to be something made before 1884, which means Petzval Portrait, Petzval Orthoskop, Landscape lens, or Aplanat (Euryskop).
At that time there was only one Euryskop, the f:7.2 - which only went to 1070mm focal length. So that's out.
Landscape lenses are an achromatic meniscus behind the aperture, and came in f:33 only (the f:15 started in 1888), so that's out too.
Petzval Portrait lenses are, as I said, about as long as the focal length and were no slower than f:6.8. So that's eliminated, too!
That leaves the Orthoskop, and Thiele lists a 3" lens of 615mm focal length, at f:11.7. That fits!