The entrance pupil seems to be about 2 1/2", so a f:3.8 Petzval would be about 9 1/2" - or 240mm or so.

That fits in well with a total length of 10" - Petzvals are just a little bit shorter than the focal length, so subtracting the hood brings us into that range.

And that focal length would be made for 9x12cm or smaller. If it had been some decades newer I would have guessed it was made for "Cartes des Visite", but at that time I think more like lantern slides.