A cursory look at Cope's book suggest that your is a "16in weighted engine lathe" (fig. 22, page 130) made in 1897. Personally, I find somehow surprising that P&W would offer at the turn of the century a lathe with raise and fall carriage, non-webbed bed and carriage weight, characteristics that, I believe, were generally abandoned a decade earlier.
The tailstock is definitely different from P&W lathes from the 1880s.
Paolo
PS By the way: unless you have it somewhere, not in the pictures, the tailstock is missing the quill and leadscrew.