Look on the forward most plane of the vise under the screw and handle. It should read "P V CO" and this would make it a Prentiss Vice Company swiveling rear jaw machinist's vise. Otherwise known as a self-adjusting rear jaw vise.
In my research, I've only seen the unique profile of the vise jaws ("U" shaped, arranged horizontally) on a Prentiss vise. There are no visible markings on my vise other that unreserved the screw handle.
Dave