The least-best-known of what was once a prolific number of American-based producers of precision "bench lathes", the Remington Company's example looked suspiciously similar to the almost-as-scarce Hjorth and may well have been a badge-engineered example. Although the term "bench lathe" might not hint at a machine with any special attributes, the reality was quite different and all the plain-turning 3-inch to 4-inch centre height lathes made by such manufacturers as B.C.Ames, Hjorth, Potter  Pratt & Whitney, Rivett, Stark, Wade, Waltham Machine Works, Wade,  Pratt & Whitney, Rivett, Cataract, Hardinge, Elgin,, Remington, Sloan & Chace, were of the very highest quality and very expensive. Designed for clock, instrument, experimental (and in some cases production work) they were all designated as adaptable, expandable systems able to mount a variety of useful accessories to enable, grinding, high-speed milling filing and even horizontal milling to be undertaken. The headstock assemblies in particular, usually with glass-hard spindles and honed steel bearings, represented the very best that the technology and  metallurgy of the day could offer and were capable of absorbing thousands of hours of use without wearing out.
For further examples of lathes like this go to: http://www.lathes.co.uk/precision-bench-lathes-list/
If you have a Remington lathe the writer would be very interested indeed to hear from you.