Are the two lathes shown below - one in photographs and the other as an extract from a book of the 1800s - related? If so (and your comments on this are welcome), the maker was the Paris-based Deshays Company.
Clearly intended for use in a clock or instrument-maker's workshop, the beautifully-finished lathe in the photographs was of the plain turning type i.e. without screwcutting - though it did have a carriage driven up and down the bed by a hand-turned, fully-shielded leadscrew running down the centre line of the bed. As the leadscrew was placed centrally, it was attached to the carriage immediately beneath the toolpost, so providing the shortest possible and most rigid path between the cutting tool and the force making it act.
Particularly wide, the bed carried a single pair of V-way guides these being arranged so that (as far as can be determined from the pictures) the tailstock was located by the inner faces of the Vs (while also resting on a pair of front and back flats) with the inner surfaces of the Vs used to guide the carriage. Obviously, the carriage must also have had some form of keeper plates on its underside to prevent lift.
Equipped with a proper compound slide rest, the toolpost was an American-style "lantern" type, this able to be rotated by slackening a clamping screw. While the cross slide was driven by a covered screw - fitted with a zeroing micrometer dial - the 360-degree swivelling top slide was controlled by a lever working, presumably from the slide's external appearance, by rack-and-pinion gearing.
Typically for the period on many light lathes, the headstock used a pair of unsupported pillars to carry the plain-bearing spindle, this being lubricated by oil cups with what might have been lift-off lids. Drive was by a narrow round belt, probably 8 mm in diameter, the largest pulley having, on its face, an indexing plate drilled with what could have been up to twenty circles of indexing holes. The two-jaw chuck fitted was not self-centering--and one wonders how many hands have been injured by the exposed bolts protruding from the periphery of its boy.
Just possibly by the same maker - the drawings show a lathe somewhat different to the one in the photographs - those ostensibly of the same general arrangement - but equipped with a train of screwcutting changewheels, though, as with the other, no slow speed backgear..