British made - though details its manufacturer are unknown - the plain-turning Baye looks to have been a product from the early 1950s and was unusual in being of all-aluminium construction. With a 2.25" centre height and about 8" between centres, the Baye had its slide-rest assembly bolted to the flat-topped bed by two set-screws secured in a central T-slot. Unfortunately, the compound slide rest was "fixed" - that is,  the top slide could not be rotated, a most unusual (and unsatisfactory) state of affairs. The top slide travel - for taking parallel cuts - was 2", with the cross slide limited to just 1.5" of movement. Fitted with a No. 1 Morse taper, the headstock spindle ran in plain, split bronze bearings and was fitted with a 3-step pulley intended for a round drive belt - the designer unfortunately failing to realise that the round instead of V-shaped profile he provided ensured the belt would (unless set very tight indeed) spend all its time trying to walk up the sides and escape. Happily the tailstock was a better proposition, its No. 1 Morse barrel being fitted with a cheap-to-produce but effective lever control.
One cannot for a moment imagine that the Baye would have appealed to other than the most undemanding of amateur turners - with the use of aluminium against aluminium on the ways providing one of the least desirable of all sliding surfaces.
If you have a product of the Baye Company, or any literature about their machines, the writer would be interested to hear from you.