With a 4-inch swing and able to take around 12 inches between centres, the Turnex lathe was believed to have been designed by a Mr Bert Walker, made in Massachusetts USA, and employed by him in his Ormond Beach machine shop in Florida.  It was used to make some small precision military parts.
Some of its features include a headstock, tailstock, and linear slides all supported on a single large granite surface plate. The plate is supported on a steel cabinet that houses a 3-phase transformer, relays, contactors, a pneumatic coolant system, an 8-position turret shift control, power monitoring, and connection capability to  another cabinet that has the CNC control, programming, and monitoring features.
The headstock spindle, made by Pope Spindles, takes 5C collets with manual or pneumatic draw-in control with an air-operated Micro-Centric chuck also available as an accessory to mount on the spindle.
The headstock motor is a variable-speed 5 h.p. Gettys DC type with direct drive up to 5000 r.p.m.; the axis drive motors are also DC units by Gettys and of the programmable, variable-speed  type that directly drive precision ball screws.
Four heavy chromed round precision linear slides provide support for the X & Z axis driven tool turret.
The McDonnell Douglas CNC Actrion III controller (probably '70s or early '80s) houses the programmable logic, Gettys DC motor drive controllers, battery backup for the programmed code, memory, paper tape reader, a full alarm and display panel and several DC power supplies.  A port is provided to input or output programs or tool offsets to an external computer or tape punch machine.
Programming and X, Z positioning is selectable for inch (to .0001") or metric (to .001 mm). Typical G and M codes are used as well as special canned routines for CSS, radius, and many other operations.
There is also a No. 2 Morse overhead tailstock supported between the headstock and the opposite end of the surface plate.  This upper beam has two parallel linear slides that allow the hanging tail stock to be rapidly positioned to provide longer parts appropriate support.
The present owner was told that this lathe could hold parts to within 20 millionths and was intended to compete with Hardinge. The lathe is powered and operational and several parts have been machined successfully on it. It came with good electrical schematics and programming documentation and some spare parts--but little detailed parts documentation. It's thought that very few variations of this lathe made and only one with the overhanging tail stock.
If you own a Turnex, the owner of this one, vkelly.tools@gmail.com, would be delighted to hear from you.