Potter precision bench lathe
Like most other genuine "Precision Bench Lathes" manufacturers, Potter offered the option of a "Chase" screwcutting attachment. The method involved a Master Thread (also variously known as a hob or leader) mounted behind the headstock and driven through a set of changewheels. A "half-nut" pressed onto the Master Thread and conveyed its pitch, via a sliding bar connected to an adjustable toolholder, to the cutting tool which was in contact with the workpiece. The interconnection of the cutter holder and the half nut allowed the nut to be lifted out of engagement (by a handle attached to the toolpost upright) and the cutting tool returned by hand to the start without stopping or reversing the lathe. A little additional depth of cut could then be applied by the tool slide, the half-nut rested back on the Master Thread - and the cut restarted.
Whilst this system produced absolutely accurate threads (and was especially suited to delicate operations on thin-wall tubes used to construct such items as microscopes) the length and pitch of thread that could be cut depended upon the availability of the appropriate Master - although in the case of the Potter the thread length of five inches would have been sufficient for most jobs and the eight additional changewheels supplied as standard multiplied by eight the number of threads each Master could generate. Each hardened Master Thread - they were available in both inch and metric forms - was provided with a fluted section at one end so that it could be used to "hob out" its own replacement half-nut.
To use the attachment the lathe was run in reverse for right-hand threads - with the toolholder moving from left to right. For left-hand threads, the master thread and its nut were reversed, and the toolholder moved from right to left.
Unusually, unlike many of its competitors, the Potter needed neither another slot in the back of the bed nor a special headstock casting to use the attachment; instead, the whole unit was mounted on brackets which clamped to the top of the bed. A neat touch was the provision of a pad which fitted on the bed and protected it from accidental blows by the rather heavy hand lever..

Goodell-Pratt Bench Lathes Nos. 125 & 494
The Screwcutting Attachment, (No. 166) could only be supplied if it was built into the lathe when new.  Although just a  24 t.p.i master was supplied as standard, any pitch could be ordered. 

Waltham lathe fitted with "Chase" Master-Thread screwcutting
This picture shows clearly the well-proportioned items used on the Waltham to perform this early type of screwcutting. The bed was turned so that the T slot ran down the back of the bed; in the slot were three adjustable supports two of which carried the Master Thread (also known as a hob or leader) - whilst at the headstock end the third bracket supported an arm that carried additional gearing to extend the threading range.
A "half-nut", held in the base of an adjustable tool-slide, pressed on the thread and transmitted its form to the workpiece. The interconnection of the cutter holder and the half nut allowed the nut to be lifted out of engagement and the cutting tool returned by hand to the start of the thread without stopping or reversing the lathe; a little additional depth of cut could then be applied by the tool slide, the half-nut rested back on the master thread - and the cut restarted.
Whilst this system produced absolutely accurate threads, and was especially suited to delicate operations on thin-wall tubes used to construct such items as microscopes, the length of thread that could be cut, and the number of threads per inch or mm, depended upon the availability of the appropriate thread master.
In order to reduce the spindle speed for screwcutting, or larger faceplate work, Waltham offered a special headstock with a completely enclosed 4 : 1 ratio epicyclic-reduction gear.
Alternative and sometimes more highly developed arrangements of the same system can be seen. on the Stark,  Pratt & Whitney, Ames,  Potter and Wade pages.

Start precision plain-turning lathe fitted with chase screwcutting
The Stark lathe, like many in its class, could be fitted with traditional "chase screwcutting" where a T slot, which ran down the back of the bed, held supports which carried a sliding shaft to which was attached a toolholder. Above the shaft, at the headstock end of the lathe, was a "master thread" driven by a selection of gears from the end of the main spindle in such a way that its threading range was extended by a multiple of six.
A follower (with an insert carrying a few threads of the same pitch) pressed against the master thread and transmitted its form to the workpiece via the sliding shaft and a threading tool held in an adjustable slide rest.
Whilst this system produced absolutely threads of a high accuracy - and was especially suited to delicate operations on thin-wall tubes used to construct such items as microscopes and telescopes -  the length of thread that could be cut, and the number of threads per inch or mm, depended upon the availability of the appropriate master.
Here is a short video of thread chasing in action from Gerrit van der Meulen in the Netherlands