Almost as soon as the first Precision bench lathe had first appeared in 1862, there was a demand for some form of screwcutting facility and before long most manufactures of this class of lathe were offering the facility in one (or both) of two ways: either a long-travel top slide through a universally jointed shaft from a train of changewheels driven from the headstock spindle, or by the "Chase" system, using a "Master Thread" and "Follower". The latter system was developed by Joseph Nason of New York who obtained US Patent No. 10,383 on January 3, 1854 for an "arrangement for cutting screws in lathes."
Stark choose to use the "Chase" system and their first lathe fitted with the device (but not later ones) required the use of both a different headstock and bed to that supplied as standard. The headstock was formed with two bosses cast onto its back surface in order to support the Master Thread, whilst the bed was given a T slot which ran the full length of the back, and another which occupied a proportion of the middle section of the front.
The Master Thread was driven by a train of gears connected to the headstock spindle in such a way that the number of threads that could be generated (from one Master) was multiplied by a factor of six. A long rod, held in brackets secured in the rear T slot carried a bracket holding, at its upper tip, a follower which engaged with the Master Thread (also known as a hob or leader) the rotation of the Master Thread caused the rod to slide in its support brackets and transmit its movement to a toolholder mounted in slide which could be adjusted for height as well as the depth of cut it was applying. Because the rod was free to move, the follower could be manually lifted out of engagement with the Master Thread and returned by hand to the start without having to stop or reverse the lathe. Once the follower was free, a little more depth of cut could be applied to the threading tools, the Follower returned to the start of 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.
A very simple form of this screwcutting mechanism can be seen on the Goodell-Pratt  Pages whilst similar arrangements, differing only in the detail of their construction, can be seen on the pages devoted to the precision lathe American makers:  Pratt & Whitney,  Ames,  Potter, Waltham Machine Works and Wade.