Normally, a parting tool, (or any other for that matter) in a rear toolpost, is mounted inverted, (ie cutting edge facing down) and the lathe is run in the normal "forward" rotation.
Various theories have been advanced as to why a rear toolpost is better, and less prone to chatter or dig ins. Most seem to revolve around the way that the forces acting in the opposite direction, affect the clearances between the dovetails.
Suffice to say that most folk seem to find that they work better, free up a space in the front 4 way!
If a lathe has a screw on chuck, WITH chuck retainers, it can be run in reverse, safely. Reverse running without them is possible, with care, but RISKY and not advised, because of the obvious risk of the chuck coming off the Mandrel.
There are various plans available for making a back toolpost, to take either a single tool, or to carry two, parting or chamfer. ( See "The Amateurs Lathe", G H Thomas etc) Some, locate the tool at an angle, whilst others place it horizontal so that the top rake has to be ground in to the tool itself.
Howard
Edited By Howard Lewis on 30/06/2016 23:05:09