Schor,
Your speed reducer looks similar to the ones that Atlas offered as accessories. I have a similar one on my Enco but never thought of its purpose being for speed reduction per se. Without it, you would only have four speeds. Like an Atlas 10A lathe (no countershaft).
JamesJinks,
The name of the Atlas manual is Manual of Lathe Operations (MOLO or MoLO for short). Originally, both Atlas and Sears supplied one with each lathe, plus either a parts manual or an Owners manual which included the parts manual. If you have or acquire a machine made about 1958 or later, the current edition still supplied by Clausing will have photos mostly of your machine. There were only about three small changes made after 1958. If your machine is a 10" or earlier 12", I would personally get an edition from 1955 or earlier, although all of the photos seem to be of the 10"and not the early 12". Even if the front cover says "Craftsman".
The reason that you won't find a PDF copy of the MoLO on this site or on the Yahoo ones is that it is still in print and hence still technically copyrighted. Unlike apparently the similar book that used to be printed by South Bend. However, you will find parts lists or Owner's manuals for many of the Atlas or Craftsman lathes (and many other makes) in this site's Downloads section. And as someone else wrote, there are more on Yahoo.
Robert D.