Dumb Morse taper question

So my lathe has a #2 Morse taper in the head stock according to the catalog. SB 10S catalog #999A. The tailstock is also a #2MT. I haven't needed a headstock center so never really cared to look into it much. But I am looking for projects to do and decided a dead center for the headstock would be a good idea to have. So I got to looking at it and the 2MT tailstock and the 2MT headstock are clearly not the same size.

Looking on the web gives me size of a 2MT as .700 at the large end and .572 at the small end with 2-7/8" length between the 2 diameters. The minimum bore size of the spindle on the lathe is 1.05 so a .700 MT will slide right through.

So the question is, how is that a #2MT?
If you have the machinery handbook all the dimensions of the MT are listed. You can also find the information on the web, Google Morse taper. Most of the usual suspects that sell tooling will also have the adapters available. To turn between centers you will need the adapter and a dead center, a lathe dog for the work size and a way to drive the dog. Cast iron lathe dogs are cheap or you can make one as a project. I usually drive mine with the face plate. They can be driven by the chuck. Be sure to align your tail stock or when you reverse the work the results will be less than ideal. This hobby can get expensive buying all the bits and pieces!
 
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