spindle taper

I have just aquired a jet model 1024 lathe and don't have all the tools. What I need is the dead center that goes into the headstock when turning between centers. The manual says the taper in the spindle nose bushing is a no 4 morse taper, but the taper of the spindle center is a #2 morse taper. I am a little confused. Measuring the spindle bore it seems like it is the no 4, but what do they mean by spindle center? While I am at it, where can I get the #4 taper? they don't come very cheep from what I see and since it is used with the face plate can I just turn one down and not have it hardened? I am new to machining with the lathe so excuse me if these are dumb questions. Thanks for any help in advance.