Taper adapter questions?

Hello all,
I am interested in this thread because I have a South Bend 13" I just purchased and am just getting familiar with it and finding what I am missing etc. There seems to be some confusion, at least for me, in regards to the internal taper of the spindle on these lathes. The specs indicate the spindle taper to be a #3 Morse taper. My lathe has a 1 3/8" bore through the spindle and the large end of the internal taper measures 1.625". This seems a bit big for a #3 Morse Taper and I have read that there is a sleeve adapter that reduces the South Bend taper to accept a #3 MT. Am I correct in this and if so where does one look for this adapter sleeve?
Thanks,
David
 
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