I was working on turning a log into a round, and noticed all of a sudden the lathe acted really unbalanced. I kept going a little bit, figuring the part I wasn't cutting was causing the problem. When I shut the lathe off to move the tool rest, I saw the problem: The center had slipped into the pith and the piece really was off.
So the morals of the story is to avoid turning wood with the pith still in it and if the lathe is suddenly off balance shut things down and figure out why!
The leg you save might just be the one attached to you at the hip; don't become attached at the hip to the turning leg. :-)
Puckdropper