Evan's got it right. Any center which rotates with the work, regardless of whether it is in the headstock or the tailstock end of the work, can be considered as a "live" center. The "dead" center by way of comparison does not rotate with the work and thus develops an element of friction as the workpiece rotates against it.
In today's shop, common shop language refers to a ball bearing center as a "live" center as a means of differentiating it from a center which has no bearing, but I don't believe that anyone who is a working machinist would argue if you referred to a "driven" center as a live center. It is a matter of context.
In one context, the terms "live" or "dead" refers to the actual physical characteristic of the center itself, without reference as to how the center is to be used. In the other context, the same terms are used as a way of defining how the center is being used in the actual application.
A lot of older machinists , (older meaning those who were learning their trade in a time or place where ball bearing centers were not commonplace), learned to think of centers in the context of how they were used in application, and thus spoke of them as being either "live" or "dead".
In today's shop, both are correct, depending on the context being used, but as previously stated, in today's world a "live" center usually means a ball bearing center.
Last edited by Ed Tipton; 12-30-2006 at 09:36 PM.
There is no shortage of experts, the trick is knowing which one to listen to!