There are 2 things about that manual which will cause no end of confusion.
First, on page 7 there are some typing errors ...
The part in the diagram which is labelled L is not a center spur, it's a center cup, and it goes in the tailstock spindle (part F, which sits in part E with part G as an adjustment handwheel).
The part in the diagram which is labelled M is a center spur. It goes into the headstock (K) and provides the drive power to the piece of wood positioned between those centers.
Second, there has been a terminology change since that manual was written.
In their glossary of terms on page 5, they say that a SPUR CENTER is also called a LIVE CENTER because it turns.
Not according to modern terminology. A spur center is a spur center, but it isn't a live center.
A live center is a device which has a free-spinning front cone, typically with bearing races to reduce friction. You can't drive anything with it because of this free-wheeling attribute.
In today's terminology, a live center goes in the tailstock, in place of a cup center (which as John points out burns the wood since it is a dead center, meaning it doesn't spin freely.)
Hope this didn't pile more confusion on ...