Clive Arthur brought next idea :
Yes, it's a 'carbon pile rheostat' patented by Singer in 1949 - lots of
carbon discs in a tube and you lower the resistance by squeezing them
together. Google the phrase and there are some instructions on repairing
them.

I always had in mind to try to put together something better, like a
TRIAC control with speed feedback. On the rare occasions I have used
out machine, I found the sudden take off at speed awkward to control
and use. Someone must have tried such an improved design?